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Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:33:00Z

Sree: /* 5. Discussion */

== 1. Introduction==

This study investigates the thermoelectric response of an undoped zinc oxide (ZnO) pellet through direct measurement of its Seebeck coefficient under controlled thermal gradients. The Seebeck effect refers to the generation of an electrical potential when a material is subjected to a temperature difference, and it provides a direct way to probe charge transport behaviour in semiconductors.

In materials such as ZnO, the thermoelectric response is strongly influenced by intrinsic defects, grain boundaries, and carrier concentration. These features make ZnO a useful system for studying how microstructure affects transport properties, even at room temperature.

The aim of this work is to determine the Seebeck coefficient of a sintered ZnO pellet using a high-resolution Source Measure Unit under open-circuit conditions. In addition, the study examines how reliably a linear thermoelectric response can be maintained under applied temperature gradients, with particular attention given to microvolt-level signal detection and uncertainties in thermal gradient measurement.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/K)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===

<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== 8. References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:32:38Z

Sree: /* 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) */

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:32:10Z

Sree: /* 2. Theoretical Background */

== 1. Introduction==

This study investigates the thermoelectric response of an undoped zinc oxide (ZnO) pellet through direct measurement of its Seebeck coefficient under controlled thermal gradients. The Seebeck effect refers to the generation of an electrical potential when a material is subjected to a temperature difference, and it provides a direct way to probe charge transport behaviour in semiconductors.

In materials such as ZnO, the thermoelectric response is strongly influenced by intrinsic defects, grain boundaries, and carrier concentration. These features make ZnO a useful system for studying how microstructure affects transport properties, even at room temperature.

The aim of this work is to determine the Seebeck coefficient of a sintered ZnO pellet using a high-resolution Source Measure Unit under open-circuit conditions. In addition, the study examines how reliably a linear thermoelectric response can be maintained under applied temperature gradients, with particular attention given to microvolt-level signal detection and uncertainties in thermal gradient measurement.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/K)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== 8. References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:31:42Z

Sree: Undo revision 1063 by Sree (talk)

== 1. Introduction==

This study investigates the thermoelectric response of an undoped zinc oxide (ZnO) pellet through direct measurement of its Seebeck coefficient under controlled thermal gradients. The Seebeck effect refers to the generation of an electrical potential when a material is subjected to a temperature difference, and it provides a direct way to probe charge transport behaviour in semiconductors.

In materials such as ZnO, the thermoelectric response is strongly influenced by intrinsic defects, grain boundaries, and carrier concentration. These features make ZnO a useful system for studying how microstructure affects transport properties, even at room temperature.

The aim of this work is to determine the Seebeck coefficient of a sintered ZnO pellet using a high-resolution Source Measure Unit under open-circuit conditions. In addition, the study examines how reliably a linear thermoelectric response can be maintained under applied temperature gradients, with particular attention given to microvolt-level signal detection and uncertainties in thermal gradient measurement.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/K)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== 8. References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:31:16Z

Sree: /* 2.1. Seebeck Effect */

== 1. Introduction==

This study investigates the thermoelectric response of an undoped zinc oxide (ZnO) pellet through direct measurement of its Seebeck coefficient under controlled thermal gradients. The Seebeck effect refers to the generation of an electrical potential when a material is subjected to a temperature difference, and it provides a direct way to probe charge transport behaviour in semiconductors.

In materials such as ZnO, the thermoelectric response is strongly influenced by intrinsic defects, grain boundaries, and carrier concentration. These features make ZnO a useful system for studying how microstructure affects transport properties, even at room temperature.

The aim of this work is to determine the Seebeck coefficient of a sintered ZnO pellet using a high-resolution Source Measure Unit under open-circuit conditions. In addition, the study examines how reliably a linear thermoelectric response can be maintained under applied temperature gradients, with particular attention given to microvolt-level signal detection and uncertainties in thermal gradient measurement.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/K)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

Physically, the Seebeck coefficient can be interpreted as the entropy carried per unit charge within the material. Its magnitude and sign depend on the dominant charge carriers as well as the details of how those carriers scatter and transport energy.

For n-type semiconductors such as ZnO, electrons dominate the transport process, which results in a negative Seebeck coefficient. In polycrystalline ZnO, however, the situation is more complex. Grain boundaries introduce potential barriers that affect carrier motion, while intrinsic defects such as oxygen vacancies and zinc interstitials contribute additional free electrons, reinforcing n-type behaviour.

At sufficiently small temperature gradients, the Seebeck response can be treated as linear. In practice, however, small deviations may arise due to non-uniform temperature distribution, interfacial effects at contacts, and non-ideal transport across grain boundaries.

It is also important to note that the measured voltage is not purely intrinsic to the sample. Contributions from electrical contacts and connecting leads are inevitably present and must be considered when interpreting the extracted Seebeck coefficient.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== 8. References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:30:15Z

Sree: /* 2.1. Seebeck Effect */

== 1. Introduction==

This study investigates the thermoelectric response of an undoped zinc oxide (ZnO) pellet through direct measurement of its Seebeck coefficient under controlled thermal gradients. The Seebeck effect refers to the generation of an electrical potential when a material is subjected to a temperature difference, and it provides a direct way to probe charge transport behaviour in semiconductors.

In materials such as ZnO, the thermoelectric response is strongly influenced by intrinsic defects, grain boundaries, and carrier concentration. These features make ZnO a useful system for studying how microstructure affects transport properties, even at room temperature.

The aim of this work is to determine the Seebeck coefficient of a sintered ZnO pellet using a high-resolution Source Measure Unit under open-circuit conditions. In addition, the study examines how reliably a linear thermoelectric response can be maintained under applied temperature gradients, with particular attention given to microvolt-level signal detection and uncertainties in thermal gradient measurement.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/K)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== 8. References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:29:54Z

Sree: /* 1. Introduction */

== 1. Introduction==

This study investigates the thermoelectric response of an undoped zinc oxide (ZnO) pellet through direct measurement of its Seebeck coefficient under controlled thermal gradients. The Seebeck effect refers to the generation of an electrical potential when a material is subjected to a temperature difference, and it provides a direct way to probe charge transport behaviour in semiconductors.

In materials such as ZnO, the thermoelectric response is strongly influenced by intrinsic defects, grain boundaries, and carrier concentration. These features make ZnO a useful system for studying how microstructure affects transport properties, even at room temperature.

The aim of this work is to determine the Seebeck coefficient of a sintered ZnO pellet using a high-resolution Source Measure Unit under open-circuit conditions. In addition, the study examines how reliably a linear thermoelectric response can be maintained under applied temperature gradients, with particular attention given to microvolt-level signal detection and uncertainties in thermal gradient measurement.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== 8. References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:07:23Z

Sree: /* References */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== 8. References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:07:14Z

Sree: /* Future Works */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== 7. Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:07:01Z

Sree: /* Conclusion */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== 6. Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:06:46Z

Sree: /* Discussion */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== 5. Discussion ==

=== 5.1. Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== 5.2. Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== 5.3. Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:05:56Z

Sree: /* Results (Thermoelectric Characterisation of Undoped ZnO Pellet) */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== Discussion ==

=== Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:05:03Z

Sree: /* Experimental Setup */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== 3. Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== 3.1. Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== Discussion ==

=== Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:04:27Z

Sree: /* Theoretical Background */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== 2. Theoretical Background ==
=== 2.1. Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== 2.2. Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

==== 2.2.1. Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ====
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== 2.3. Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== Discussion ==

=== Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T04:02:51Z

Sree: /* Introduction */

== 1. Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== Theoretical Background ==
=== Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

=== Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ===
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== Discussion ==

=== Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== Future Works ==

Several things came out of this study that point clearly toward what should be done differently or explored further.

The most immediate change worth making is moving to a four-probe Seebeck measurement configuration. In the current setup, the same leads that carry the signal also pick up the thermoelectric contribution of the connecting wires, and these cannot be separated from the pellet's own response. A four-probe arrangement — where voltage sensing is done through separate probes placed directly on the pellet surface — would eliminate this problem and bring the extracted Seebeck coefficient much closer to the true material value (Rawat & Paul, 2016).

Thermocouple placement is another straightforward improvement. Placing the temperature sensors directly against the pellet faces, rather than near the heater and heat sink, would give a more accurate reading of the actual ΔT across the pellet. The current off-sample placement introduces a systematic error that pulls the extracted S downward, and fixing this alone would noticeably improve the accuracy of the measurement.

Carrying out the measurements under an inert atmosphere — nitrogen or argon — rather than in ambient air would remove the effect of oxygen adsorption at grain boundary surfaces. Oxygen adsorption depletes near-surface electrons in ZnO and raises local resistivity, both of which suppress the thermoelectric signal during measurement (Look, 2001). Beyond just removing a source of error, this would also make the conditions more comparable to those used in the literature, which is where most of the reported reference values come from.

Extending the temperature range of the measurements would be a natural next step. The literature values of −350 to −430 μV/K are measured at 600 K to 1273 K, and at those temperatures the carrier concentration in undoped ZnO is thermally activated to levels well above what it is at room temperature (Rowe, 2006; Goldsmid, 2010). Measuring at elevated temperatures — even just up to 400 or 500 K — would allow a much more meaningful comparison with published data and would likely yield a larger and more easily measured Seebeck signal.

Improving the pellet itself is also worth pursuing. Sintering at higher temperatures or under a reducing atmosphere has been shown to reduce grain boundary barrier heights, lower resistivity, and improve carrier transport in ZnO ceramics (Özgür et al., 2005). A denser, better-sintered pellet would produce a stronger thermoelectric signal and would behave more predictably across a wider range of conditions.

Finally, replacing the hand-applied silver paste contacts with something more reproducible — sputtered or evaporated metal contacts, for instance — would reduce the run-to-run variability that was clearly present in this study. The spread in extracted slope values from 0.836 to 1.066 μV/K across the four runs was largely a contact issue, and a more controlled contacting method would tighten that spread and give a more precise final value for the Seebeck coefficient.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Main Page

2026-04-21T04:01:50Z

2026-04-21T03:40:30Z

Sree: /* Conclusion */

==Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== Theoretical Background ==
=== Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

=== Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ===
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== Discussion ==

=== Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== Conclusion ==

This study set out to measure the Seebeck coefficient of an undoped ZnO pellet at room temperature using a Keysight B2901A Source Measure Unit with silver paste contacts. Four independent measurement runs were carried out, each covering a temperature difference range of 1°C to 14°C, and the Seebeck coefficient was extracted from the slope of the Vout versus ΔT relationship in each case.

The clearest finding across all four runs was the consistently negative output voltage — every reading, at every temperature difference, in every run, came out negative. That alone is a meaningful result. It confirms that the undoped ZnO pellet behaves as an n-type semiconductor, with electrons as the dominant charge carriers — behaviour that is well documented in the literature and understood to arise from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the ZnO lattice (Özgür et al., 2005; Look, 2001). Averaging the slopes extracted from the four linear fits gave a final Seebeck coefficient of S = −0.934 ± 0.094 μV/K, where the spread in values across the runs reflects primarily the variability introduced by reapplying the silver paste contacts before each run.

This value is considerably smaller in magnitude than what the literature reports for undoped ZnO pellets, where values of −350 to −430 μV/K are typical. That gap is large, but it has a clear explanation — and more than one factor feeds into it. The thermocouples were not placed directly on the pellet faces, which means the recorded ΔT was larger than the real temperature difference across the pellet, pulling the extracted S downward. The connecting wires contribute their own thermoelectric voltages to the circuit, and without correcting for these, the measured slope cannot be taken as the pellet's Seebeck coefficient alone. The narrow temperature differences used in some runs pushed the signal into the sub-microvolt range, where noise and drift become competitive. And the pellet itself — sintered in ambient air, carrying high resistivity from grain boundary Schottky barriers — limited how much of the thermoelectric voltage could be extracted at the terminals (Rawat & Paul, 2016; Goldsmid, 2010; Rowe, 2006; Snyder & Toberer, 2008). Crucially, the literature values of −350 to −430 μV/K are not room-temperature figures — they come from measurements at 600 K to 1273 K under inert atmospheres, which is a fundamentally different regime from what was used here. The comparison is therefore not a straightforward one.

A reproducible anomaly was also identified beyond ΔT = 14°C, where the output voltage reversed its upward trend rather than continuing to climb. This happened consistently every time the measurement was repeated past that threshold, pointing to a genuine physical change in the pellet's response rather than a measurement glitch. Grain boundary Schottky barrier breakdown and resistive self-heating within the pellet are the most likely causes, both of which are characteristic of polycrystalline undoped ZnO sintered in air at elevated thermal gradients (Özgür et al., 2005; Rowe, 2006). All primary measurements were kept within ΔT ≤ 14°C on this basis.

Overall, the study demonstrates that the undoped ZnO pellet exhibits thermoelectric behaviour that is physically consistent and interpretable. The n-type character of the material was confirmed unambiguously, a Seebeck coefficient was successfully extracted within a well-defined linear measurement window, and the limitations of the two-probe room-temperature setup were identified and accounted for. The results, while not matching literature values in magnitude, are defensible and informative within the context of the experimental conditions employed.

== Future Works ==

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T03:38:37Z

Sree: /* Discussion */

==Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== Theoretical Background ==
=== Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

=== Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ===
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== Discussion ==

=== Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== Conclusion ==

== Future Works ==

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T03:36:30Z

Sree: /* Discussion */

==Introduction==

The aim of this project is to design, construct, and validate a thermoelectric measurement system for determining the Seebeck coefficient of bulk materials through the Seebeck effect. This system measures the voltage that a material produces when a temperature gradient is applied and turns it into useful thermoelectric parameters.

Unlike conventional temperature sensors, such as thermistors or integrated circuit sensors, thermoelectric measurements directly reveal material properties by correlating temperature differences with electrical voltage. However, the thermoelectric voltage generated typically resides in the microvolt range, making accurate measurement a challenge.

In this work, a high-precision measurement methodology is employed, using a nanovoltmeter to directly capture the thermoelectric voltage without the need for external amplification. A controlled temperature gradient is set up across the sample, and the voltage that comes out is measured to find the Seebeck coefficient. The system is designed to ensure accuracy, stability, and minimal noise interference in microvolt-level measurements.

== Theoretical Background ==
=== Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
We measure <math>\Delta T</math> using two K-type thermocouples by making contacts on the sample. The <math>V</math> is measured using the nanovoltmeter. We use the trigger function to directly download 4 values for each <math>\Delta T</math> in a csv format. The reason we take 4 values is to consider the uncertainty in the measurement.

To get the Seebeck Coefficient we plot Voltage vs <math>\Delta T</math> and calculate the slope of the linear fit curve plotted using the equation above.

=== Two-Probe Measurement Technique ===
[[File:Schematic Diagram of the Two probe measurement.jpeg|thumb|center|500px|Schematic diagram of the experiment - two probe measurement]]

In this work, a two-probe measurement technique is employed to measure the Seebeck voltage generated across the sample. In this method, the same pair of contacts is used for voltage measurement.
The thermoelectric voltage is directly measured across the sample using a high-precision nanovoltmeter. Since the Seebeck effect inherently produces a voltage under open-circuit conditions, no external current is required, making the two-probe method well-suited for this application.
Although contact resistance can influence measurements in general electrical characterisation, its effect on Seebeck voltage measurements is minimal because no current flows through the sample. Therefore, voltage drops associated with contact and lead resistances are negligible. As a result, the two-probe configuration provides a simple and effective approach for determining the Seebeck coefficient in this setup.

=== Why Two-Probe Measurement Technique over Four-Probe Measurement Technique? ===
A two-probe measurement technique is preferred in this study because the Seebeck voltage is measured under open-circuit conditions, where no external current flows through the sample. Consequently, errors arising from contact and lead resistances are insignificant.
In contrast, the four-probe method is primarily used for electrical resistivity measurements, where current is passed through the sample and voltage drops due to contact resistance must be eliminated. Since resistivity measurement is not the objective of the present work, the additional complexity of a four-probe configuration is unnecessary.
Thus, the two-probe method offers a simpler, reliable, and sufficiently accurate approach for Seebeck coefficient measurement in this experimental setup.

=== Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

The ZnO was prepared by grinding 3 grams of Sigma-Aldrich 99% pure ZnO and making a pellet. The pellet was first annealed for 5 hours at 300°C. Since the pellet was not hard enough, it was re-annealed at 500°C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.

== Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experiment.png|thumb|center|700px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final_1.jpeg|thumb|500px|Experimental setup of the sample]]
[[File:Tempearture difference measurement final.jpg|thumb|200px|Temperature Difference Measurement]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO slab with a thickness of 3mm and length about 6mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO slab using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T<sub>c</sub>. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T<sub>c</sub> to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

=== Configuration of the Nano-voltmeter ===

<div style="display:flex; gap:10px;">
[[File:Image of the Nanovoltmeter.jpeg|thumb|center|700px|Configuration of the Nano-voltmeter]]
</div>

Since we are doing only a 2 probe measurement we connect the force outputs to the sample as mentioned in the manual for the source/measurement unit.We configure the measurement unit to measure the voltage and set the source to current. We give a fixed current of 0.001nA which is essentially close to zero so the measured voltage is just the voltage generated from the sample. We set the measurement speed to normal.

To take into account errors we take 4 values for each temperature difference considered and then take an average. To do this we can use the trigger function in the measurement unit.The trigger function was set to collect 4 values in 10ms and the data was collected as a csv file using a usb device.

== Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== Output Voltage Response to Applied Temperature Difference ===
<div style="display:flex; gap:10px;">
[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
</div>
<div style="display:flex; gap:10px;">
[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
</div>

The thermoelectric response of the undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. To establish the temperature gradient, the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values generally lying between −59 μV and −80 μV across the different runs. The fact that Vout remained negative without exception is significant — it points directly to n-type conduction, where electrons are the dominant charge carriers. This behaviour is well documented for undoped ZnO and is understood to stem from native point defects, chiefly oxygen vacancies and zinc interstitials, that introduce free electrons into the material. The Vout versus ΔT data for all four runs are presented graphically in Figures 1 through 4.

=== Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! S (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

Averaging these four values gives a final Seebeck coefficient of:
S = −0.934 ± 0.094 μV/K

The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the natural variation that came with reapplying the silver paste contacts between each run. The negative sign follows directly from the consistently negative output voltage observed throughout all four runs and reinforces the n-type character of the pellet established in the previous section.

=== Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

The graph above shows how the output voltage across an undoped ZnO pellet changes as the temperature difference (ΔT) is gradually increased. From ΔT = 2°C onwards, the voltage rises steadily from around −71 μV toward less negative values — a trend that makes sense physically, since a larger thermal gradient should drive a stronger thermoelectric response in an n-type material like ZnO.

What is notable, however, is what happens at the far end of the graph. The steady climb continues predictably all the way to ΔT = 14°C, where the voltage peaks at roughly −61.5 μV. At that point, rather than continuing the trend, the voltage at ΔT = 16°C falls back to around −63.5 μV. The reversal is clearly visible in the graph — a sharp downturn after what had been a consistent curve across every preceding data point.

What makes this particularly worth discussing is that the drop was not a one-time occurrence. Repeating the measurement under the same conditions produced the same result each time, which rules out a loose contact or an instrument fluctuation. The anomaly is real, and it points to something happening inside the pellet itself once the thermal gradient crosses that threshold.

The most likely explanation lies in the grain boundary structure of the sintered pellet. Unlike a single crystal, a compressed ZnO pellet consists of countless microscopic grains packed together, with the interfaces between them acting as small electrical barriers. Under moderate temperature gradients — as seen throughout the linear portion of the graph — these barriers remain stable and the thermoelectric voltage builds up steadily along the pellet. Once ΔT pushes beyond around 14°C, however, the associated electric field across the grains becomes large enough to begin breaking those barriers down. Charge carriers start crossing grain boundaries through tunnelling or avalanche-type processes, disrupting the orderly voltage accumulation and pulling the measured output back down — exactly as the graph shows at ΔT = 16°C.

A second contributing factor is resistive self-heating. Driving a steeper temperature gradient requires more heater power, and at higher ΔT values the pellet's own electrical resistance causes it to generate internal heat through Joule heating. This internally generated heat partially counteracts the externally applied gradient, reducing the effective thermal driving force that the measurement relies on. In undoped ZnO, which has a naturally high resistivity at room temperature, this effect is more pronounced than it would be in a doped or more conductive sample, and tends to be concentrated at the silver paste contact regions where current density is highest.

Taken together, these two mechanisms — grain boundary breakdown and resistive self-heating — account for the kink visible at the tail end of the graph. The data collected below ΔT = 14°C falls within a well-behaved linear window and can be treated as reliable. The reversal beyond that point serves as a practical upper limit for this particular measurement configuration. This kind of threshold behaviour is consistent with what has been reported elsewhere for sintered polycrystalline ZnO, where grain boundary characteristics are known to play a significant role in governing both electrical and thermoelectric behaviour under applied gradients.

== Discussion ==

=== Interpretation of the Output Voltage Response ===

The output voltage across the undoped ZnO pellet stayed negative throughout all four measurement runs, sitting broadly between −59 μV and −80 μV across the applied temperature difference range. This was not something that varied between runs or required careful interpretation — every single reading, across every ΔT step, in every run, came out negative. That kind of consistency carries weight. In n-type semiconductors, electrons are the dominant carriers and under a thermal gradient they drift from the hot end toward the cold end, building up a negative potential at the cold terminal. The fact that this polarity held without exception across four independently conducted runs — each starting fresh with newly applied silver paste contacts — makes it a reliable indicator of n-type conduction rather than an artefact of any one measurement. This is entirely in line with what is known about undoped ZnO, where oxygen vacancies and zinc interstitials act as shallow electron donors and drive n-type behaviour as a matter of course (Özgür et al., 2005; Look, 2001).

What is also worth noting is that the absolute magnitude of Vout was small throughout — firmly in the microvolt range. Some of this is simply a consequence of the narrow temperature differences applied, but it also reflects the high electrical resistivity that undoped ZnO sintered in air tends to carry. Grain boundary Schottky barriers — formed when zinc vacancies and oxygen interstitials accumulate at grain interfaces during sintering — make it harder for carriers to move across the pellet, and this suppresses the thermoelectric voltage that ultimately reaches the measurement terminals (Özgür et al., 2005). On top of that, a large background offset of roughly −60 to −80 μV was present across all runs. This offset did not change meaningfully with ΔT, which tells us it is not a thermoelectric signal — it most likely comes from parasitic contact potentials at the metal junctions in the circuit and residual voltage offsets at the silver paste–ZnO interface (Rawat & Paul, 2016).

=== Discussion of the Extracted Seebeck Coefficient ===

The linear fits carried out on the four runs gave individual slope values of 0.900, 1.066, 0.933, and 0.836 μV/K, with R² values ranging from 0.949 to 0.994. The fits themselves were good — the R² values confirm that a linear relationship between Vout and ΔT held reasonably well across all four runs. The more interesting observation is the spread in the slope values, which ranged from 0.836 to 1.066 μV/K. This level of run-to-run variation points most naturally toward the silver paste contacts. Each time the paste was reapplied, the thickness, coverage, and curing of the contact layer changed slightly, and those changes show up as differences in the contact EMF at the silver–ZnO interface and, consequently, scatter in the extracted slope. Graph 2 2 is the clearest example of this — it gave the highest slope and the lowest R², which together suggest the contact conditions were less stable in that particular run than in the others.

The mean Seebeck coefficient of S = −0.934 ± 0.094 μV/K, while internally consistent and physically meaningful in its sign, sits far below the values reported in the literature for undoped ZnO pellets, where the typical range at room temperature is −350 to −430 μV/K. This gap is large enough that it cannot be pinned on any single factor — several things contributed to it simultaneously.

The positioning of the temperature sensors is one of them. Rather than being placed directly against the pellet faces, the thermocouples sat near the heater and heat sink, which means the recorded ΔT includes the thermal resistance drop between the sensor and the pellet surface. The actual temperature difference across the pellet was therefore smaller than what was recorded. Since S is pulled from the slope of Vout against ΔT, a ΔT that is too large in the denominator will push the extracted S downward — a systematic error that is well recognised in two-probe Seebeck measurement configurations (Rawat & Paul, 2016).

The connecting wires between the pellet and the Keysight B2901A SMU are another factor. Those wires carry their own Seebeck coefficients, and since the instrument measures the voltage of the full circuit rather than the pellet alone, the extracted slope reflects the combined thermoelectric response of every component in the loop (Rowe, 2006). Without knowing and subtracting the wire contribution, the slope cannot be taken as the pellet's Seebeck coefficient in isolation. The B2901A, while offering a voltage measurement resolution of 100 nV, is a two-probe instrument in this configuration and therefore cannot decouple the sample voltage from the lead contributions (Keysight Technologies, 2020).

The narrow ΔT range — particularly in runs where it extended down to 1°C — also played a role. At those small temperature differences, the thermoelectric voltage across the pellet drops into the sub-microvolt range, which is where electromagnetic interference and thermal drift in the lab environment start to compete with the signal itself. A minimum ΔT of 3–5 K is generally recommended for this reason (Goldsmid, 2010).

Beyond these instrumentation-level factors, the pellet itself contributes to the underestimation. Its high resistivity — a product of grain boundary barriers and residual porosity from conventional air sintering — limits the thermoelectric voltage that can be drawn out at the terminals (Özgür et al., 2005). There is also the question of bipolar conduction. In lightly doped or near-intrinsic semiconductors, a small population of thermally excited minority carriers — holes in this case — contribute a Seebeck voltage of opposite sign to the electron contribution, which partially cancels the net thermopower and reduces the measured value of S (Snyder & Toberer, 2008). On top of this, oxygen adsorption at grain boundary surfaces during measurement in ambient air acts to deplete near-surface electrons and raise local resistivity, adding another layer of suppression to the already modest signal (Look, 2001).

Perhaps the most fundamental point of all, though, is that the literature values of −350 to −430 μV/K are not room-temperature numbers. They are almost universally measured at elevated temperatures — typically between 600 K and 1273 K — using dedicated instruments operating under controlled inert atmospheres (Rowe, 2006). At those temperatures, carrier concentration and mobility are thermally activated to levels far above what they are at room temperature, putting those measurements in a completely different transport regime. Comparing a room-temperature measurement in ambient air with high-temperature literature values is therefore not a like-for-like comparison, and the gap between the two should not be read as a straightforward indication of measurement failure.

=== Physical Interpretation of the Anomalous Behaviour Beyond ΔT = 14°C ===

The reproducible reversal in the Vout versus ΔT trend beyond 14°C is worth examining carefully. Up to ΔT = 14°C, the voltage climbs steadily toward less negative values in the manner expected of a well-behaved thermoelectric response. At ΔT = 16°C, it drops back down instead of continuing upward, and this happened the same way every time the measurement was repeated. That rules out a contact issue or an instrument fluctuation. Something in the pellet's response genuinely changes once the temperature difference crosses that threshold.

The most straightforward explanation is grain boundary Schottky barrier breakdown. Within the linear regime, the electrostatic barriers at ZnO grain boundaries are stable, and the thermoelectric voltage builds up coherently along the pellet. As ΔT climbs beyond 14°C, the electric field across individual grains grows to the point where it begins to overwhelm those barriers. Carriers start crossing grain boundaries through tunnelling or avalanche-type mechanisms, which disrupts the orderly voltage accumulation and pulls the net measured output back down (Özgür et al., 2005; Rowe, 2006). This is closely related to the varistor-like switching behaviour that ZnO grain boundaries are well known for, where each active grain boundary interface sustains a charge barrier before breakdown occurs.

Resistive self-heating adds to this. At higher heater input voltages, more power is dissipated within the pellet, creating an internal temperature gradient that partially works against the externally applied ΔT. The net thermal driving force is reduced, and with it the thermoelectric voltage. In undoped ZnO, which already carries high resistivity, this effect is more significant than it would be in a more conductive sample, and it tends to concentrate at the silver paste contacts where current density peaks (Goldsmid, 2010). Between these two mechanisms — barrier breakdown and self-heating — the reversal at ΔT = 16°C has a clear physical basis, and restricting the primary measurements to ΔT ≤ 14°C was the appropriate response to it.

== References ==
Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104

Goldsmid, H. J. (2010). Introduction to thermoelectricity. Springer. https://doi.org/10.1007/978-3-642-00716-3

Rowe, D. M. (Ed.). (2006). Thermoelectrics handbook: Macro to nano. CRC Press.

Snyder, G. J., & Toberer, E. S. (2008). Complex thermoelectric materials. Nature Materials, 7(2), 105–114. https://doi.org/10.1038/nmat2090

Özgür, Ü., Alivov, Y. I., Liu, C., Teke, A., Reshchikov, M. A., Doğan, S., … Morkoç, H. (2005). A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 041301. https://doi.org/10.1063/1.1992666

Look, D. C. (2001). Recent advances in ZnO materials and devices. Materials Science and Engineering: B, 80(1–3), 383–387. https://doi.org/10.1016/S0921-5107(00)00604-8

Keysight Technologies. (2020). B2901A Precision Source/Measure Unit datasheet. https://www.keysight.com/

Precision Thermocouple Based Temperature Measurement System

2026-04-21T03:32:44Z

Sree: /* Results (Thermoelectric Characterisation of Undoped ZnO Pellet) */

Precision Thermocouple Based Temperature Measurement System

2026-04-21T03:22:07Z

Sree: /* Results */

Precision Thermocouple Based Temperature Measurement System

2026-04-20T10:44:11Z

Sree: /* What happens when the temperature difference is high? */

Main Page

Precision Thermocouple Based Temperature Measurement System

2026-04-10T03:21:41Z

Sree: /* Theoretical Background */

Precision Thermocouple Based Temperature Measurement System

2026-04-10T03:14:37Z

Sree: /* Introduction */

Precision Thermocouple Based Temperature Measurement System

2026-04-09T03:46:27Z

Sree: /* Experimental Setup */

==Introduction==

The objective of this project is to design, build, and validate a precision thermocouple-based temperature measurement system using the Seebeck effect. The system converts the extremely small thermoelectric voltage generated by a thermocouple into accurate, real-time temperature data.
Unlike thermistors or integrated circuit temperature sensors, thermocouples are capable of:

* Operating over a very wide temperature range
* Withstanding harsh and high-temperature environments
* Responding rapidly due to low thermal mass

However, the output signal from a thermocouple lies in the microvolt range, making accurate measurement challenging. This project addresses that challenge by implementing:
* A low-noise instrumentation amplifier
* Cold junction compensation (CJC)
* Microcontroller-based digitization, linearization, and calibration
== Theoretical Background ==
=== Seebeck Effect ===
The Seebeck effect states that when two dissimilar conductors are joined to form a loop and their junctions are maintained at different temperatures, a voltage is generated.

The thermoelectric voltage is given by:
<math>
V = S \cdot \Delta T
</math>
where:
* <math>V</math> = thermoelectric voltage
* <math>S</math> = Seebeck coefficient (µV/°C)
* <math>\Delta T</math> = temperature difference between junctions
For common thermocouples such as **Type K**:
<math>
S \approx 41 \, \mu V/^\circ C
</math>

=== Four-Probe (Kelvin) Measurement Technique ===
To accurately measure the microvolt-level thermoelectric voltage generated by the Type K thermocouple, a four-probe (Kelvin) measurement approach is employed. In this method, separate pairs of conductors are used for signal transmission and voltage sensing.

The primary thermocouple wires act as the signal-carrying path, while an additional pair of high-impedance sensing leads are connected directly to the input terminals of the instrumentation amplifier. Since the sensing circuit draws negligible current, voltage drops due to lead resistance and contact resistance are effectively eliminated.

This configuration ensures that the measured voltage corresponds closely to the true thermoelectric voltage generated at the junction, thereby improving measurement accuracy and stability.

=== Why Four-Probe Measurement Technique over Two-Probe Measurement Technique? ===
In thermoelectric material characterization, both two-probe and four-probe methods are used for measuring the Seebeck coefficient. While the two-probe method can provide higher accuracy for direct Seebeck voltage measurement, the four-probe method is often preferred in conventional setups because it enables simultaneous measurement of electrical resistivity and Seebeck coefficient, thereby reducing overall experimental time.

In the present work, however, the objective is not material characterization but precise measurement of thermoelectric voltage for temperature sensing. Therefore, a modified Kelvin (four-probe) sensing approach is adopted to minimize errors arising from lead and contact resistances, ensuring accurate acquisition of microvolt-level signals.

=== Material Selection ===
Zinc oxide (ZnO) is recognised as an n-type semiconductor and exhibits a pronounced Seebeck effect. When a temperature gradient is established across the material, charge carriers migrate from the hotter side to the cooler side, resulting in the generation of a thermoelectric voltage. The magnitude and polarity of this voltage depend on the properties of the material, with ZnO typically exhibiting a negative Seebeck coefficient due to the predominant conduction of electrons. The Seebeck coefficient for zinc oxide (ZnO) usually falls within the range of approximately –100 to –500 µV/K, which can vary based on factors such as temperature, doping, and the methods used in material preparation. The negative value indicates that ZnO functions as an n-type semiconductor, with electrons serving as the dominant charge carriers.

== Experimental Setup==
<div style="display:flex; gap:10px;">
[[File:Schematic diagram of the experimental - four probe mesasurement.png|thumb|500px|Schematic diagram of the experiment - four probe measurement]]

[[File:Schematic diagram of the experiment.png|thumb|500px|Schematic diagram of the experiment]]
</div>

<div style="display:flex; gap:10px;">
[[File:Experimental setup_final.jpg|thumb|500px|Experimental setup]]
[[File:Experimental setup of the sample_final.jpg|thumb|500px|Experimental setup of the sample]]
</div>

The experimental setup comprises two copper blocks functioning as thermal reservoirs, separated by a gap of approximately 3–4 mm. Each copper block has dimensions of about 12–15 mm in width and 8–10 mm in height, providing mechanical stability while minimizing thermal mass. A ZnO pellet with a diameter of 6 mm is positioned across the gap, overlapping slightly (~1 mm) on both blocks to ensure optimal thermal contact.

On the hot side, a layered structure is implemented, consisting of a copper block, a layer of Kapton tape for electrical insulation, and a power resistor serving as the heating element. The cold side features a similar configuration without the heater, allowing it to remain near ambient temperature. This arrangement establishes a controlled temperature gradient across the ZnO sample.

Four electrical contacts are applied to the top surface of the ZnO pellet using conductive silver paste, arranged in succession from the hot side to the cold side as Tₕ, V⁺, V⁻, and T_c. The total probe span is maintained at approximately 4 mm to ensure that all contact points fall within the pellet surface. Thermocouples are connected at Tₕ and T_c to measure the temperature difference across the sample.

The Seebeck voltage is measured between the V⁺ and V⁻ contacts, while the temperature gradient is obtained from the thermocouple readings. This configuration facilitates accurate determination of the Seebeck coefficient while minimizing errors associated with contact resistance and thermal instability.

== References ==
Oh, A. J., Stoddard, C. J., Queenan, C., & Oh, S. (2025). Efficient and affordable thermoelectric measurement setup using Arduino and LabVIEW for education and research. American Journal of Physics, 93(12), 991–999. https://doi.org/10.1119/5.0289649

Rawat, P. K., & Paul, B. (2016). Simple design for Seebeck measurement of bulk sample by 2-probe method concurrently with electrical resistivity by 4-probe method in the temperature range 300–1000 K. Measurement, 94, 297–302. https://doi.org/10.1016/j.measurement.2016.05.104