Editing Precision Thermocouple Based Temperature Measurement System (section)

=== 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.