Editing Precision Thermocouple Based Temperature Measurement System (section)

== 2. Theoretical Background ==

=== 2.1. Seebeck Effect ===
The Seebeck effect describes the generation of an electrical potential across a material subjected to a temperature gradient. When a thermal difference is imposed, charge carriers at the high-temperature end possess greater thermal energy and diffuse preferentially toward the cooler region, establishing a charge imbalance that induces an internal electric field. Equilibrium is reached when this field opposes further carrier migration, and the resulting open-circuit voltage called the Seebeck voltage which is linearly proportional to the applied temperature difference:

<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 across the sample

The sign of S directly reflects the dominant carrier type. A negative Seebeck Coefficient is characteristic of electron-dominated (n-type) transport, while a positive value indicates hole conduction (p-type).Here in our work, ΔT is determined from the readings of two K-type thermocouples placed in contact with the sample surface, and V is acquired using a nanovoltmeter. Four voltage readings are recorded at each ΔT increment and subsequently averaged to minimise the effect of short-term measurement fluctuations. The Seebeck coefficient is then extracted from the slope of a linear fit applied to the V versus ΔT dataset.

=== 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 circular pellet under mechanical pressure. The pellet was first annealed for 5 hours at 300&deg;C. Since the pellet was not hard enough to cut, it was re-annealed at 500&deg;C for 3 hours. On cooling, it was cut into a rectangular shape of thickness 3 mm.