Measurements of electrical resistivity and Seebeck coefficient for disc-shaped samples

Abstract

Herein we develop a methodology to measure the resistivity of discs by deriving a mathematic formula between resistivity and resistance from solving the electrostatic Laplace equation in polar coordinates. Then the resistivity and Seebeck coefficient of disc samples of p- and n-type bismuth telluride are measured experimentally either in nitrogen or helium atmosphere. The validity of Seebeck coefficient is demonstrated by the excellent linearity between Seebeck voltages and temperature differences. The bar samples are also measured for comparison. Finite element simulation is utilized to display the two-dimensional potentials and currents and have an error analysis. Furthermore, the resistivity error due to the probe distance error is discussed analytically based on the mathematic formula, and the probe distance can be optimized to minimize the resistivity error. The disclosed approach would extend the applicability of the present instruments to the disc-shaped samples and be useful in the emerging transverse thermoelectricity.