On the Analytical Determination of the Seebeck Coefficient Using the Fermi–Dirac Approximation

Abstract

The Seebeck coefficient, or thermoelectric power, is a key physical parameter that quantifies the voltage generated in response to a temperature gradient across a material. Accurate evaluation of this coefficient is essential in order to optimize the performance of thermoelectric devices. This study proposes a theoretical approach to the analytical determination of the Seebeck coefficient in semiconductors, based on the Fermi– Dirac statistical approximation. The model incorporates the temperature dependence of the Fermi level, which introduces an intrinsic gradient along the thermoelectric structure under non-equilibrium thermal conditions. This framework enables a more precise understanding of the interplay between the carrier distribution, energy levels, and temperature variation. The analytical expressions obtained here show good agreement with the results of numerical methods, and offer significant advantages in terms of modeling and designing high-performance thermoelectric materials. The proposed approach proves to be an efficient and insightful tool for theoretical investigations and optimization studies in semiconductor thermoelectrics.