Numerical investigation of the maximum thermoelectric efficiency

Abstract

The maximum thermoelectric efficiency that is given by the so-called dimensionless figure of merit ZT is investigated here numerically for various energy dependence. By involving the electrical conductivity σ, the thermopower α, and the thermal conductivity κ such that ZT = α2 × σ × T/κ, the figure of merit is computed in the frame of a semiclassical approach that implies Fermi integrals. This formalism allows us to take into account the full energy dependence in the transport integrals through a previously introduced exponent s that combines the energy dependence of the quasiparticles’ velocity, the density of states, and the relaxation time. While it has been shown that an unconventional exponent s = 4 was relevant in the context of the conducting polymers, the question of the maximum of ZT is addressed by varying s from 1 up to 4 through a materials quality factor analysis. In particular, it is found that the exponent s = 4 allows for an extended range of high figure of merit toward the slightly degenerate regime. Useful analytical asymptotic relations are given, and a generalization of the Chasmar and Stratton formula of ZT is also provided.