Numerical investigation of the maximum thermoelectric efficiency

Patrice Limelette

doi:10.1063/5.0041224

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.

Highlights

While some models have accounted for this quasi-universal law over a restricted range of parameters,24 a successful demonstration of the latter power law has been given in the frame of a charge transport model with s = 3.25 More recently, this approach has been extended in order to explain the exponent s = 4 by considering that charge carriers could behave as Dirac quasiparticles, namely, massless pseudorelativistic particles
This has required us to take into account all the energy dependence in the transport integrals by showing that s is, the sum of the exponents of the power law energy dependence of the relaxation time τE, the quasiparticles’ velocity vx,E, and the density of states gE as defined in the following: τE
By using the corresponding limits, it can be demonstrated that a standard activated behavior is found for the electrical conductivity in the non-degenerate regime if μ ≪ −1, while a power law dependence is expected if μ ≫ 1 in the degenerate one, σμ≫1 = σE0 × μs, σμ≪−1 = σE0 × Γ(s + 1) × eμwith the well known Γ function

Summary

Introduction

By calculating the Fermi integrals Fs−1(μ), the normalized electrical conductivity σ/σE0 can be computed as a function of the reduced temperature kBT/∣μ∣ as displayed in Fig. 1(a) for the various investigated exponents s. The use of the corresponding Fermi integrals according to Eq (1) allows us to plot in Fig. 1(b) the temperature dependence of thermopower, in absolute value, for the various investigated exponents s.

Results

Conclusion