Universal Behavior of the Thermoelectric Figure of Merit, zT, vs. Quality Factor

TL;DR

This study reveals a universal behavior in thermoelectric materials where complex electronic structures do not outperform simple parabolic bands in terms of the figure of merit, zT, at a given quality factor, simplifying material search.

Contribution

The paper demonstrates that complex electronic band structures do not surpass simple parabolic bands in thermoelectric performance at a fixed quality factor, revealing a universal behavior.

Findings

zT depends only on the ratio of electrical to thermal conductivity.

Complex electronic structures do not outperform simple parabolic bands.

Universal behavior simplifies the search for thermoelectric materials.

Abstract

To increase the performance of thermoelectric materials, the electronic parameters in the figure of merit must be improved. In this paper, we use full, numerical band structures and solve the Boltzmann equation in the relaxation time approximation using energy-dependent scattering times informed by first principles simulations. By varying the strength of the electron-phonon coupling or the lattice thermal conductivity, we compute the thermoelectric figure of merit, zT, vs. a generalized thermoelectric quality factor. More than a dozen different complex electronic structures are examined. Surprisingly, we find that at a given quality factor, none provides a better figure of merit than that of a material with a simple, parabolic band and acoustic deformation potential scattering. A qualitative argument for this unexpected finding is presented. This apparent universal behavior suggests that even for complex electronic band structures, the thermoelectric figure of merit depends solely on the ratio of electrical to thermal conductivity; the Seebeck coefficient and Lorenz number need not be considered. This observation should simplify the search for promising new materials, but if exceptions to this behavior can be identified, new paths for increasing thermoelectric material performance will open up.