The Limits of Thermoelectric Performance with a Bounded Transport Distribution

TL;DR

This paper derives the optimal bounded transport distribution for thermoelectric materials, establishing theoretical upper limits on the figure of merit and guiding material design strategies.

Contribution

It identifies the optimal bounded transport distribution as a boxcar function for ZT, providing practical upper limits and design targets for thermoelectric materials.

Findings

Maximum ZT scales with $rac{ ext{TD magnitude} imes T}{ ext{lattice thermal conductivity}}$

Optimal transport distribution is a boxcar function for ZT

Provides upper bounds to guide material engineering

Abstract

With the goal of maximizing the thermoelectric (TE) figure of merit $ZT$, Mahan and Sofo [Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] found that the optimal transport distribution (TD) is a delta function. Materials, however, have TDs that appear to always be finite and non-diverging. Motivated by this observation, this study focuses on deriving what is the optimal bounded TD, which is determined to be a boxcar function for $ZT$ and a Heaviside function for power factor. From these optimal TDs upper limits on $ZT$ and power factor are obtained; the maximum $ZT$ scales with $\Sigma_{\rm max} T /\kappa_l$, where $\Sigma_{\rm max}$ is the TD magnitude and $\kappa_l$ is the lattice thermal conductivity. These results help establish practical upper limits on the performance of TE materials and provide target TDs to guide band/scattering engineering strategies.