Optimal Band Structure for Thermoelectrics with Realistic Scattering and Bands

TL;DR

This paper investigates how realistic electronic band structures and scattering models influence thermoelectric performance, revealing optimal bandwidths and challenging the practicality of certain high-performance band designs.

Contribution

It introduces rigorous scattering treatments for realistic band structures and identifies bounds on performance improvements due to multiple pockets and band shapes.

Findings

Interband scattering limits performance gains from multiple pockets.

Anisotropic 'flat-and-dispersive' bands may not be practically advantageous.

Optimal bandwidth depends on temperature and thermal conductivity, potentially exceeding current $zT$ values.

Abstract

Understanding how to optimize electronic band structures for thermoelectrics is a topic of long-standing interest in the community. Prior models have been limited to simplified bands and/or scattering models. In this study, we apply more rigorous scattering treatments to more realistic model band structures - upward-parabolic bands that inflect to an inverted parabolic behavior - including cases of multiple bands. In contrast to common descriptors (e.g., quality factor and complexity factor), the degree to which multiple pockets improve thermoelectric performance is bounded by interband scattering and the relative shapes of the bands. We establish that extremely anisotropic `flat-and-dispersive' bands, although best-performing in theory, may not represent a promising design strategy in practice. Critically, we determine optimum bandwidth, dependent on temperature and lattice thermal conductivity, from perfect transport cutoffs that can in theory significantly boost $zT$ beyond the values attainable through intrinsic band structures alone. Our analysis should be widely useful as the thermoelectric research community eyes $zT>3$.