On Landauer vs. Boltzmann and Full Band vs. Effective Mass Evaluation of Thermoelectric Transport Coefficients

TL;DR

This paper compares Landauer and Boltzmann formalisms for thermoelectric transport, develops methods to derive transport coefficients from full band structures, and relates detailed band descriptions to effective mass approximations.

Contribution

It introduces a comprehensive comparison between full band and effective mass models for thermoelectric properties, and provides a procedure to derive effective mass descriptions from detailed band structures.

Findings

Full band calculations align with effective mass models under certain conditions.

A method to extract effective mass parameters from full band data is proposed.

Numerical examples demonstrate the accuracy of the full band approach.

Abstract

The Landauer approach to diffusive transport is mathematically related to the solution of the Boltzmann transport equation, and expressions for the thermoelectric parameters in both formalisms are presented. Quantum mechanical and semiclassical techniques to obtain from a full description of the bandstructure, E(k), the number of conducting channels in the Landauer approach or the transport distribution in the Boltzmann solution are developed and compared. Thermoelectric transport coefficients are evaluated from an atomistic level, full band description of a crystal. Several example calculations for representative bulk materials are presented, and the full band results are related to the more common effective mass formalism. Finally, given a full E(k) for a crystal, a procedure to extract an accurate, effective mass level description is presented.