On Landauer versus Boltzmann and full band versus effective mass evaluation of thermoelectric transport coefficients

Abstract

Using a full band description of electronic bandstructure, 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 density of modes in the Landauer approach or the transport distribution in the Boltzmann solution are compared and thermoelectric transport coefficients are evaluated. 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.