Thermoelectric transport in the coupled valence-band model

Abstract

The Boltzmann transport equation (BTE) is applied to the problem of thermoelectric transport in p-type semiconductors whose valence band-structure is describable in terms of two bands degenerate at the Γ point. The Seebeck coefficient and mobility are calculated from the solution to two coupled BTEs, one for each band, with interband scattering and scattering by inelastic mechanisms treated exactly by the application of an algorithm developed by the authors in an earlier work. Most treatments of this problem decouple the two bands by neglecting certain terms in the BTE, greatly simplifying the mathematics: the error in the Seebeck coefficient and mobility introduced by this approximation is quantified by comparing with the exact solution. Degenerate statistics has been assumed throughout, and the resulting formalism is therefore valid at high hole concentrations. Material parameters are used that have been deduced from optical, strain and other experiments often not directly related to hole transport. The formulations in this work thus do not use adjustable or fitting parameters. The transport coefficients of heavily doped gallium antimonide, a typical high-efficiency p-type thermoelectric material, are calculated and agreement to experimentally determined values is found to be satisfactory.