Thermoelectric transport of GaAs, InP, and PbTe: Hybrid functional with ${\bf \it k \cdot p}$ interpolation versus scissor-corrected generalized gradient approximation
Boltzmann transport calculations based on band structures generated with density functional theory (DFT) are often used in the discovery and analysis of thermoelectric materials. In standard implementations, such calculations require dense ${\it k}$-point sampling of the Brillouin zone and are therefore typically limited to the generalized gradient approximation (GGA), whereas more accurate methods such as hybrid functionals would have been preferable. GGA variants, however, generally underestimate the band gap. While premature onset of minority carriers can be avoided with scissor corrections, the band gap also affects the band curvature. In this study, we resolved the ${\it k}$-point sampling issue in hybrid-functional based calculations by extending our recently developed ${\it k}\cdot\tilde{\it p}$ interpolation scheme [Comput. Mater. Sci. 134, 17 (2017)] to non-local one-electron potentials and spin-orbit coupling. The Seebeck coefficient generated based on hybrid functionals were found to agree better than GGA with experimental data for GaAs, InP, and PbTe. For PbTe, even the choice of hybrid functional has bearing on the interpretation of experimental data, which we attribute to the description of valley convergence of the valence band.