First-principles study of electron and hole mobilities of Si and GaAs

With first-principles calculated electron-phonon coupling matrix elements, the phonon-limited electron and hole mobilities of Si and GaAs are studied using the Boltzmann transport equation. The calculated mobilities agree well with the experimental measurements. For electrons in GaAs, the calculated mobility is very sensitive to the band structure characterized by the effective mass and the energy gap between $\mathrm{\ensuremath{\Gamma}}$ and L valleys, which clarifies the discrepancies between recent literature findings [J.-J. Zhou and M. Bernardi, Phys. Rev. B 94, 201201(R) (2016); T.-H. Liu et al., Phys. Rev. B 95, 075206 (2017)]. Unlike electrons in GaAs, where the longitudinal optical phonon dominates the scattering, the other phonon branches have a comparable influence on the mobility of holes in GaAs. In Si and GaAs, the spin-orbit coupling interaction has a significant effect on the valence bands and, further, on the hole mobilities, without which the calculated mobility is underestimated, especially at relatively low temperatures, while it has almost no effect on the electrons.