Full-Boltzmann-equation solutions of the acoustic-phonon-limited conductivity and Hall mobilities for p -type silicon and germanium

Acoustic-phonon-limited conductivity and Hall mobilities for p-type silicon and germanium have been calculated from solutions of the full Boltzmann equation without the relaxation-time approximation. Using the deformation-potential scattering theory of Tiersten, we obtain the necessary hole-acoustic-phonon transition rates, with no adjustable parameters, as a first-principles input into the transport equations. Excellent agreement is found for both mobilities in silicon, and the conductivity mobility in germanium, as compared with experimental data. The Hall mobility for germanium is within 12% of the measured Hall mobility---the closest agreement to date for a first-principles theory. The success of this calculation is due to the inclusion of all three top valence bands, careful treatment of the scattering matrix elements, and the use of the full-Boltzmann-equation solutions to obtain the transport coefficients. Results of our calculation confirm the quantitative accuracy of the deformation-potential theory.