Calculation of optical- and acoustic-phonon—limited conductivity and Hall mobilities forp-type silicon and germanium

Abstract

Optical- and acoustic-phonon---limited mobilities for $p$-type silicon and germanium have been calculated, without the relaxation-time approximation, from solutions of the full Boltzmann equation. The valence-band dispersions are obtained from Kane's $6\ifmmode\times\else\texttimes\fi{}6 \stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ Hamiltonian. Hole-phonon transition rates are calculated using the deformation-potential theory with one adjustable parameter for hole---optical-phonon interaction strength which is fitted to mobility data at room temperature. This represents the first such calculation for silicon. Very good agreement is found between experiment and theory for both mobilities in silicon and for the conductivity mobility in germanium. The agreement between experiment and theory for the Hall factor in Ge is better than 20%, which may still be improved upon with more reliable deformation-potential parameters. However, the agreement is better than that attained by earlier calculations. The fitted values of the hole---optical-phonon deformation potentials are within bounds of independent estimates for their values. It may therefore be concluded that the deformation-potential theory is well suited for quantitative modeling of phonon-limited mobilities.