Polar Mobility of Holes in III-V Compounds

Ehrenreich has shown that the transition probability for scattering from state $\overrightarrow{\mathrm{k}}$ to state ${\overrightarrow{\mathrm{k}}}^{\prime }$ depends on the overlap between initial- and final-state wave functions $G(\overrightarrow{\mathrm{k}},{\overrightarrow{\mathrm{k}}}^{\prime })$. This function has been calculated for intraband and interband scattering in the $p$-type III-V compounds using Kane's valence-band wave functions. A simple model is proposed for polar-mode scattering in the valence bands and it is shown that the polar mobility is nearly four times larger than previously calculated for $p$-type III-V compounds. Approximately half of this increase is a consequence of the reduced overlap of $p$-like wave functions, and the other half is contributed by the presence of high-mobility carriers in the light-hole band. It is shown that the $p-\mathrm{G}\mathrm{a}\mathrm{P}$ Hall mobility data of Casey, Ermanis, and Wolfstirn can be fitted quite well throughout the lattice scattering regime and that the dominant scattering mechanisms are acoustic and nonpolar optical modes.