Lattice-Scattering Mobility of Holes in Germanium

The lattice-scattering mobility of holes in germanium is calculated by using the transition probabilities for scattering by acoustical and optical phonons derived in an earlier paper, in which both the rigid- and deformable-ion models were used to determine the interaction between holes and the lattice. Coupled Boltzmann equations are considered, describing the distribution of carriers under the influence of an electric and phonon field in the two valence bands of germanium, degenerate at $k=0\mathrm{}$. The results involve two previously described constants $C_1$ and $C_4$ which are treated as arbitrary parameters. Results are presented for several sets of these parameters and also for values of the temperature $\Theta =300\mathrm{}°\mathrm{K} \mathrm{and} 500°\mathrm{K}$ which might correspond to the fundamental optical frequency of the germanium lattice. The curves, $log\mu$ vs $logT$, closely resemble straight lines over the lattice-scattering range. It is possible to find values of $C_1$ and $C_4$ for both rigid- and deformable-ion models which agree well with the observed mobility if $\Theta =300\mathrm{}°$K but not if $\Theta =500\mathrm{}°$K. The question as to whether these values of $C_1$ and $C_4$ are correct is not considered in this paper.