Energy band structure in p-type germanium and silicon

Abstract Energy-band calculations are made for the three valence bands in silicon and germanium in terms of the cyclotron resonance parameters. The energy in the band measured from k = 0 is not assumed small compared to the spin-orbit splitting so that parabolic bands do not result. The above calculation results from considering the first term of a perturbation expansion of the k.p and spin-orbit perturbations. The contributions from higher-order terms are examined and found to be important for germanium but not for silicon. Matrix elements for direct optical transitions between the valence bands are calculated from the cyclotron resonance constants. The free-carrier absorption is computed from the present band-structure calculations, and comparison is made with recent experimental data of R. N ewman for germanium. A correction to the split-off valence-band calculations is estimated, using the experimental data. Formulae are derived for degenerate perturbation theory with two perturbations of different orders acting.