Valence band structure of germanium

The absorption produced by direct inter-valence band transitions provides a sensitive test for the calculated valence band shapes. A calculation by Kane of the valence band shapes of p-type germanium near k = 0 using second-order degenerate k. p perturbation theory and of the resulting absorption spectrum indicated that the mass of the split-off valence band had not been determined accurately. This inadequacy was shown up even more when the Kane model was used to predict the change in absorption produced by a small change in lattice temperature and a comparison made with recent experimental results. The availability of these accurate absorption data has stimulated a more accurate calculation of the valence band structure. Here the interactions between the valence bands and the two neighbouring conduction bands are calculated exactly rather than by perturbation theory. The next nearest conduction band is included as a perturbation. It is then found that the mass of the split-off band is substantially heavier than calculated by Kane, a requirement that better agreement with the observed spectrum be obtained. An expression for the conduction band energy is also presented. The coefficients of k 2 and k 4 in this expression are calculated and compared with the results of magneto-absorption experiments. Agreement within experimental error is achieved.