Electronic Spectra of Crystalline Germanium and Silicon

A detailed calculation of the energy bands of germanium and silicon has been performed by use of the pseudopotential method. The first three potential coefficients have been determined empirically, and all higher ones set equal to zero. This potential was used to compute the energy eigenvalues at 50 000 points throughout the Brillouin zone. By use of this sample, we calculated the imaginary part of the dielectric constant in the optical and near ultraviolet where direct transitions between the valence and low-lying conduction bands dominate the response. Photoelectric yield curves were obtained for comparison with recent experiments. In all cases agreement of theory and experiment was reasonable. Energy contours were constructed in several of the principal symmetry planes. These were used to explain the structure in the optical properties of Ge and Si in terms of transitions near certain important critical points. Effective masses and the static dielectric constant were also computed.