Crystal Potential and Energy Bands of Semiconductors. I. Self-Consistent Calculations for Diamond

Approximate self-consistent potentials are constructed for diamond, first with exchange ignored, and then with exchange included according to the Slater free-electron approximation and according to a refined momentum-dependent free-electron approximation. The Hartree charge densities and energy gap are in fair agreement with experiment. Inclusion of valence exchange by the Slater approximation shows that Herman's earlier calculation was nearly self-consistent in this approximation. Agreement with experiment on charge densities and energy gap is greatly improved in comparison with the Hartree results. Further inclusion of the momentum dependence of the exchange potential does not greatly improve the charge densities and the energy gap but does alter the valence band width.