ELECTRONIC BAND STRUCTURE AND COVALENCY IN DIAMOND-TYPE SEMICONDUCTORS

The band structure of a diamond-type semiconductor near the energy gap can be described simply in terms of the Jones zone. The energy gap is nearly constant over the Jones-zone faces except close to the edges and corners. This accounts for the success of the spherically symmetric Penn model of the dielectric constant ε. It also explains the qualitative shape of the optical absorption spectrum, in particular the occurrence of the first peak. Specifically covalent effects arise from the fact that the ν(111) Fourier component of the pseudopotential is relatively large and has to be treated beyond lowest order of perturbation theory. Simple algebraic formulae give the principal energy gap and the position of the minimum in the conduction band along ΓΔX, which agree with the large computer calculations to within about 25%. This picture accounts in a simple approximate way for the variation with pressure of the dielectric constant and of the position of the main peak in the optical absorption spectrum. Finally a microscopic calculation of the extra charge Qb located in the covalent bond gives agreement with Phillips' conjecture that Qb = 2ε-1.