The problem of the band structure of semiconductor alloy systems is treated by both the dielectric two-band method and by the use of an empirical (local) pseudopotential. With both methods, calculations are made in the virtual-crystal approximation assuming linear dependence on alloy concentration of the lattice constant and the parameters of the two methods. Contrary to some previous assertions, both methods predict, in general, a nonlinear dependence of the interband gaps on concentration. An estimate is also made of the effects of second-order perturbations to the virtual-crystal approximation, i.e., the effect of disorder. Of particular interest are the lowest direct and indirect energy gaps and the deviations of these from linearity. The treatment is confined to alloys of compounds having the formula $A^N{B}^{8-N}$, but quaternary and more complicated alloys may be treated as easily as the ternary alloys to which most previous experimental work has been confined. Results are compared to experiment and to the empirical formula of Thompson and Woolley. We find that, with one free parameter, the dielectric method gives good agreement with experiment, but that the local-pseudopotential method apparently does not yield satisfactory results for this problem.

• Received 30 October 1969

DOI:https://doi.org/10.1103/PhysRevB.1.3351