Energy bands of ternary alloy semiconductors: Coherent-potential-approximation calculations

Abstract

A method for calculating compositional variations of energy bands of ternary alloy semiconductors based on the coherent-potential approximation is presented. A generalized, Soven-type equation in a matrix form is derived and then solved by subsequent iterations. Zeroth-order approximation for band-gap energies is taken from the virtual-crystal approximation. The nonlinear dependence of the energy upon the alloy composition at various symmetry points within the first Brillouin zone is calculated for $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x}$ and ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P}$ crystals. Significant band bowing has been found in both cases. The theoretical results are compared with experimental data available for these systems.