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

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 $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ and ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{P}$ crystals. Significant band bowing has been found in both cases. The theoretical results are compared with experimental data available for these systems.