Electronic structure of pseudobinary semiconductor alloys ${\mathrm{Al}}_x$ ${\mathrm{Ga}}_{1-x}\mathrm{As}$, $\mathrm{Ga}{\mathrm{P}}_x{\mathrm{As}}_{1-x}$, and ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{P}$

A method for calculating detailed electronic properties of the pseudobinary III-V compound semiconductor alloys is presented. The technique begins with realistic band structures obtained for the constituent compounds by fitting the band-gap symmetry-point energies and effective masses to experimental data, where they are available, and to more sophisticated theoretical results. Then the coherent-potential approximation is used to calculate the alloy band structures and scattering rates. Detailed comparisons between the theoretical predictions and experimental data for three alloys ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$, $\mathrm{Ga}{\mathrm{P}}_x{\mathrm{As}}_{1-x}$, and ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{P}$ demonstrate the quantitative nature of the method. Bowing parameters for the $\Gamma$, $X$, and $L$ gaps and the direct-to-indirect band-gap crossover concentrations are all predicted to within the present degree of experimental certainty.