Modification of the virtual-crystal approximation for ternary III-V compounds

We discuss a modification of the virtual-crystal approximation for alloys in the semiempirical tight-binding method of band-structure calculations, which explicitly includes the interactions between unlike second neighbors. The results are applied to the quaternary ${\mathrm{Ga}}_y{\mathrm{In}}_{1-y}{\mathrm{As}}_x{\mathrm{P}}_{1-x}$ and its constituent ternary compounds.