Molecular coherent-potential approximation for zinc-blende pseudobinary alloys

A detailed description is presented of the recently developed molecular coherent-potential approximation (MCPA) theory of the electronic structure of zinc-blende pseudobinary alloys [K. C. Hass, R. J. Lempert, and H. Ehrenreich, Phys. Rev. Lett. 52, 77 (1984)]. This approach is superior to previous CPA treatments because of its ability to treat the dominant effects of both random chemical and random bond-length variations. The two effects are modeled as diagonal and off-diagonal disorder, respectively, in an empirical tight-binding framework. A straightforward application of the MCPA is made possible by the presence of one chemically ordered sublattice. General consequences of this approach are illustrated through detailed applications to ${\mathrm{In}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ga}}_{\mathrm{x}}$As and ${\mathrm{ZnSe}}_{\mathrm{x}}$ ${\mathrm{Te}}_{1\mathrm{-}\mathrm{x}}$. The interference between chemically and structurally induced scattering in different energy regions is analyzed by comparing MCPA, site CPA, and virtual-crystal spectral densities and band-edge properties. Differences between the two materials are used to contrast the behavior in cation-substituted III-V and anion-substituted II-VI alloys. The merits of the MCPA are discussed in relation to some alternative alloy theories (bond-centered CPA, supercell, and recursion method).