Band gaps and spin-orbit splitting of ordered and disordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ and $\mathrm{Ga}{\mathrm{As}}_x{\mathrm{Sb}}_{1-x}$ alloys

Spontaneous long-range ordering of the otherwise disordered isovalent semiconductor alloys $A_x{B}_{1-x}C$ has been recently observed in numerous III-V alloy systems exhibiting the CuAu-I, CuPt, and chalcopyrite structures. We present a theory for the ordering-induced changes in the Brillouin-zone-center electronic properties, with application to the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ and $\mathrm{Ga}{\mathrm{As}}_x{\mathrm{Sb}}_{1-x}$ alloys. The dominant effect for these systems is shown to be level repulsion between different-symmetry states of the binary constituents which fold into equal-symmetry states in the ordered ternary structures. Strong variations in the band gaps, spin-orbit splittings, and charge densities among the three basic ordered structures reflect the different magnitudes of the symmetry-enforced coupling between the folded states. An extension of the model to the disordered alloys yields good agreement with the observed optical bowing parameters for the fundamental gaps; however, the positive (downward concave) bowing of the spin-orbit splitting observed in some common-cation semiconductor alloy remains an unexplained puzzle.