Predicted energy band gaps of ($A^{\mathrm{III}}$$B^{\mathrm{V}}$${)}_{1\mathrm{-}x}$$X_{2x}^{\mathrm{IV}}$ metastable, substitutional, crystalline alloys

Predictions of the energy band gaps as functions of alloy composition are given for the Greene alloys, which are metastable, crystalline, substitutional alloys of III-V compounds and group-IV elemental materials. All possible combinations of these alloys involving Al, Ga, In, P, As, Sb, Si, Ge, and Sn are considered. The Γ and L conduction-band minima, relative to the valence-band maxima, exhibit characteristic V-shaped bowing and kinks as functions of composition x; the band edges at point X bifurcate at critical compositions corresponding to the order-disorder transition of Newman et al. The V-shaped bowing due to the transition offers the possibility of band gaps significantly smaller than expected on the basis of the conventional virtual-crystal approximation. Alloys with modest lattice mismatches that are predicted to have especially interesting band gaps include (InP${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{2\mathrm{x}}$, (AlSb${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Sn}}_{2\mathrm{x}}$, (GaSb${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Sn}}_{2\mathrm{x}}$, and (InAs${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Sn}}_{2\mathrm{x}}$, which are alloys with potentially small band gaps, and (AlAs${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{2\mathrm{x}}$ and (GaAs${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Si}}_{2\mathrm{x}}$, which are alloys with larger gaps and several interesting band-edge crossings as functions of composition.