Electronic structure of the quaternary alloy GaxIn1−xAsyP1−y: A coherent-potential-approximation calculation

Abstract

The complex energy band structure of the quaternary alloy ${\mathrm{Ga}}_{\mathit{x}}$ ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{As}}_{\mathit{y}}$ ${\mathrm{P}}_{1\mathrm{-}\mathit{y}}$ obtained in the coherent-potential approximation. Self-energy effects are studied in detail for ${\mathrm{Ga}}_{0.5}$ ${\mathrm{In}}_{0.5}$ ${\mathrm{As}}_{0.5}$ ${\mathrm{P}}_{0.5}$ and ${\mathrm{Ga}}_{\mathit{x}}$ ${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{As}}_{\mathit{x}}$ ${\mathrm{P}}_{1\mathrm{-}\mathit{y}}$ lattice matched to InP as well as GaAs. Good agreement with experiment is obtained for the calculated values of the direct and $E_1$ energy gaps of the InP lattice-matched quaternary alloy.