Zinc-blende—diamond order-disorder transition in metastable crystalline(GaAs)1−xGe2xalloys

Abstract

A model of a zinc-blende—diamond order-disorder transition is proposed and applied to ${\left(\mathrm{GaAs}\right)}_{1-x}{\mathrm{Ge}}_{2x}$ substitutional crystalline alloys. In disordered Ge-rich alloys, the stable phase is one in which either Ga or As atoms can occupy nominal cation and nominal anion sites with approximately equal probabilities; in ordered GaAs-rich material, Ga (As) atoms preferentially occupy nominal cation (anion) sites. A three-component spin Hamiltonian, mean-field theory, and empirical tight-binding theory are all used in conjunction to predict equilibrium phase diagrams and the dependence on alloy composition $x$ of the direct band-gap energy $E_0\mathrm{}\left(x\right)\mathrm{}$. The theory accounts for the observed $V$-shaped dependence of $E_0\mathrm{}\left(x\right)\mathrm{}$ in ${\left(\mathrm{GaAs}\right)}_{1-x}{\mathrm{Ge}}_{2x}$ and for several qualitative facts concerning the growth of these interesting metastable crystalline alloys.