Electronic theory of ordering in (GaAs)1−xGe2xalloys

The electronic energy of (GaAs${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{2\mathrm{x}}$ alloys is investigated as a function of the degree of short-range order in these ternary systems. The generalized cluster Bethe-lattice method, with a minimal ${\mathrm{sp}}^3$ set of orbitals, is used in the calculation. The results are parametrized in terms of nearest-neighbor pair interaction energies which are independent of the degree of short-range or long-range order and consistent with known defect energies. This confirms the validity of previously used Ising-like Hamiltonians for such systems. The theory allows a critical examination of both the thermodynamic and growth models proposed for the zinc-blende–diamond transition observed in these alloys. The transition temperature calculated from the pair interaction energies is much higher than actual sample preparation temperatures, indicating that kinetics must determine the observed structure. However, previous kinetic models have essentially neglected Ge correlations which are shown to be important.