Properties of (GaAs${)}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ge}}_{2\mathrm{x}}$ and (GaSb${)}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ge}}_{2\mathrm{x}}$: Consequences of a stochastic growth process

A new model is presented for the structure of the pseudobinary alloys of the III-V semiconductors GaAs and GaSb with the group IV semiconductor germanium. This model is based upon the random arrival of the constituent atoms at the growing {100} surface. The main postulates are that Ga—Ga and As—As or Sb—Sb nearest-neighbor pairs are prohibited and that each incorporated Ga atom acquires a nearest-neighbor As (or Sb) atom from the excess of the group V constituent that is present during growth. The model has been implemented by Monte Carlo simulation and analyzed by analytic approximations. The results are in good agreement with the measured energy gap of (GaAs${)}_{1\mathrm{-}x}$ ${\mathrm{Ge}}_{2\mathrm{x}}$ and with the results of x-ray, Raman, and extended x-ray-absorption fine-structure determinations of the order parameter and the nearest-neighbor environments in (GaSb${)}_{1\mathrm{-}x}$ ${\mathrm{Ge}}_{2\mathrm{x}}$. We also present calculations of the, as yet unreported, energy gap of the latter compound.