Long-range order in (GaAs${)}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ge}}_{2\mathrm{x}}$ and (GaSb${)}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ge}}_{2\mathrm{x}}$: Predictions for 〈111〉 growth

We present an analysis of epitaxial growth of the pseudobinary alloys of the III-V semiconductor compounds GaAs and GaSb with the group IV semiconductor germanium. This work extends the growth model of Davis and Holloway from 〈100〉-oriented to 〈111〉-oriented growth, which has not yet been explored experimentally. We find that the direction of growth has a large influence on the long-range order in these alloys. Particularly we predict the following: (1) The order-disorder transition that is observed at about 30 mol?Ge in 〈100〉-grown alloys does not occur with 〈111〉 growth. Instead, some zinc-blende order is retained so long as any of the III-V component is present. (2) Growth in the 〈111〉Ga direction is unstable with a tendency for spontaneous conversion to 〈111〉As growth. (3) The short-range order is similar for both directions of growth. From this we infer that the energy gap of (GaAs${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{2\mathrm{x}}$ will also be similar for 〈111〉-grown and 〈100〉-grown specimens.