Gap properties of ${\mathrm{Al}}_{\mathit{n}}$${\mathrm{Ga}}_{8\mathrm{-}\mathit{n}}$${\mathrm{As}}_8$ ordered compounds

The small-crystal approach with a 16-site basic cluster is used to determine the electronic structure of 16 inequivalent ordered structures of ${\mathrm{Al}}_{\mathit{n}}$ ${\mathrm{Ga}}_{8\mathrm{-}\mathit{n}}$ ${\mathrm{As}}_8$ compounds. The energy gaps and oscillator strengths for the main gap transitions are calculated, and different results are obtained for different structures of the same composition n, which illustrates the role of compositional ordering in the electronic properties of alloys. Average values of these quantities are used as an attempt to describe ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As alloys. Important features of our results are (a) a positive curvature in the averaged gap versus x dependence for small x and (b) a smooth featureless decrease of the averaged oscillator strength with x. This last feature implies that the direct-indirect gap crossover in the alloy system cannot be genuinely obtained by any sort of averaging among ${\mathrm{Al}}_{\mathit{n}}$ ${\mathrm{Ga}}_{8\mathrm{-}\mathit{n}}$ ${\mathrm{As}}_8$ ordered compounds.