Electronic structure of randomAl0.5Ga0.5As alloys: Test of the ‘‘special-quasirandom-structures’’ description

The spectral properties of an ${\mathit{sp}}^3$ ${\mathit{s}}^{\mathrm{*}}$ tight-binding Hamiltonian for a random, unrelaxed ${\mathrm{Al}}_{0.5}$ ${\mathrm{Ga}}_{0.5}$As alloy are calculated using three different techniques: the coherent-potential approximation, the recursion method (as applied to a >2000 atom supercell), and the recently introduced ‘‘special-quasirandom-structures’’ (SQS) approach. Over a broad range of scattering strengths, the dominant spectral features predicted by the first two techniques are well reproduced by calculations for an SQS with 16 atoms/unit-cell (‘‘SQS-8’’). This suggests that the SQS approach might also be useful in cases where the other methods are difficult to apply, e.g., in first-principles calculations for structurally relaxed alloys.