Electronic properties of random alloys: Special quasirandom structures

Structural models needed in calculations of properties of substitutionally random ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$ alloys are usually constructed by randomly occupying each of the N sites of a periodic cell by A or B. We show that it is possible to design ``special quasirandom structures'' (SQS's) that mimic for small N (even N=8) the first few, physically most relevant radial correlation functions of an infinite, perfectly random structure far better than the standard technique does. These SQS's are shown to be short-period superlattices of 4--16 atoms/cell whose layers are stacked in rather nonstandard orientations (e.g., [113], [331], and [115]). Since these SQS's mimic well the local atomic structure of the random alloy, their electronic properties, calculable via first-principles techniques, provide a representation of the electronic structure of the alloy. We demonstrate the usefulness of these SQS's by applying them to semiconductor alloys. We calculate their electronic structure, total energy, and equilibrium geometry, and compare the results to experimental data.