Electronic properties of random alloys: Special quasirandom structures (original) (raw)

Structural models needed in calculations of properties of substitutionally random A ] B alloys are usually constructed by randomly occupying each of the X sites of a periodic cell by 3 or B. We show that it is possible to design "special quasirandom structures" (SQS's) that mimic for small N (even %= 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/ce11 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. I. INTRODUCTION: NONSTRUCTURAL THEORIES OF RANDOM ALLOYS Early experiments' on bulk isovalent semiconductor alloys A & "B"revealedthat many of their properties represent a simple and continuous compositional (x) interpolation between the properties of the end-point solids A and B. For example: (i) alloy lattice parameters are nearly linear with x (Vegard's rule); (ii) unlike glasses, amorphous semiconductors, or heavily doped systems, isovalent semiconductor alloys generally do not exhibit any substantial gap or "tail" states; (iii) diffraction patterns of melt-grown semiconductor alloys have the same symmetry as those of the constituent solids (with no extra spots); (iv) absorption and reflectance spectra are rather sharp, showing only small alloy broadening near the edge transitions; the A, th transition energy e&(x) shifts rigidly with composition as ez(x) = [(1x)e&(A)+xe&(B)] box(1x),where b& (the "bowing coefficient") is nearly composition independent; (v) the principal Raman peaks shift smoothly with composition; and (vi) the mixing enthalpy AH(x) is small, positive, and has a simple composition dependence Qx(1x) with nearly constant "interaction parameter" Q, as expected from a regular solution model.