Effective Band Structure of Random Alloys

Random substitutional A(x)B(1-x) alloys lack formal translational symmetry and thus cannot be described by the language of band-structure dispersion E((k) over right arrow). Yet, many alloy experiments are interpreted phenomenologically precisely by constructs derived from wave vector (k) over right arrow, e. g., effective masses or van Hove singularities. Here we use large supercells with randomly distributed A and B atoms, whereby many different local environments are allowed to coexist, and transform the eigenstates into an effective band structure (EBS) in the primitive cell using a spectral decomposition. The resulting EBS reveals the extent to which band characteristics are preserved or lost at different compositions, band indices, and (k) over right arrow points, showing in (In, Ga)N the rapid disintegration of the valence band Bloch character and in Ga( N, P) the appearance of a pinned impurity band.