Approximate bandstructures of semiconductor alloys from tight-binding supercell calculations

Alloys such as AlGaAs, InGaAs, and SiGe find widespread usage in nanoelectronic devices such as quantum dots and nanowires. For these devices, in which the carriers probe nanometre-scale local disorder, the commonly employed virtual crystal approximation (VCA) is inadequate. Although the VCA produces small-cell E(k) relations it fails to include local disorder. In contrast, random-alloy supercell calculations do include local disorder but only deliver band extrema and supercell (not small cell) E(k) relations. Small-cell E(k) relations are, however, needed to interpret transport parameters such as effective masses. This work presents a method to extract the necessary approximate small-cell E(k) relations from the disordered supercell states. The method is applied to AlGaAs and gives significantly improved energy gaps versus the VCA, as well as approximate effective masses. The results illuminate the bowing of the Gamma-valley gap and the good agreement with bulk experimental data shows that this method is well suited for nanodevices.