Accurate and efficient band-offset calculations from density functional theory

Abstract

We perform a systematic study of the factors that determine the accuracy of heterostructure band alignments in density functional calculations. Band alignments are calculated for a number of representative test structures using either the generalized gradient approximation (GGA) or the more accurate hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE). The alignment of the bulk band structures is achieved through a potential-alignment term from an explicit superlattice calculation, with full inclusion of atomic relaxations. The potential alignments calculated within the GGA are in agreement with those calculated using HSE to within 50 meV, despite the GGA calculations being 10–100 times less computationally expensive. The GGA potential alignments are remarkably accurate, even for heterostructures between materials with a large lattice mismatch, and even when the GGA lattice parameters are markedly different from HSE. We also find that the errors in the potential alignment are small even when the optimum HSE mixing parameter (α) (to bring the band gap in agreement with experiment) is markedly different for the two materials at the interface; the error associated with using a fixed α for a superlattice calculation is small. To obtain band offsets, the potential-alignment values are combined with bulk band structure calculations. GGA exhibits large errors in the positioning of the eigenvalues at the band extrema with respect to the average electrostatic potential, and the resulting all-GGA band alignments are unreliable. HSE produces much more accurate band structures than GGA. Given the accuracy of potential alignments calculated within the GGA, they can be combined with HSE calculations of the bulk electronic band structure to achieve accurate band alignments with a high computational efficiency.