Band alignments through quasiparticle self-consistent 𝐺𝑊 with efficient vertex corrections

Within many-body perturbation theory, we calculate band offsets for a set of epitaxial interfaces, including AlP/GaP, AlAs/GaAs, Ge/AlAs, Ge/GaAs, Ge/ZnSe, Si/GaP, ZnSe/GaAs, and CaF2/Si. We consider various quasiparticle self-consistent 𝐺⁡𝑊 schemes with or without including vertex functions. In particular, we consider two types of effective vertex functions complying with the Ward identity in the long range, one of which additionally carries a short-range part, which has been found to improve ionization potentials. The obtained band offsets correspond to model interface structures that match the experimental lattice parameters of the bulk components. Strain, zero-phonon renormalization, and spin-orbit coupling effects are properly accounted for. For the band offsets of the semiconductor-semiconductor interfaces, all the self-consistent 𝐺⁡𝑊 schemes yield similar mean absolute errors on the order of 0.2 eV. In the case of the CaF2/Si interface, the calculated band offsets show large indetermination spanning an interval up to 1 eV, the discrepancy with respect to experiment being correlated with the error by which the band gap of the insulator is described. Through 𝐺⁡𝑊 calculations for selected interface models, we further assess the effect of self-consistently updating the charge density. Our result support the practice of relying on semilocal or hybrid-functional schemes for determining the line-up potential.