Self-interaction corrections in semiconductors

We propose a scheme to generate pseudopotentials from strictly self-consistent self-interaction-corrected local-density-approximation (SIC-LDA) calculations, that are firmly rooted within density-functional theory, and use them in a standard LDA calculation of the structural properties and the eigenvalue spectrum in crystalline Si, Ge, Sn, and GaAs. Thus we avoid the serious shortcomings of LDA in small atoms and nevertheless use consistently the same method in both atoms and solids, since LDA and SIC-LDA coincide for the completely delocalized valence electrons of these materials. We show that significant effects arise from an improved description of the core. In particular, Ge, which appears to be a metal with band overlap at the {Γ} point of the Brillouin zone in LDA, can be correctly described as an indirect-gap semiconductor. Still, it is argued that fully self-consistent self-interaction corrections can only eliminate a small part of the gap problem in sp-bonded semiconductors.