Analytical treatment of band-gap underestimates in the local-density approximation

Abstract

Corrections to band gaps calculated within the density-functional local-density approximation are obtained as self-energy differences, computed according to the GW approximation. Local-field and dynamical screening effects are neglected. The use of a model dielectric function and of simple tight-binding wave functions leads to an analytic formula for the gap correction valid for semiconductors and insulators crystallizing in the diamond and zinc-blende structures. The results obtained for many materials are in very good agreement with experiment.