Nonlocal-density-functional approximation for exchange and correlation in semiconductors

Abstract

Using the weighted density approximation for the exchange-correlation energy, the band-structure and bulk structural properties of the prototypical semiconductors Si and Ge have been systematically studied. The weighted density approximation is based on an improved description of the exchange-correlation hole that explicitly accounts for the inhomogeneous charge density found in real materials. We find that the approximation as proposed is inadequate for the case of semiconductors where charge inhomogeneity is intimately connected to a gap in the excitation spectrum with consequent qualitative changes in screening. We use a simple extension of the weighted density approximation which takes account of semiconductor screening. With this functional, we find substantial improvement in the calculated minimum gap over the results of the usual local-density approximation as compared to experiment. However, the direct gaps are not significantly improved. Calculated structural properties are, moreover, found to be in excellent agreement with experiment. By way of contrast, the weighted density approximation implemented with metallic screening gives a smaller change in the band structure and more importantly, substantially poorer calculated structural properties. A discussion of the qualitative differences between the weighted density approximation and the usual local-density approximation for covalently bonded semiconductors is presented.