A simplified method for the computation of correlation effects on the band structure of semiconductors

TL;DR

This paper introduces a simplified computational approach to evaluate electron correlation effects on the band structures of semiconductors like diamond and silicon, focusing on relaxation, polarization, and ground state correlation losses.

Contribution

It presents a new simplified scheme combining quasiparticle and self-consistent field calculations to estimate correlation effects on semiconductor band structures.

Findings

Method works in principle for correlation effects

Calculates shifts and bandwidth reductions

Requires further extension for more accurate results

Abstract

We present a simplified computational scheme in order to calculate the effects of electron correlations on the energy bands of diamond and silicon. By adopting a quasiparticle picture we compute first the relaxation and polarization effects around an electron set into a conduction band Wannier orbital. This is done by allowing the valence orbitals to relax within a self-consistent field (SCF) calculation. The diagonal matrix element of the Hamiltonian leads to a shift of the center of gravity of the conduction band while the off-diagonal matrix elements result in a small reduction of the conduction-electron band width. This calculation is supplemented by the computation of the loss of ground state correlations due to the blocked Wannier orbital into which the added electron has been placed. The same procedure applies to the removal of an electron, i.e., to the valence bands. But the latter have been calculated previously in some detail and previous results are used in order to estimate the energy gap in the two materials. The numerical data reported here shows that the methods works, in principle, but that also some extension of the scheme is necessary to obtain fully satisfactory results.