An approximation to density functional theory for an accurate calculation of band-gaps of semiconductors

TL;DR

This paper introduces a new approximation method based on LDA and self-energy concepts that accurately predicts semiconductor band gaps with computational efficiency comparable to standard LDA.

Contribution

It develops a novel approach that incorporates self-energy corrections into LDA, achieving GW-level accuracy for band gaps without increased computational cost.

Findings

Achieves band gap predictions similar to GW method.

Demonstrates localization of the hole in extended systems.

Requires no more computational effort than standard LDA.

Abstract

The local-density approximation (LDA), together with the half-occupation (transition state) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half-ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half-occupation is equivalent to introducing the hole self-energy (electrostatic and exchange-correlation) into the Schroedinger equation. The argument then becomes simple: the eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the SIC equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self-energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.