All-electron Exact Exchange Treatment of Semiconductors: Effect of Core-valence Interaction on Band-gap and $d$-band Position

TL;DR

This study uses all-electron exact exchange calculations to analyze semiconductors, revealing the importance of core-valence interactions for accurate band structure predictions, especially for $d$-band positions.

Contribution

It demonstrates that including core-valence interactions in all-electron EXX calculations improves the accuracy of $d$-band positions and highlights limitations of pseudopotential methods.

Findings

Full-potential EXX band-gaps are less accurate than pseudopotential results.

$d$-band positions agree well with experiment when core-valence interactions are included.

Pseudopotential calculations may lack accuracy for $d$-band energies.

Abstract

Exact exchange (EXX) Kohn-Sham calculations within an all-electron full-potential method are performed on a range of semiconductors and insulators (Ge, GaAs, CdS, Si, ZnS, C, BN, Ne, Ar, Kr and Xe). We find that the band-gaps are not as close to experiment as those obtained from previous pseudopotential EXX calculations. Full-potential band-gaps are also not significantly better for $sp$ semiconductors than for insulators, as had been found for pseudopotentials. The locations of $d$-band states, determined using the full-potential EXX method, are in excellent agreement with experiment, irrespective of whether these states are core, semi-core or valence. We conclude that the inclusion of the core-valence interaction is necessary for accurate determination of EXX Kohn-Sham band structures, indicating a possible deficiency in pseudopotential calculations.