Corrections to density-functional theory band gaps

An effective exchange-correlation potential for conduction-band states differing from that of the valence-band states is found within an extension of an extreme tight-binding model. Starting from Hedin’s GW formulation of the self-energy, simplifications are made by including only near-neighbor interactions, and by an expansion of band energies carried out around their Brillouin-zone averages. The potential difference is applied as a perturbation to the conduction-band states from a Kohn-Sham calculation with the local-density approximation, and a scissors-type band-gap correction is then obtained in a simple and efficient manner. Although the model is valid for strictly insulating systems, it is found that the correction (when adjusted to reproduce the known silicon and carbon band gaps as in a Slater $X-\alpha$ method) leads to semiconductor band gaps within 0.1–0.3 eV of their experimental values. Both zinc-blende and wurtzite semiconductors of the IV, III-V, and II-VI groups are studied here.