An efficient method of DFT/LDA band-gap correction

Abstract

It has been shown that the underestimated by DFT/LDA(GGA) band-gap can be efficiently corrected by an averaging procedure of transition energies over a region close to the direct band-gap transition, which we call the Δ(EIG) method (the differences in the Kohn–Sham eigenvalues). For small excitations the averaging appears to be equivalent to the Δ(SCF) approach (differences in the self-consistent energies), which is a consequence of Janak’s theorem and has been confirmed numerically. The Gaussian distribution in k-space for electronic excitation has been used (occupation numbers in the Δ(SCF) or eigenenergy sampling in the Δ(EIG)). A systematic behavior of the k-space localization parameter σk correcting the band-gap has been observed in numerical experiments. On that basis some sampling schemes for band-gap correction have been proposed and tested in the prediction of the band-gap behavior in InxGa(1−x)N semiconducting alloy, and a very good agreement with independent calculations has been obtained. In the context of the work the issue of electron localization in the r-space has been discussed which, as it has been predicted by Mori-Sánchez et al. [P. Mori-Sánchez, A.J. Cohen, W. Yang, Phys. Rev. Lett. 100 (2008) 146401], should reduce the effect of the convex behavior of the LDA/GGA functionals and improve the band-gap prediction within DFT/LDA(GGA). A scheme for electron localization in r-space has been suggested.