All-Electron Exact Exchange Treatment of Semiconductors: Effect of Core-Valence Interaction on Band-Gap and $d$-Band Position

We present the first all-electron full-potential exact exchange (EXX) Kohn-Sham density functional calculations on a range of semiconductors and insulators (Ge, GaAs, CdS, Si, ZnS, C, BN, Ne, Ar, Kr, and Xe). We remove one of the main computational obstacles of such calculations by the use of a highly efficient basis for inversion of the response function. We find that the band gaps are not as close to experiment as those obtained from previous pseudopotential EXX calculations. The locations of $d$ bands, determined using the full-potential EXX method, are in excellent agreement with experiment, irrespective of whether these are core, semicore, or valence states. We conclude that the inclusion of the core-valence interaction is necessary for accurate determination of EXX Kohn-Sham band structures and that EXX alone is not a complete answer to the band-gap problem in semiconductors.

Figure 1

Difference between theoretical KS gaps and experimental fundamental gaps in eV. Full-potential exact exchange (FP-EXX), FP-EXX without core-valence interaction (FP-EXX-ncv), FP-EXX with only spherical exchange (FP-EXX-sph), and LDA (FP-LDA) results are from this work. The PP-EXX results are from Refs. 5, 8, 9. The LMTO-ASA-EXX results are from Ref. 4 and the experimental data are taken from Refs. 22, 23, 24. Note that the LDA gap difference for Ne is $-10.25\mathrm{eV}$ and is off the scale of the plot.

Figure 2

Difference between theoretical $d$-band eigenvalues and experimental data in eV. Full-potential exact exchange (FP-EXX), FP-EXX without core-valence interaction (FP-EXX-ncv), and LDA (FP-LDA) results are from this work. The results obtained using the $GW$ calculation on top of the PP-EXX ground state ($GW$-PP-EXX) are from Ref. 9, and the self-interaction corrected potential within the PP approach (PP-EXX) are from Ref. 12. $GW$ results calculated using a FP-LMTO method ($GW$-FP-LMTO) and Hartree-Fock FP-LMTO (HF-FP-LMTO) are from Ref. 10. The $GW$ calculation on top of the LMTO-ASA-LDA ground state ($GW$-LMTO-ASA) are from Ref. 11.