First-principles calculation of the electronic structure of the wurtzite semiconductors ZnO and ZnS

We report ab initio calculations of the lattice constants and the electronic band structure of the hexagonal wurtzite-structure semiconductors ZnO and ZnS. We employ the local-density approximation and solve the Kohn-Sham equations for nonlocal, separable, and norm-conserving pseudopotentials self-consistently. We use basis sets of localized Gaussian orbitals with s, p, d, and ${\mathit{s}}^{\mathrm{*}}$ symmetry. In particular, we investigate the influence of the Zn 3d electrons on the results for the lattice constants and the band structure. Results of calculations employing both ${\mathrm{Zn}}^{2+}$ and ${\mathrm{Zn}}^{12+}$ ionic pseudopotentials are presented and discussed. For ZnS, both the cubic zinc blende and the hexagonal wurtzite polytype have been studied. The calculated lattice constants are found to be in excellent agreement with experiment for both semiconductors when the d electrons are explicitly taken into account as valence electrons. The agreement of the calculated bands of ZnS with experimental data and with the results of a plane-wave calculation from the literature using about 6.000 plane waves for the cubic crystal is very good except for the absolute energy position of the d bands. For ZnO the calculated bands agree better with angle-resolved photoemission data when the ${\mathrm{Zn}}^{12+}$ pseudopotential is employed. The agreement, however, is still far from satisfactory and the calculated absolute position of the d bands is off, again. The discrepancies seem to be related to correlation effects in the narrow d bands. We find the Zn 3d electrons to strongly interact with the O 2p electrons in ZnO. According to our results, the p-d mixing in ZnO is about twice as large as in ZnS.