Electronic Energy Spectra of ZnX (X = O, S, Se, Te) Crystals Obtained by Combining the Green's Function and the Hybrid Functional

We have found that the energies of the Zn semicore 3d electrons in crystals ZnX (X = O, S, Se, Te), in the wurtzite phase, are localized in narrow intervals within the valence band. It was found that the widths of these intervals at Γ point of the first Brillouin zone are equal to 1.24, 0.68, 0.50 and 0.40 eV for ZnO, ZnS, ZnSe and ZnTe crystals, respectively. It was found that the wave functions of the Zn 3d electrons strongly overlap with the states of the valence and the conduction bands. Consequently, the widely used exchange-correlation energy functionals, constructed in the LDA and GGA-PBE approaches, are inappropriate for systems with narrow band of highly correlated 3d electrons. That is why we performed calculations based on the hybrid exchange-correlation energy functional, HSE06, and the obtained eigenenergies and eigefunctions were used in the construction of the Green’s function. Consequently, the basis of this study is based on the two modern concepts of electronic theory of crystals, namely the hybrid exchange-correlation functional and quasiparticle approach. The values of the bandgap, Eg, obtained here in the GGA-PBE approximation, are well-matched to the results found by other authors. The values of Eg, calculated using the combination of Green's function methods and the hybrid functional for the exchange-correlation energy, HSE06, are equal to 2.34, 3.28, 2.35 and 2.13 eV for ZnO, ZnS, ZnSe and ZnTe crystals, respectively, if the mixing factor in the functional is 0.25, that it is the standard. We calculated the electron energy spectra for ZnO, ZnS, ZnSe and ZnTe crystals, with mixing factors, different from the standard ones, namely of 0.40, 0.375, 0.35 and 0.325. The corresponding band gaps have been acquired the values of 3.29, 3.83, 2.81 and 3.43 eV, which are very well matched with the experiment.