Effect of the Spin-orbit Interaction on the Electronic Band Energies in Cadmium Chalcogenides Evaluated within the HSE06-GW Approach

The electronic energy band spectra of CdX crystals (X = O, S, Se, Te) in the wurtzite phase have been calculated. We have revealed that Cd 4d electrons are localized in the narrow energy intervals of the valence band. The results obtained here show that the exchange-correlation functionals developed within the LDA and GGA approaches are not applicable to the strongly correlated 4d electron subsystem. Indeed, the band gap found for the CdO crystal in these approaches is E_g = 0, and its values for CdS, CdSe, and CdTe materials are 1.48, 0.67, and 0.84 eV, respectively. They all are much smaller than the measured E_g for CdX materials, which are 0.91, 2.5, 1.8 and 1.8 eV, respectively. We found that “GGA – Green’s function” calculation scheme, which is very effective for s-p electron systems, did not produce successful results for CdX crystals. That is why we have chosen a combination of “hybrid functional – Green’s function” approach. The E_g values found in CdX crystals without spin-orbit interaction are 0.90, 2.49, 1.92 and 2.10 eV, respectively. The spin-orbit interaction causes a negligible narrowing dE_SO of the E_g parameter in CdO and CdS crystals. However, in CdSe and CdTe materials, the narrowing parameter dE_SO values are 0.12 and 0.27 eV, respectively. Corrected by dE_SO band gaps of CdSe and CdTe crystals have the values of 1.80 and 1.83 eV, respectively. The E_g values found here are well compared with the experiment. It is found that the energy bands of the semicore Cd 4d electrons obtained without spin-orbit interaction overlap in CdX crystals. Spin-orbit interaction leads to a widening of Cd 4d energy bands. Moreover, in CdSe and CdTe crystals, the spin-orbit interaction leads to a clear separation of 4d electron energy bands into two parts, the lower of which contains 8 and the upper 12 branches of the spectrum.