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

Authors S.V. Syrotyuk , O.P. Malyk

Lviv Polytechnic National University, 12, S. Bandera St., 79013 Lviv, Ukraine

Е-mail svsnpe@gmail.com
Issue Volume 13, Year 2021, Number 4
Dates Received 19 March 2021; revised manuscript received 14 August 2021; published online 20 August 2021
Citation S.V. Syrotyuk, O.P. Malyk, J. Nano- Electron. Phys. 13 No 4, 04003 (2021)
DOI https://doi.org/10.21272/jnep.13(4).04003
PACS Number(s) 71.15.Mb, 71.20. ± b, 71.27. + a
Keywords CdX, Wurtzite phase, HSE06 (2) , GW (5) , Spin-orbit interaction.

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 Eg = 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 Eg 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 Eg 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 dESO of the Eg parameter in CdO and CdS crystals. However, in CdSe and CdTe materials, the narrowing parameter dESO values are 0.12 and 0.27 eV, respectively. Corrected by dESO band gaps of CdSe and CdTe crystals have the values of 1.80 and 1.83 eV, respectively. The Eg 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.

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