Optical transitions and photoluminescence in cylindrical core/layer/shell $\beta$-CdS/$\beta$-HgS/$\beta$-CdS heterostructure

In the effective mass approximation, within the framework of a simple two-band model, the states of charge carriers in the HgS quantizing layer of the cylindrical core/shell/shell $\beta$-CdS/$\beta$-HgS/$\beta$-CdS heterostructure are theoretically considered. The consideration was carried out for various intervals of geometric dimensions of sample, when the corresponding regimes of size quantization for charge carriers were realized in the layer. For each case, the electrostatic interaction between the electron and the hole is taken into account with its own specifics, and depending on the size of the sample, the corresponding values of the ground state energy of the pair are obtained. In each case, interband optical transitions in the sample and photoluminescence were also considered. It is shown that, in each individual case, taking into account the electrostatic interaction leads to a shift in the threshold frequency of interband absorption and luminescence to the short-wavelength region, and the frequency itself is determined by the geometric dimensions of the sample.