To the Theory of Dimensional Quantization in Narrow-Gap Crystals

This article discusses studies of size quantization phenomena in zero-, one-, and two-dimensional semiconductor structures. The main attention is paid to the mechanisms of photon-kinetic effects in these structures. Despite many studies of the physical properties of low-dimensional systems of current carriers, the size quantization of energy spectra in narrow-gap semiconductors and the associated photonic-kinetic effects are still insufficiently studied. Therefore, this study focuses on the quantum mechanical study of size quantization in certain cases using Kane's multiband model. The insolvability of the 8×8 matrix Schrödinger equation in the Kane model for a potential well of arbitrary shape is analyzed. The dependence of the energy spectrum on the two-dimensional wave vector is studied for various cases. In particular, the energy spectra for InSb and GaAs semiconductors are considered, depending on the band parameters and the size of the potential well. Conclusions are presented on the analysis of various cases of size quantization in narrow-gap crystals with cubic or tetrahedral symmetry in the three-band approximation. It is shown that the energy spectrum corresponds to a set of size-quantized levels that depend on the Rabi parameter, band gap, and well size. The size-quantized energy spectra of electrons and holes in InSb and GaAs semiconductors are analyzed in a multiband model.