3rd TAGRA

In recent decades, the rapid development of nanoscience and nanotechnology has significantly increased interest in the fundamental and applied properties of semiconductor nanostructures. In low-dimensional systems such as quantum wells, quantum wires, quantum dots, and other nanostructures with characteristic dimensions comparable to the electron de Broglie wavelength or the exciton Bohr radius, the phenomenon of quantum confinement arises, in contrast to bulk semiconductor materials. Quantum confinement leads to the reconstruction of the electronic density of states, alteration of charge-carrier transport properties, and reorganization of optical transitions.

The objective of this work is to analyze, within a unified physical framework, the influence of quantum confinement on the energy spectrum and the electronic density of states in semiconductor nanostructures of different dimensionalities, to identify the limitations of existing theoretical models, and to establish the conceptual foundation for the development of a generalized theoretical model capable of providing a continuous description of energy spectrum transformation in semiconductor nanostructures.

The mathematical form of the density of states (DOS) depends on the dimensionality of the system, the nature of its energy spectrum, and the spatial localization of the electron wave functions. In three-dimensional bulk crystals, the density of states follows a square-root dependence on energy. In two-dimensional systems, it exhibits a step-like behavior, whereas in one-dimensional structures, Van Hove singularities emerge. In zero-dimensional quantum dots, the complete discretization of the energy spectrum results in a density of states determined by discrete quantum energy levels.
From this perspective, the investigation of the electronic density of states extends far beyond the calculation of discrete energy levels. The principal objective is to determine how quantum confinement transforms the energy spectrum, how this transformation modifies the analytical structure of the density of states, and how these changes are manifested in the macroscopic transport and optical properties of semiconductor nanostructures.