Bandura H. Electronic and hole states of noninteracting quantum dots and their ordered arrays.

Bandura H. Ya. Electronic and hole states of noninteracting quantum dots and their ordered arrays. Qualification thesis (manuscript). Dissertation for the degree of Doctor of Philosophy (Candidate of Physical and Mathematical Sciences) in specialty 105 “Applied Physics and Nanomaterials” – Drohobych Ivan Franko State Pedagogical University, Ministry of Education and Science of Ukraine, Drohobych, 2025. The dissertation presents theoretical studies of the electronic and hole states in isolated quantum dots (QDs) and various ordered arrays of quantum dots. The research was carried out for spherical and cubic QDs within the multiband effective mass theory, using the framework of the continuum elastic and dielectric media theories. The obtained results are significant for improving the theoretical understanding of electronic and hole states in isolated quantum dots, particularly in the presence of impurities and external electric fields. The outcomes can also be used for theoretical and practical prediction of the electrical and optical properties of ordered QD arrays with different types of spatial ordering. Chapter 1. sources literature concerning ordered quantum dot arrays, methods of their experimental fabrication and theoretical analysis, and their physical properties are analyzed. It was found that hole states in QDs within a multiband effective mass model that simultaneously accounts for deformation of the QD–matrix system and interface polarization remain insufficiently studied. Chapter 2 describes hole states in an isolated spherical QD embedded in a matrix within the multiband effective mass theory framework using the spherical Baldereschi–Lipari approximation. Models based on the 6×6 Hamiltonian and a reduced 4×4 Hamiltonian were considered. The effects of strain and interfacial polarization at the QD–matrix boundary were taken into account. The results agree with known theoretical results in limiting cases. Chapter 3 investigates the combined effect of a hydrogen-like acceptor impurity and an external electric field on the hole energy spectrum. It was shown that displacement of the impurity along the direction of the electric field enhances the energy splitting of the hole states, while displacement in the opposite direction reduces it. A critical electric field was found at which the spherical symmetry of the hole density distribution is restored. Chapter 4 employs the single-band effective mass model for electrons and holes to study one-, two-, and three-dimensional ordered arrays (superlattices) of identical spherical and cubic QDs. The electron and hole energies were compared for spherical and cubic superlattices, and energies at the symmetry points of the Brillouin minibands were determined. When comparing minibands of cubic and spherical QDs of equal volume, it was found that cubic-dot arrays exhibit larger miniband widths than spherical-dot arrays for any QD volume. Chapter 5 considers ordered QD superlattices with two different QDs in the primitive cell. A theory of the miniband spectrum of such superlattices was developed within the single-band effective mass approximation using rectangular well and barrier models and the tight-binding method with nearest-neighbor approximation. This theory enabled the calculation of dispersion relations and miniband widths. It was also shown that upper minibands are always wider than lower ones. The developed theoretical models enable comprehensive analysis of how various physical factors—such as QD size, material, polarization, strain, impurities, and external fields—affect charge-carrier spectra in QDs and superlattices. The approaches based on multiband effective mass theory (4×4, 6×6) can be applied for accurate modeling of hole states in realistic nanostructures. Their demonstrated reducibility to the single-band model allows one to select the appropriate model depending on the desired accuracy. The identified compensation effects of polarization and strain are valuable for designing structures with minimized unwanted interactions, making the developed theory a useful tool for calculations in photonics, optoelectronics, and quantum technologies. The obtained miniband spectra and dispersion relations allow prediction of the optical absorption properties and tunneling behavior of materials. The proposed theory can be extended to more complex geometries and multi-component primitive cells, enabling modeling of novel types of QD superlattices. The derived dependencies of miniband widths and splitting conditions can be used to optimize nanocomposite structures with desired properties. Altogether, these results form a theoretical foundation for practical applications in modern nanoelectronic devices, quantum sensors, and memory elements. Keywords: electronic and hole states, energy spectrum, deformation and polarization, quantum dot arrays, acceptor impurity, electric field.