Investigation of the optical and magnetic properties of semiconductor heterostructures under external factors

In this thesis, the behavior of an electron in a semiconductor crystal structure is investigated using a potential model that describes its interactions with the atoms and electrons in the lattice through an average field potential. While the interaction between an electron and another electron is typically modeled using the Coulomb potential, in many-body interactions, the deformed Coulomb potential is employed. In this study, the deformed Coulomb potential in the form of an inverse square-root exponential potential is used as the confining potential. This potential provides a smoothly varying continuous structure that aligns with the nature of physical interactions. Furthermore, the inverse square-root exponential potential offers an analytical solution when the angular momentum quantum number is zero, serving as a reference to evaluate the accuracy of the numerical calculations performed. In the first part of this thesis, the bound state energy eigenvalues of a GaAs quantum dot with an inverse square-root exponential potential were calculated by numerically solving the Schrödinger wave equation using the Runge-Kutta method. In the calculations, the electron's effective mass was not taken as constant but was treated as a position-dependent effective mass (PDEM) based on the \textit{E-k} band diagram, justified by physical considerations. Since the exact position-dependent form of the effective mass is unknown, two continuous models with different forms were constructed, and their effects on optical observables were examined. The geometries of the mass models have been observed to play a significant role in the observables. It was found that when the parameters of the position-dependent effective mass models were adjusted to approach the constant mass, the peaks of the optical observables shifted toward the values calculated for the constant mass. External factors such as temperature and hydrostatic pressure have significant effects on the band structures of semiconductors. In the second part of this study, the electron's effective mass, potential depth, and effective electron density in the conduction band were modeled as functions of temperature and hydrostatic pressure. The behavior of an electron in a GaAs semiconductor under the influence of electric and magnetic fields was analyzed by numerically solving the Schrödinger wave equation using the Numerov method. The effects of factors such as temperature, hydrostatic pressure, electric and magnetic fields, and potential parameters on optical observables were comprehensively discussed. In the literature, the dependence of potential depth and conduction band effective electron density on temperature and hydrostatic pressure has not been considered, and this dependence has been examined for the first time in this study. Temperature is one of the most critical parameters when examining the thermodynamic and magnetic observables of a quantum dot. This is because all thermodynamic and magnetic observables are calculated via partition functions, which are derived based on the temperature dependence of bound state energies. In the literature, analytical solutions are available only for the harmonic oscillator and rectangular well potentials, where energy eigenvalues are treated as functions of temperature to determine thermodynamic and magnetic observables. In the third part of this study, the Schrödinger wave equation for a GaAs quantum dot confined by an inverse square root exponential potential under the influence of a magnetic field was solved using the Finite Difference method. Partition functions were calculated over all bound states, and magnetization and magnetic susceptibility were analyzed as functions of temperature and magnetic field, with a focus on their relationship to the effective potential geometry.