THEORETICAL STUDY OF UNIAXIAL STRESS, SPATIAL DIELECTRIC FUNCTIONS AND TEMPERATURE DEPENDENCE OF PHOTOIONIZATION CROSS-SECTION OF DONOR IMPURITIES IN A GaAs QUANTUM WELL DOT

Abstract

he present work considers photoionization cross-section of donor impurities in a GaAs quantum well dot of cylindrical geometry. The quantum dot is itself embedded in a Ga Al As 1x x matrix. A trial wave function that can be written as a product of an ‘envelope function’, and a function containing a variational parameter is used to describe the ground state of a donor impurity. For the envelope function, an ordinary Bessel function of the first kind and of order zero was chosen. This envelope function satisfies the boundary condition that the trial wave function vanishes at the surface of the quantum well dot. Using a variational technique within the framework of effective mass approximation, we employed the trial wave function to calculate the total energy of the donor impurity in the ground state. We then minimized the total energy with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized energies were then used to determine the hydrogenic and non-hydrogenic donor binding energies in the ground state. In the non-hydrogenic donor impurity case, we have employed Hermanson’s spatial dielectric function in the Coulomb potential while in the hydrogenic case we have used a dielectric constant in the Coulomb potential. We have used the binding energies we obtained to compute the photoionization crosssection for the transition from the donor impurity ground state to a first conduction sub band in the quantum dot. We have observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the incident photon frequency increases until they become almost constant for high photon frequencies. The photoionization cross-section is much higher for donor impurity located nearest to the center of the quantum dot than for the donor impurity located farther away from the dot vii Copyright by Fredrick Omboga Oketch, 2020 center. We have also studied the effect of Hermanson’s spatial dielectric function, finite and infinite barrier potentials and axial lengths on the photoionization cross-sections of hydrogenic and non-hydrogenic donor impurities in the quantum dot. For the hydrogenic donor impurities, the photoionization cross-sections are larger in the infinite barrier potential region than in the finite potential barrier. Furthermore, for longer quantum well dots, the cross-sections are also larger than they are for the shorter quantum dots. Similar trends are observed in the results obtained in the case of the non-hydrogenic donor impurities, except that in this case, the cross-sections are much smaller than they are for the hydrogenic donor impurities under the same conditions. Additionally, we have studied variation of the photoionization cross-section of a donor impurity with uniaxial applied stress. Here we find that for a particular quantum dot length, the photoionization cross-section decreases with increasing applied uniaxial stress. Finally, we have studied the variation of the photoionization cross-section with temperature and applied uniaxial stress for a donor impurity. The results show that the increment of temperature leads to an enhancement of the cross-section.