Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section

Abstract

In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.

Impact of overlapping vibrational wave functions on the spectra of the photoionization cross section

“…Winnie Otieno et al showed that the cross section of photoionization in quantum wells is sensitive to the location of the impurity and the frequency of the incident photons [6]. In particular, Zorkani et al [7] studied the computation of the cross section of photoionization taking into account the carrier interaction load -phonon as well as the central correction by means of an analytical potential of impurity proposed by Munnix et al [8] in the case of gallium arsenide doped with manganese.…”