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

摘要

In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and theaxial position of ahydrogenicdonor impurity in GaAsquantum well dot of square cross-sectionis carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential wellis 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 isobserved 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 hydrogenicdonor 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.