THE VARIATION OF PHOTOIONIZATION CROSS-SECTION WITH INCIDENT PHOTON FREQUENCY AND WITH POSITION OF A DONOR IMPURITY IN A QUANTUM WELL DOT OF SQUARE CROSS-SECTION USING A VARIATIONAL TECHNIQUE

Abstract

In the present work, we carried out a theoretical study of the variation of the photoionization cross-section with the position of a hydrogenic donor impurity along the growth axis of a square GaAs quantum well dot. In our calculation, we used a trial wave function in the effective mass approximation. 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. We employed the trial wave function to calculate the total energy of the hydrogenic 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 total energies were then used to determine the donor binding energies within the quantum well dot. We observed that the binding energy increases with decreasing dot length for constant dot cross-section up to a certain value when it then decreased rapidly towards zero. We used the binding energies obtained to compute the photoionization cross-section of the donor impurity as a function of the incident photon frequency for different positions of the donor impurity. We observed that the photoionization cross-sections rises steeply to their peaks from almost zero value then gradually decrease as the photon frequencies increase 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 hydrogenic donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the hydrogenic donor impurity in the quantum dot and to the incident photon frequency.