A Study of the Effect of Hermanson’s Spatial Dielectric Function on the Photoionization Cross-Section of a Hydrogenic and a non-Hydrogenic Donor Impurity in a GaAs Quantum Dot of Cylindrical Geometry in the Region of Finite and Infinite Barrier Potentials

Abstract

In this work, we have 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 a GaAs quantum dot of cylindrical geometry. In the nonhydrogenic 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. This studyhas been carried out for a range of incident photon frequencies. Our results show that, for the hydrogenic donor impurities, the photoionization cross-sections are larger in the infinite barrier potential region than in the finite potential barrier one. We also observe that the cross-sections rise from some minima at some low frequencies and reach maxima at a small cluster of close frequencies after which they fall off gradually and eventually merge at higher frequencies. Furthermore, for longer (larger) quantum well dots, the cross-sections are also larger than they are for the smaller 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.