A theoretical study of the effects of Thomas–Fermi and Hermanson’s dielectric functions and temperature on photoionization cross-section of a donor impurity in GaAs quantum dots of circular and rectangular cross-sections

We have carried out a comparative theoretical study of the effects of Thomas–Fermi and Hermanson’s spatial dielectric functions and temperature gradients on the photoionization cross-section of a donor impurity in GaAs quantum dots of cylindrical and of rectangular cross-sections. We have assumed an infinite barrier potential that confines the donor impurity within the quantum dots. The calculation of the photoionization cross-section has been carried out for a dielectric constant and two different spatial dielectric functions. This was carried out for constant temperature, axial length, and volume of the quantum dots and then for constant axial length and volume of the quantum dots but at different temperatures. Our results show that the photoionization cross-sections of the rectangular quantum dot are much smaller than those of the cylindrical quantum dot and they also peak at much lower frequencies compared to the latter for the same physical conditions. Additionally, the photoionization cross-sections increase with increasing temperature for both geometrical shapes of the quantum dots, but, again, the donor photoionization cross-sections of the cylindrical quantum dot are much larger over the range of temperatures considered in our study. Furthermore, Hermanson’s and Thomas–Fermi dielectric functions suppress the cross-sections with the former having a more pronounced effect than the latter.