Dielectric response to a donor ion in a Ga1−xAlxAs-GaAs-Ga1−xAlxAs quantum well of infinite depth

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Abstract
We consider the dielectric response to a donor ion in a GaAs quantum well of infinite depth in two cases: (1) The ion is placed at the center of the well; (2) the ion is placed into off-center positions in the well. In each of these cases we calculate the binding energy of the donor atom as a function of the width of the well and compare our values with those arising from Bastard’s theory, where the donor atom is considered as a hydrogenic impurity. We find that consideration of the dielectric response of the GaAs quantum well leads to important deviations with respect to Bastard’s hydrogenic theory. Specifically, we find that, in case (1), our binding energies at different well widths are larger in magnitude than those calculated from Bastard’s theory. We also find that the discrepancy between the two sets of binding energies is a function of the width of the well, becoming less pronounced as the width of the well is increased. We further find that, in case (2), as the donor atom is moved from the center of the well toward the wall of the well, our binding energies at different well widths rise toward those calculated from Bastard’s theory and practically merge with them at a certain impurity position. We analyze our findings, and conclude that the dielectric response in a narrow GaAs quantum well is an important factor in the theory of impurity states in the well.