Thickness effect on impurity-bound polaronic energy levels in a parabolic quantum dot in magnetic fields

Energy levels of an impurity atom and its binding energy in a quantum dot with or without electron-phonon interactions are obtained by the second-order perturbation theory. The dot is confined laterally by a parabolic potential in quantum-well structures. The energy correction is expressed as a function of the strength of lateral confinement, the applied magnetic field, and the thickness of the quantum dot in question. It is shown that the binding energy depends sensitively on the thickness if it is of the order of the polaron size or less. In the case of thicker quantum dots, the finite thickness reduces the binding energy by approximately 10%.