A method of measuring the contribution of the image potential energy of the shallow impurity ground state in a quantum well

We show that the binding energy of the shallow impurity (at the center of the quantum well) ground state is strongly reduced by the presence of a metallic mirror at a few effective Bohr radii from the quantum well. For a given depth of the quantum well, we find that the absolute value of the image potential energy without the metallic mirror is equal to that with a fixed metallic mirror while a certain width of the quantum well is met. Hence, it is proposed that the binding energy of the shallow impurity ground state in the quantum well with and without the metallic mirror can be separately measured by the variation of the width of quantum well. The contribution of the image potential energy to the binding energy of the shallow impurity ground state may then be deduced.