Effective carrier interaction in semiconductor thin films: A model-independent formula

It is shown that the effective carrier interaction in semiconductor thin films, which is essentially of a non-Coulomb type, depends on the layer thickness but it is not sensitive to the form of quantum well. As a consequence the analytical expression for the effective 2D interaction potential, obtained using the parabolic quantum well model, can be used as a general (model-independent) formula. As an example, we have considered the electrons localized in a quantum dot. It is demonstrated that, when the quantum well confinement is much stronger than the lateral one, the results obtained using the 2D approach with the effective potential are in a good agreement with the full 3D calculations.