Impurity scattering in resonant tunneling

Abstract

When an electron is sent perpendicularly to a stack of flat layers, S-B-S-B-S (S: semiconductor, B: potential barrier, high and thick), they tunnel through the two barriers, normally with only a small probability. However, when the electron wavelength fits nicely in between the two barriers the transmission probabilty becomes 1, which is the resonant tunneling. We ask: how is the resonance affected if there are some scatterers in the space between the two barriers? Perturbation theory is useless here, because the probability amplitude in that space, and therefore at the scatterers, is particularly large at resonances. We consider the case of impurity scattering, and make use of the fact that the scattering potentials have ranges much shorter than the electron wavelength, to solve the problem almost exactly by constructing the Green function for the Schrödinger equation incorporating the two potential barriers. The resonance wave number nor the width is affected when there is only one impurity, probably the same if the impurities are finite in number. It is found that the scattered wave resonates after the scattering, and not before.