Resonant states induced by impurities in heterostructures

A study of the formation of resonant states in the conduction band, induced by impurities outside heterostructure quantum wells, is presented. We derive general expressions for the capture and scattering amplitudes, the resonance position and width, and we also calculate the effect on the energy spectrum and the density of states in the quantum well. The theory is applied to two typical impurity potentials, the zero-range potential of deep levels and the Coulomb potential. It is found that the perturbation of the density of states can be significant over wide energy intervals, and that the resonance position may behave nonmonotonically with the modulation-doping distance. The resonance width decays exponentially with the distance, but becomes of the same order as the band discontinuity as we approach close to the quantum well interface. The capture and scattering coefficients may vary by several orders of magnitude over narrow energy intervals, producing a pronounced and strong scattering mechanism.