Impurity levels, impurity bands, excited impurity bands, and band tails: The electronic density of states in quantum wells and heterostructures

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Abstract
We have investigated in quantum wells (QW’s) and heterostructures (HS’s) the modification of the electronic structure near the band edge, which is induced by selective doping. The density of states has been calculated as a function of the relevant parameters, namely, carrier and impurity concentrations (and depletion concentrations for HS’s), QW width, and impurity position. Using a multiple-scattering method which includes a finite-range screened potential and impurity concentration to all orders, we have succeeded in obtaining ground-state and excited-state impurity bands (IB’s). We observed these bands merging gradually with the lowest conduction subband as the impurity concentration is increased, leading to the formation of a band tail into the energy gap. Other main results obtained for different values of the parameters are the binding energy for a single impurity, the widths and energy shifts of ground- and excited-state IB’s, and the contribution of the electron-impurity interaction to the gap shrinkage in the band-tail regime. Our results are compared with experiments and other theories.