Hydrogenic impurity states in a quantum well: A simple model

A variational calculation of hydrogenic impurity states in a quantum well has been performed. The binding energy of donor (acceptor) levels is calculated as a function of layer thickness and of the impurity position. It is found that the ground impurity state degeneracy with respect to the impurity position is lifted, leading to the formation of some sort of an "impurity band." The density of states of this impurity band exhibits one or two peaks energetically located at the "band" extrema. This one-dimensional feature can be evidenced in the optical absorption associated with valence subband\ensuremath{\rightarrow}donor transitions, whereas acceptor\ensuremath{\rightarrow}conduction processes are almost featureless. In the case of conduction\ensuremath{\rightarrow}acceptor luminescence a smooth curve is obtained for degenerate electronic distribution, whereas nondegenerate electron\ensuremath{\rightarrow}trapped hole recombination spectra should again exhibit a double peak.