Theory of resonant states of hydrogenic impurities in quantum wells

The binding energy and the density-of-states spectrum of resonant impurity states in quantum well structure have been theoretically studied with variation of the impurity position taken into account, using the multisubband model and the resolvent operator technique. Calculations for the ${2p}_0$ resonant state in a $\mathrm{GaAs}-{\mathrm{Al}}_{0.2}{\mathrm{Ga}}_{0.8}\mathrm{As}$ quantum well have been performed. It has been found that there can be a considerable resonant coupling in the ${2p}_0$ state, causing a $\sim 0.1\mathrm{ps}$ capture or escape time of electrons between the ${2p}_0$ localized state and the first subband states. The maximum shift of the impurity energy is in general of the order of 0.1 meV, much smaller than the maximum binding energy of the ${2p}_0$ state.