Resonant hydrogenic impurity states and $1s-{2p}_0$ transitions in coupled double quantum wells

Calculations of the $1s$ and resonant ${2p}_0$ states of a shallow donor in double-quantum-well structures are performed. The variational method is used to calculate the localized part of the impurity states, taking into account the effect of intersubband mixing. The resonance coupling of the ${2p}_0$ state with the first subband is then dealt with using the Green function technique. The results show that for an asymmetric double-quantum-well structure the $1s$ state has a maximum binding energy as the donor is around the center of the wider well while the ${2p}_0$ state has in general a maximum binding energy as the donor is in the narrower well. The resonant coupling of the ${2p}_0$ state is stronger for the structures with a stronger intersubband mixing, where the ${2p}_0$ energy level is closer to the first subband bottom. The resonance-induced broadening of the ${2p}_0$ state can be as large as 6 meV, corresponding to a lifetime of $\sim 0.1$ ps. The resonance in general causes a negligibly small blueshift but can give a redshift of the order of 1 meV when the resonance is strong. A phase transition of the ${2p}_0$ state can occur from the resonant nature to the bound nature by modulation of the interwell coupling. The $1s-{2p}_0$ transition energy is also calculated. The possibility of population inversion between the $1s$ and ${2p}_0$ states is discussed.