Impurity cyclotron resonance lines of barrier donor electrons in quantum wells

We have investigated by numerical simulation the zero-temperature line broadening of the cyclotron resonance transitions of a dilute system of randomly situated barrier donors, with centers consisting of positive donor ions fixed in the barrier region of a quantum well to which are bound electrons in the adjacent well. Inhomogeneous line shapes due to interdonor Coulomb interactions are obtained. Discussion is restricted to the case in which magnetic fields are sufficiently high that the electrons can be treated semiclassically (exchange can be neglected). The simulations indicate that a monolayer of donor ions produces a single highly asymmetric and relatively broad line, with the excitation induced by each absorbed photon being shared among a number of donors. However, if the same donor ions are distributed among several monolayers the absorption predicted is a finely spaced comb of well-resolved relatively narrow transition lines, each line deriving from a different monolayer. In this case the excitation induced by an individual absorbed photon is more localized. Parameters chosen for the simulation are realistic for ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells.