Energy transfer of excitons between quantum wells separated by a wide barrier

We present a microscopic theory of the excitonic Stokes and anti-Stokes ene rgy-transfer mechanisms between two widely separated unequal quantum wells with a large energy mismatch (Delta) at low temperatures (T). Several impor tant intrinsic energy-transfer mechanisms have been examined, including dip olar coupling, real and virtual photon-exchange coupling, and over-barrier ionization of the excitons via exciton-exciton Auger processes. The transfe r rate is calculated as a function of T and the center-to-center distance d between the wells. The rates depend sensitively on T for plane-wave excito ns. For localized excitons, the rates depend on T only through the T depend ence of the exciton localization radius. For Stokes energy transfer, the do minant energy transfer occurs through a photon-exchange interaction, which enables the excitons from the higher-energy wells to decay into free electr ons and holes in the lower:energy wells. The rate has a slow dependence on d, yielding reasonable agreement with recent data from GaAs/AlxGa1-xAs quan tum wells. The dipolar rate is about an order of magnitude smaller for larg e d (e.g., d= 175 Angstrom) with a stronger range dependence proportional t o d(-4). However, the latter can be comparable to the radiative rate for sm all d (e.g., d less than or equal to 80 Angstrom). For anti-Stokes transfer through exchange-type (e.g., dipolar and photon-exchange) interactions, we show that thermal activation proportional to exp(-Delta /k(B) T) is essent ial for the transfer, contradicting a recent nonactivated result based on t he Forster-Dexter's spectral-overlap theory. Phonon-assisted transfer yield s a negligibly small rate. On the other hand, energy transfer through over- barrier ionization of excitons via Auger processes yields a significantly l arger nonactivated rate which is independent of d. The result is compared w ith recent data.