Calculation of capture of carriers by quantum wells

We calculate the probability that a carrier incident on a quantum well at low temperature is captured with emission of a longitudinal-optical phonon. Our method makes use of the one-phonon self-energy of the carrier, and includes some (though not all) contributions from every order in the carrier--phonon coupling constant. Such an approach is needed because straightforward application of Fermi's golden rule can predict capture probabilities greater than unity. We show that for wide quantum wells our self-energy calculation can be replaced by the much simpler one of scattering by a constant, complex-valued potential. Inside a quantum well the carrier's wave function is attenuated over a distance comparable with the mean free path, so that resonances in the scattering properties of the well are eventually suppressed.