We report a theoretical study of the carrier relaxation in a quantum cascadelaser (QCL) subjected to a strong magnetic field. Both the alloy (GaInAs)disorder effects and the Frohlich interaction are taken into account when theelectron energy differences are tuned to the longitudinal optical (LO) phononenergy. In the weak electron-phonon coupling regime, a Fermi's golden rulecomputation of LO phonon scattering rates shows a very fast non-radiativerelaxation channel for the alloy broadened Landau levels (LL's). In the strongelectron-phonon coupling regime, we use a magneto-polaron formalism and computethe electron survival probabilities in the upper LL's with including increasingnumbers of LO phonon modes for a large number of alloy disorder configurations.Our results predict a nonexponential decay of the upper level population onceelectrons are injected in this state.
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