Quantum well electron scattering rates through longitudinal optic-phonon dynamical screened interaction: An analytic approach.

A quantum model is developed to obtain electron capture and hot electron intraband relaxation times in a quantum well, for electron-longitudinal optic (LO) phonon scattering. In particular, we have investigated the effect of carrier density and electron energy, obtaining semi-analytic expressions as function of carrier density, a topic often neglected in literature, despite its fundamental interest in semiconductor physics. We demonstrated that the usual approximation of constant scattering time in modeling applications is often not adequate, because these parameters vary considerably with the injected or photogenerated carrier density. Furthermore we show that the scattering through the emission of pure LO-phonons is not a good approximation when the population increases, whereas the interplay between LO-phonon and collective plasma modes must be considered. We obtained novel semi-analytic expressions in the single plasmon pole dynamical form of the random phase approximation, without making use of the more usual static limit of it.