Nonparabolicity effects on electron–optical-phonon scattering rates in quantum wells

Abstract

The scattering rates for intrasubband and intersubband transitions due to electron--optical-phonon interaction are calculated for ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}\ensuremath{-}\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wells taking into account the conduction subband nonparabolicity. For the description of the confined- and interface-phonon modes we use a dielectric continuum model and the nonparabolic conduction-subband energy is introduced as a second order expansion of ${k}^{2}$, the square of the electron wave vector. Our results show that for transitions due to the emission of confined phonons the scattering rates are significantly increased, while for interface phonons the scattering rates are decreased. In particular, we show that for high kinetic energies electrons will relax at an almost constant rates for quantum wells larger than 120 \AA{}. We show that our results can be understood in terms of the phonon wave vector (or Fr\"ohlich electron-phonon coupling), the density of final states, and the electron-phonon overlap.