Practical formulations of the electron capture rate in quantum wells by phonon emission at low carrier density

Abstract

In this article the Green’s functions formalism is exploited to describe the coupled phonon-plasmon system in the plasmon pole approximation for the longitudinal dielectric constant, for two-dimensional quantum wells. Electron capture time in quantum wells is obtained in a closed form, separating contributions coming from different two-dimensional plasmon modes. Moreover, useful criteria are pointed out, in order to decide under which conditions a simpler description in the static limit of the plasmon pole approximation may be enough accurate. In the limit of low carrier density, an analytical expression for the capture rate by LO-phonon emission has been given, in the two-dimensional static limit of the longitudinal dielectric constant. By means of this analytic description, effects of screening, Fermi filling, and electrons momentum distribution at finite temperature on capture time may be separately investigated in detail.