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.

Carrier capture in InGaN/GaN quantum wells: Role of electron-electron scattering

“…(3) that we obtained following a long but straightforward procedure. Instead, considering the phonon emission, the method was already outlined by one of the authors in a previous work 36 and applied to III-V compounds. The formulation presented in Ref.…”

Dielectric Function of a Quantum-Confined Thin Film with a Modified Pöschel–Teller Potential

“…It is known that, in the two-dimensional geometry, the screening results in an essentially different spatial dependence of the dielectric function, as compared with that obtained in the three-dimensional case. If the interaction between particles is considered, the screening of the electric field created by charges in those structures has to be taken into account correctly [10][11][12].…”

“…is the modified Pöschel-Teller potential confining the electron motion. The energy spectrum and the oneelectron normalized wave functions for the charge carriers were obtained in works [10][11][12][13]:…”

Phonon-assisted intersubband transitions in wurtzite GaN/InxGa1−xN quantum wells

“…The scattering rates were also investigated using Green's function formalism by considering the influence of twodimensional electron gas (2DEG). [16,17] However, the leading-order electron self-energy was obtained under the bulk-phonon approximation.…”