Electron-phonon bound states and impurity band formation in quantum wells

TL;DR

This paper investigates how local Einstein phonons influence electron transmission in quantum wells, revealing impurity band formation and phonon sidebands, with an effective theory for small electron-phonon coupling and implications for current-voltage behavior.

Contribution

It introduces a generalized propagation matrix method to analyze phonon effects on resonant transmission and develops an effective theory for phonon sidebands in quantum wells.

Findings

Formation of low-energy impurity bands at high phonon channels

Dependence of satellite resonances on phonon scattering channels

Accurate description of phonon sidebands for small electron-phonon coupling

Abstract

A generalized propagation matrix method is used to study how scattering off local Einstein phonons affects resonant electron transmission through quantum wells. In particular, the parity and the number of the phonon mediated satellite resonances are found to depend on the available scattering channels. For a large number of phonon channels, the formation of low-energy impurity bands is observed. Furthermore, an effective theory is developed which accurately describes the phonon generated sidebands for sufficiently small electron-phonon coupling. Finally, the current-voltage characteristics caused by phonon assisted transmission satellites are discussed for a specific double barrier geometry.