Phonon-mediated sticking of electrons at dielectric surfaces

TL;DR

This paper investigates how electrons temporarily stick to dielectric surfaces via phonon interactions, using a quantum-kinetic model that accounts for multi-phonon processes, revealing small sticking probabilities and a relaxation bottleneck.

Contribution

It introduces a quantum-kinetic approach to analyze phonon-mediated electron trapping, including multi-phonon effects, and distinguishes prompt from kinetic sticking at dielectric surfaces.

Findings

Sticking coefficients are generally very small, around 10^{-3}.

Multi-phonon processes are crucial for accurate modeling when one-phonon transitions are forbidden.

A relaxation bottleneck significantly suppresses the kinetic sticking coefficient.

Abstract

We study phonon-mediated temporary trapping of an electron in polarization-induced external surface states (image states) of a dielectric surface. Our approach is based on a quantum-kinetic equation for the occupancy of the image states. It allows us to distinguish between prompt and kinetic sticking. Because the depth of the image potential is much larger than the Debye energy multi-phonon processes are important. Taking two-phonon processes into account in cases where one-phonon processes yield a vanishing transition probability, as it is applicable, for instance, to graphite, we analyze the adsorption scenario as a function of potential depth and surface temperature and calculate prompt and kinetic sticking coefficients. We find rather small sticking coefficients, at most of the order of $10^{-3}$, and a significant suppression of the kinetic sticking coefficient due to a relaxation bottleneck inhibiting thermalization of the electron with the surface at short timescales.