Non-equilibrium effects on electron-phonon coupling constant in metals

TL;DR

This paper introduces a new model for electron-phonon coupling in metals that accounts for non-equilibrium effects at micro- and nanoscale, verified by ultrafast experiment simulations, revealing significant reductions in coupling strength.

Contribution

It proposes a relaxation time approximation model for electron-phonon interactions that includes non-equilibrium effects, enhancing the understanding of energy exchange at small scales.

Findings

Non-equilibrium effects significantly reduce the e-ph coupling constant.

The model aligns with ultrafast pump-probe experimental results.

Spatial and temporal non-equilibrium both impact electron-phonon interactions.

Abstract

Understanding of the energy exchange between electrons and phonons in metals is important for micro- and nano-manufacturing and system design. The electron-phonon (e-ph) coupling constant is to describe such exchange strength, yet its variation remains still unclear at micro- and nanoscale where the non-equilibrium effects are significant. In this work, an e-ph coupling model is proposed by transforming the full scattering terms into relaxation time approximation forms in the coupled electron and phonon Boltzmann transport equations. Consequently, the non-equilibrium effects are included in the calculation of e-ph coupling constant. The coupling model is verified by modeling the ultrafast dynamics in femtosecond pump-probe experiments on metal surface, which shows consistent results with the full integral treatment of scattering terms. The e-ph coupling constant is strongly reduced due to both the temporal non-equilibrium between different phonon branches and the spatial non-equilibrium of electrons in confined space. The present work will promote not only a fundamental understanding of the e-ph coupling constant but also the theoretical description of coupled electron and phonon transport at micro- and nanoscale.