Nonequilibrium effects on the electron-phonon coupling constant in metals
Wuli Miao, Moran Wang
Abstract
Understanding of the energy exchange between electrons and phonons in metals is important for micro- and nanomanufacturing and system design. The electron-phonon ($e\text{\ensuremath{-}}ph$) coupling constant describes such exchange strength, yet its variation remains still unclear at micro- and nanoscale where the nonequilibrium effects are significant. In this work, an $e\text{\ensuremath{-}}ph$ 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 nonequilibrium effects are included in the calculation of the $e\text{\ensuremath{-}}ph$ coupling constant. The coupling model is verified by modeling the ultrafast dynamics in femtosecond pump-probe experiments on a metal surface, which shows consistent results with the full integral treatment of scattering terms. The $e\text{\ensuremath{-}}ph$ coupling constant is strongly reduced due to both the temporal nonequilibrium between different phonon branches and the spatial nonequilibrium of electrons in confined space. The present work will promote not only a fundamental understanding of the $e\text{\ensuremath{-}}ph$ coupling constant but also the theoretical description of coupled electron and phonon transport at micro- and nanoscale.