  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.
