  The low temperature electron-phonon (e-ph) relaxation near the surface of
noble metals, Cu and Ag, is studied by using the density-functional theory
approach. The appearance of the surface phonon mode can give rise to a strong
enhancement of the Eliashberg function at low frequency $\omega$. Assuming the
Eliashberg function proportional to the square of $\omega$ in the low frequency
limit, the e-ph relaxation time obtained from the surface calculations is
shorter than that from the bulk calculation. The calculated e-ph relaxation
time for the former is in agreement with a recent experiment for thin films.
