Relaxation between electrons and surface phonons in nanoscale metal films

The Two Temperature model of M I Kaganov, I M Lifshitz and L V Tanatarov (Sov. Phys. JETP 4, 173 (1957)) about relaxation between electrons and bulk phonons is extended to the case of surface phonons. The state of electrons and phonons is described by equilibrium Fermi and Bose functions with different temperatures. The new feature added is the geometric constraint of surface phonons. We obtain expressions for the energy transfer rate from degenerate hot electrons to surface-phonons, which is order of magnitude less than that for the bulk.