  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.
