We discuss the heating of electrons by a steady-state electric field i
n an unbounded thin metal film by considering the energy flow from the
electron system to the acoustic modes of the film. Using the dispersi
on relationships and the resulting density of states for the acoustic
modes calculated from a non-Debye model, and a deformation potential c
oupling between the electrons and the acoustic modes, it is shown that
the relationship between the electric field and the electron temperat
ure is dependent on the coupling between acoustic modes at the surface
of the film. At low excitation we show the energy relaxation is domin
ated by the antisymmetric Rayleigh mode.