Temporal evolution of the longitudinal- and transverse-phonon distributions in nonequilibrium metal films

We discuss the evolution of the nonequilibrium longitudinal- and transverse-phonon energy-density distributions in a thin metal film resulting from electron heating by the onset of an electric field. For a gold film on a sapphire substrate, we show that the ratio of the energy-density distributions for the T₁ and T₂ modes generated by longitudinal-phonon decay varies with time. The steady-state ratio is found to be a function of wave-vector magnitude; at high wave vectors it is determined by the relaxation rates for the spontaneous-phonon-decay processes in the film. We also find that the time taken for different parts of the energy-density spectra to reach their steady-state value depends on the magnitude of the phonon wave vector.