Femtosecond spectroscopy of electron-electron and electron-phonon energy relaxation in Ag and Au

We show experimentally that the electron distribution of a laser-heated metal is a nonthermal distribution on the time scale of the electron-phonon (e-ph) energy relaxation time t_E. We measured t_E in 45-nm Ag and 30-nm Au thin films as a function of lattice temperature (T_i=10-300 K) and laser-energy density (U_l = 0.3-1.3 J cm^-3), combining femtosecond optical transient-reflection techniques with the surface-plasmon polariton resonance. The experimental effective e-ph energy relaxation time decreased from 710-530 fs and 830-530 fs for Ag and Au, respectively, when temperature is lowered from 300 to 10 K. At various temperatures we varied U_l between 0.3-1.3 J cm^-3 and observed that t_E is independent from U_l within the given range. The results were first compared to theoretical predictions of the two-temperature model (TTM). The TTM is the generally accepted model for e-ph energy relaxation and is based on the assumption that electrons and lattice can be described by two different time-dependent temperatures T_e and T_i, implying that the two subsystems each have a thermal distribution. The TTM predicts a quasiproportional relation between t_E and T_i in the perturbative regime where t_E is not affected by U_l. Hence, it is shown that the measured dependencies of t_E on lattice temperature and energy density are incompatible with the TTM. It is proven that the TTM assumption of a thermal electron distribution does not hold especially under our experimental conditions of low laser power and lattice temperature. The electron distribution is a nonthermal distribution on the picosecond time scale of e-ph energy relaxation. We developed a new model, the nonthermal electron model (NEM), in which we account for the (finite) electron-electron (e-e) and electron-phonon dynamics simultaneously. It is demonstrated that incomplete electron thermalization yields a slower e-ph energy relaxation in comparison to the thermalized limit. With the NEM we are able to give a consistent description of our data and obtain values for the e-e scattering rate K = 0.10 ± 0.05 fs^-1eV^-2 for Ag and Au and for the e-ph coupling g_ = 3.5 ± 0.5 x 10¹⁶ Wm^-3K^-1 for Ag and 3.0 ± 0.5 x 10¹⁶ Wm^-3K^-1 for Au.