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 tE. We measured tE in 45-nm Ag and 30-nm Au thin films as a function of lattice temperature (Ti=10-300 K) and laser-energy density (Ul = 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 Ul between 0.3-1.3 J cm-3 and observed that tE is independent from Ul 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 Te and Ti, implying that the two subsystems each have a thermal distribution. The TTM predicts a quasiproportional relation between tE and Ti in the perturbative regime where tE is not affected by Ul. Hence, it is shown that the measured dependencies of tE 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.

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Journal Phys. Rev. B
Groeneveld, R. H. M, Sprik, R, & Lagendijk, A. (1995). Femtosecond spectroscopy of electron-electron and electron-phonon energy relaxation in Ag and Au. Phys. Rev. B, 51, 11433–11445.