Ultrafast dynamics of nonequilibrium electrons in metals under femtosecond laser irradiation

Abstract

Irradiation of a metal with an ultrashort laser pulse leads to a disturbance of the free-electron gas out of thermal equilibrium. We investigate theoretically the transient evolution of the distribution function of the electron gas in a metal during and after irradiation with a subpicosecond laser pulse of moderate intensity. We consider absorption by inverse bremsstrahlung, electron-electron thermalization, and electron-phonon coupling. Each interaction process is described by a full Boltzmann collision integral without using any relaxation-time approach. Our model is free of phenomenological parameters. We solve numerically a system of time- and energy-dependent integro-differential equations. For the case of irradiation of aluminum, the results show the transient excitation and relaxation of the free-electron gas as well as the energy exchange between electrons and phonons. We find that laser absorption by free electrons in a metal is well described by a plasmalike absorption term. We obtain a good agreement of calculated absorption characteristics with values experimentally found. For laser excitations near damage threshold, we find that the energy exchange between electrons and lattice can be described with the two-temperature model, in spite of the nonequilibrium distribution function of the electron gas. In contrast, the nonequilibrium distribution leads at low excitations to a delayed cooling of the electron gas. The cooling time of laser-heated electron gas depends thus on excitation parameters and may be longer than the characteristic relaxation time of a Fermi-distributed electron gas depending on internal energy only. We propose a definition of the thermalization time as the time after which the collective behavior of laser-excited electrons equals the thermalized limit.