Relaxation of a nonequilibrium phonon distribution induced by femtosecond laser irradiation

Ultrafast laser irradiation of solids leads to a thermodynamic nonequilibrium within and between the electron and phonon subsystems of the material. Due to electron-electron and phonon-phonon collisions, both subsystems relax into respective new thermodynamic equilibria within a characteristic thermalization time, which is different for each one of them. Moreover, they equilibrate their temperatures by electron-phonon coupling. The relaxation of the electronic nonequilibrium and its effect on the electron-phonon coupling was the subject of a number of studies, and it is comparably well understood, while the nonequilibrium within the phononic subsystem is usually neglected and the influence of the nonequilibrium phonons on other relaxation processes is unclear. Our calculations show significant differences in the energy transfer rate between the electrons and the phonons depending on whether a nonequilibrium distribution is assumed for the phonons or not. Here, we present a model to study the relaxation of the nonequilibrium phonon subsystem. Collisions between phonons are described within the frame of Boltzmann integrals. From this, an energy-dependent relaxation time can be extracted and inserted into a relaxation-time approach. Within the frame of this model, we study the thermalization of a phonon distribution induced by ultrafast laser irradiation. We show that the thermalization time of such a distribution is of the order of some hundreds of picoseconds. Moreover, we discuss the energy transfer between Fermi-distributed electrons and nonequilibrium phonons and compare it to the energy transfer for equilibrium distributions in both subsystems.