  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 subject to a
number of studies and it is comparably well understood, while the
nonequilibrium within the phononic subsystem is usually neglected and its
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 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 this to the
energy transfer for equilibrium distributions in both subsystems.
