Relaxation of a nonequilibrium phonon distribution induced by femtosecond laser irradiation

TL;DR

This paper develops a model to analyze how nonequilibrium phonon distributions relax after femtosecond laser irradiation, revealing their impact on energy transfer rates between electrons and phonons and showing thermalization occurs over hundreds of picoseconds.

Contribution

The study introduces a phonon relaxation model using Boltzmann integrals to account for nonequilibrium phonons, highlighting their significant role in ultrafast energy transfer processes.

Findings

Phonon thermalization time is approximately hundreds of picoseconds.

Nonequilibrium phonons significantly affect electron-phonon energy transfer rates.

Energy transfer differs notably between equilibrium and nonequilibrium phonon distributions.

Abstract

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.