Influence of Recombination on the Free-Electron Avalanche in Laser-Irradiated Dielectrics

When transparent solids are irradiated with laser intensities above a certain threshold, strong absorption of laser energy occurs. The increasing absorptivity is caused by the formation of a free electron gas in the conduction band of the dielectric. The temporal evolution of the free-electron density in a dielectric during ultrashort pulse laser irradiation plays a fundamental role for numerous investigations. Applying a kinetic approach to describe the electron dynamics in the conduction band of a dielectric, we have shown that the simple rate equation, usually applied to describe the transient free-electron density, fails on ultrashort time scales [1]. The reason is a nonstationary shape of the electronic distribution function: since impact ionization can be performed only by electrons above a certain critical engery, the total free-electron density does not determine the rate of impact ionization in this case. With the multiple rate equation (MRE), introduced in [2], I have developed a new widely applicable description, which is valid on a broad range of time scales. This system of rate equations represents the first description of the transient free-electron density which keeps track of the electrons energy distribution while maintaining the conceptual and analytic simplicity of standard rate equations. It considers the nonstationary electron energy distribution at the initial stage of ionization and provides the transition to the asymptotic avalanche regime at longer time scales. The analytic solution for the asymptotic regime yields the avalanche parameter entering the standard rate equation and the condition of its applicability. In [2] the evolution of the free-electron density was studied for the case of irradiation of SiO2 on timescales in the femtoto picosecond range. However, recombination processes were neglected, though they may play a considerable role. Especially for quartz, fast recombination processes on a timescale of about 150 fs are known; here ultrafast recombination in self-trapped exciton states have been experimentelly found [3]. Generally, recombination may be included in the multiple rate equation analogously to the extension of the standard rate equation as proposed in Refs. [4]. Aiming to calculate the stationary long-time behavior, we allow for reexcitation from the exciton states with a probability Wexc. With the recombination time τrecomb a modified MRE may be formulated as: