Effect of recombination on ultrashort pulse laser material removal by Coulomb explosion

The femtosecond laser material interaction takes place on a very short time scale. The transfer of energy from the pulse to the material cannot be described using thermal concepts as these are based on a time scale which is much longer than that during femtosecond pulse interaction. Therefore the femtosecond pulse may be considered as an intense electromagnetic wave. When a ultra short laser pulse impinges a semiconductor, the atoms are ionized by two processes mainly multiphoton ionization and impact ionization. These processes are responsible for exciting the electrons from the valence band to the conduction band. We also study how collisional absorption of photons affects the ionization rate and bring out its significance. As the atoms are ionized the cohesive energy which binds them together becomes very small, the intermolecular bonds between nuclei are weakened and the positively charged nuclei repel each other. As the substrate is ionized by each laser pulse, the cohesive energy decreases and the material ablation results due to Coulomb explosion which is the hypothesis for this study. As they are repelled, the electrons that were excited from the valence band to the conduction band show a tendency to recombine with the holes created in the valence band. This process is called recombination. For very high carrier densities generated by ultra short pulses the primary recombination mechanism is called Auger recombination. The recombination mechanism causes the repulsion between atoms to reduce and our purpose is to try and understand how much of an effect the recombination mechanism has on the ablation rate and hence the expansion of the ablation zone. In this paper we present a model for the ionization processes and hence solve for the ionization rate at the end of the pulse. As the material expands the electrons are assumed to move with it and hence this process can be aptly described by the 1-D convection equation with recombination. This convection equation is solved along with the Euler equations and the ionization rate is used as the initial condition to predict expansion velocity, pressure and the temperature in the ablation zone.