Advanced Irradiation Schemes for Target Shaping in Droplet-Based Laser-Produced Plasma Light Sources

Abstract

The presented work is in the field of droplet-based laser produced plasma light sources. The preshaping of the liquid droplet target before it's irradiation by the plasma generating main pulse has been of growing interest in the field of EUV and soft x-ray light sources. Research in this field has already proven that improvements in system performance are achievable in terms of conversion efficiency and debris mitigation when the target is carefully preshaped before the primary irradiation. The increase in conversion efficiency of the source leads to higher throughput for these light sources, whereas the improvement of debris mitigation leads to a reduction in the cost of ownership. The neutral cluster debris dynamics of a droplet-based laser-produced plasma generated by a single nanosecond scale laser pulse is studied experimentally and analytically. Experiments were done imaging the debris with a high-speed shadowgraph system and using image processing to determine the droplet debris mean radial velocity $\overline{V}$ dependence on laser pulse irradiance $E_e$. The data shows a power law dependence between the mean radial debris velocity and the incident irradiance giving $\overline{V} \propto E_e^n$ with $n \approx 0.65$. A scaled analytical model was derived modeling the plasma ablation pressure on the droplet surface as the primary momentum exchange mechanism between the unablated droplet material and the laser pulse. The relationship between droplet debris trajectory and the droplet alignment with the laser was quantified analytically. The derived analytical model determines that the neutral cluster debris trajectory for an ablated droplet is a function of the laser profile $f_L$, the droplet diameter $d_0$ and the axial misalignment $\psi$ between the laser axis and the droplet center. The analytical calculations from these models were found to be in good agreement with the measurements. This analysis has practical significance for understanding ablated droplet debris, droplet deformation by laser pulsing, and droplet breakup from very short timescale shocks. Liquid Sn droplets were irradiated with shaped bursts of picosecond laser pulses. The shape of the deforming droplets following the impact of the recoil pressure induced by these bursts were imaged using a high speed shadowgraph system. It is observed that the modified Weber number $We_s$ describes the unruptured sheet expansion over a wide variation in burst shapes. The splash Weber $We_s$ scales as $\sim 0.5 N_p^{1-2n}(N_p +1)$ relative to the nominal Weber number $We$ by distributing the laser energy evenly among $N_p$ pulses, where the laser pulse peak ablation pressure $P_s$ is exponentially proportionate by a factor of $n$ to the laser irradiance $I_0$ as $P_s \propto I_0^n$. The deforming droplet sheet forms various cup shapes whose depth is dependent upon $N_p$. The timing and energy arrangement of pulses within the burst has been shown to influence the shape of the cup formed by the expanding droplet sheet. Cavitation within the droplets are observed evidenced by hydrodynamically focused microjets ejected behind droplet. The threshold conditions for cavitation are approximated from the ablation pressure and gain and loss terms for the focused acoustic wave when it reaches the droplet center. The predicted cavity size and growth rate are compared against the dimensions of the ejected microjets and found to be in good agreement. The rupture time $\tilde{t}_b$ of the droplet expanding as a thin fluid film was measured for each case. A Rayleigh-Taylor instability analysis is done in order to determine the dependences governing $\tilde{t}_b$. The evidence supports the hypothesis that the initial perturbations of the developing Rayleigh-Taylor instabilities are on the order of the ablation depth and that there is a lower cutoff wavelength of these initial perturbations of $\sim 10 \: \mu$m. Multiphase CFD simulations are constructed of a droplet impacted by the ablation pressure wave of a pulsed laser. These simulations were performed in Fluent 18.0 using the multiphase Volume of Fluid with the coupled level set model, explicit formulation, the geo-reconstruct scheme, and adaptive meshing. The pressure and velocity distribution from the laser ablation induced shockwave was calculated analytically and set as the initial condition for the droplet. The laser pulse irradiance is varied across several cases. The cases were run until the droplet fragmentation ceased. Final fragment size distributions and mass flux distributions are compared for the cases. It was determined that the fragment size of the disintegrating droplet is determined by the splash Weber number $We_s$, and the initial states of the surface perturbations wavenumber $k$, and amplitude $\eta_0$, which are calculated analytically with the Rayleigh-Taylor instability model. This analytical model is validated by the numerical simulations and the experimental results.