Modeling the hundreds-of-nanoseconds-long irradiation of tin droplets with a 2 textmu m-wavelength laser for future EUV lithography

The properties of an extreme ultraviolet (EUV) source driven by hundreds-of-nanoseconds-long laser pulses of 2 µm wavelength are investigated through radiation-hydrodynamic simulations. We show that single-pulse irradiation of 30 µm-diameter tin droplets can generate in-band energies mJ directed in the 2π sr solid angle subtended by the collector mirror, yielding energies ∼100 mJ produced from 45 µm-diameter droplets. Time-integrated in-band EUV emission profiles, generated by taking Abel transforms of the local net in-band emissivity, reveal EUV source sizes in the axial (laser) direction × radial direction of ∼600 (1000) × 100 (150) µm2 for 30 (45) µm-diameter droplets. We find that approximately 74% of the total in-band emission is produced during the first half of the total propulsion distance irrespective of droplet size or laser intensity. Furthermore, we propose a one-dimensional analytical propulsion model to qualitatively explain the simulated droplet trajectory and to predict the time taken for the droplet to vaporize. These findings offer motivation for the development of high-power EUV sources based on single-pulse, hundreds-of-nanoseconds-long irradiation of tin droplets.