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

The properties of an extreme ultraviolet (EUV) source driven by hundreds-of-nanoseconds-long laser pulses of λₗₐₛₑᵣ = 2 m wavelength are investigated through radiation-hydrodynamic simulations. We show that single-pulse irradiation of 30 m-diameter tin droplets can generate in-band energies ~ 30 mJ directed in the 2π solid angle subtended by the collector mirror, yielding energies ~ 100 mJ produced from 45 m-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) m² for 30 (45) m-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. % show that the derived relation between laser intensity and vaporization rate yields a reliable prediction for the time at which the droplet fully vaporizes. These findings offer motivation for the development of high-power EUV sources based on single-pulse, hundreds-of-nanoseconds-long irradiation of tin droplets.