Radiation transport and scaling of optical depth in Nd:YAG laser-produced microdroplet-tin plasma

Experimental scaling relations of the optical depth are presented for the emission spectra of a tin-droplet-based, 1-μm-laser-produced plasma source of extreme-ultraviolet (EUV) light. The observed changes in the complex spectral emission of the plasma over a wide range of droplet diameters (16-65 μm) and laser pulse durations (5-25 ns) are accurately captured in a scaling relation featuring the optical depth of the plasma as a single, pertinent parameter. The scans were performed at a constant laser intensity of 1.4 × 10¹¹ W/cm², which maximizes the emission in a 2% bandwidth around 13.5 nm relative to the total spectral energy, the bandwidth relevant for industrial EUV lithography. Using a one-dimensional radiation transport model, the relative optical depth of the plasma is found to linearly increase with the droplet size with a slope that increases with the laser pulse duration. For small droplets and short laser pulses, the fraction of light emitted in the 2% bandwidth around 13.5 nm relative to the total spectral energy is shown to reach high values of more than 14%, which may enable conversion efficiencies of Nd:YAG laser light into - industrially - useful EUV radiation rivaling those of current state-of-the-art CO₂-laser-driven sources.