Simplified 1-D calculation of 13.5-nm emission in a tin plasma including radiation transport

Abstract

Many next generation lithography schemes for the semiconductor industry are based on a 13.5-nm tin plasma light source, where hundreds of thousands of 4d-4f, 4p-4d, and 4d-5p transitions from Sn5+–Sn13+ ions overlap to form an unresolved transition array. To aid computation, transition arrays are treated statistically, and Hartree-Fock results are used to calculate radiation transport in the optically thick regime with a 1-D Lagrangian plasma hydrodynamics code. Time-dependent spectra and conversion efficiencies of 2% in-band 13.5-nm emission to laser energy are predicted for a Nd:YAG laser incident on a pure tin slab target as a function of laser power density and pulse duration at normal incidence. Calculated results showed a maximum conversion efficiency of 2.3% for a 10-ns pulse duration at 8.0 x 1010 W/cm2 and are compared to experimental data where available. Evidence for the need to include lateral expansion is presented.