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Title: Simplified modeling of 13.5 nm unresolved transition array emission of a Sn plasma and comparison with experiment

Abstract

One key aspect in the drive to optimize the radiative output of a laser-produced plasma for extreme ultraviolet lithography is the radiation transport through the plasma. In tin-based plasmas, the radiation in the 2% bandwidth at 13.5 nm is predominantly due to 4d-4f and 4p-4d transitions from a range of tin ions (Sn{sup 7+} to Sn{sup 12+}). The complexity of the configurations involved in these transitions is such that a line-by-line analysis is, computationally, extremely intensive. This work seeks to model the emission profiles of each ion by treating the transition arrays statistically, thus greatly simplifying radiation transport modeling. The results of the model are compared with experimental spectra from tin-based laser-produced plasmas.

Authors:
; ; ; ; ; ;  [1]
  1. School of Physics, University College Dublin, Belfield, Dublin 4 (Ireland)
Publication Date:
OSTI Identifier:
20714138
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 98; Journal Issue: 11; Other Information: DOI: 10.1063/1.2128055; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPARATIVE EVALUATIONS; EXTREME ULTRAVIOLET RADIATION; LASER-PRODUCED PLASMA; LASERS; MULTICHARGED IONS; PLASMA PRODUCTION; RADIATION TRANSPORT; SIMULATION; TIN; TIN IONS

Citation Formats

White, J., Hayden, P., Dunne, P., Cummings, A., Murphy, N., Sheridan, P., and O'Sullivan, G. Simplified modeling of 13.5 nm unresolved transition array emission of a Sn plasma and comparison with experiment. United States: N. p., 2005. Web. doi:10.1063/1.2128055.
White, J., Hayden, P., Dunne, P., Cummings, A., Murphy, N., Sheridan, P., & O'Sullivan, G. Simplified modeling of 13.5 nm unresolved transition array emission of a Sn plasma and comparison with experiment. United States. doi:10.1063/1.2128055.
White, J., Hayden, P., Dunne, P., Cummings, A., Murphy, N., Sheridan, P., and O'Sullivan, G. Thu . "Simplified modeling of 13.5 nm unresolved transition array emission of a Sn plasma and comparison with experiment". United States. doi:10.1063/1.2128055.
@article{osti_20714138,
title = {Simplified modeling of 13.5 nm unresolved transition array emission of a Sn plasma and comparison with experiment},
author = {White, J. and Hayden, P. and Dunne, P. and Cummings, A. and Murphy, N. and Sheridan, P. and O'Sullivan, G.},
abstractNote = {One key aspect in the drive to optimize the radiative output of a laser-produced plasma for extreme ultraviolet lithography is the radiation transport through the plasma. In tin-based plasmas, the radiation in the 2% bandwidth at 13.5 nm is predominantly due to 4d-4f and 4p-4d transitions from a range of tin ions (Sn{sup 7+} to Sn{sup 12+}). The complexity of the configurations involved in these transitions is such that a line-by-line analysis is, computationally, extremely intensive. This work seeks to model the emission profiles of each ion by treating the transition arrays statistically, thus greatly simplifying radiation transport modeling. The results of the model are compared with experimental spectra from tin-based laser-produced plasmas.},
doi = {10.1063/1.2128055},
journal = {Journal of Applied Physics},
number = 11,
volume = 98,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 2005},
month = {Thu Dec 01 00:00:00 EST 2005}
}
  • Extreme ultraviolet lithography schemes for the semiconductor industry are currently based on coupling radiation from a plasma source into a 2% bandwidth at 13.5 nm (91.8 eV). In this paper, we consider the case for a laser-produced plasma (LPP) and address the calculation of ionic level populations in the 4p{sup 6}4d{sup N}, 4p{sup 6}4d{sup N-1}4f{sup 1}, 4p{sup 5}4d{sup N+1}, and 4p{sup 6}4d{sup N-1}5p{sup 1} configurations in a range of tin ions (Sn{sup 6+} to Sn{sup 13+}) producing radiation in this bandwidth. The LPP is modeled using a one-dimensional hydrodynamics code, which uses a hydrogenic, average atom model, where the levelmore » populations are treated as l degenerate. Hartree-Fock calculations are used to remove the l degeneracy and an energy functional method to calculate the nl level populations involved in n=4-4 transitions as a function of distance from the target surface and time. Detailed data are presented for the tin ions that contribute to in-band emission.« less
  • 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 Sn{sup 5+}-Sn{sup 13+} 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 one-dimensional 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 (yttrium aluminum garnet) laser incident on a pure tin slab targetmore » 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 8.0x10{sup 10} W/cm{sup 2} and are compared to experimental data where available. Evidence for the need to include lateral expansion is presented.« less
  • The angular distribution of extreme ultraviolet emission at 13.5 nm within 2% bandwidth was characterized for laser irradiated, planar, Sn targets at prototypic conditions for a lithography system. We have found that two dimensional plasma expansion plays a key role in the distribution of in-band 13.5 nm emission under these conditions. The angular distribution was found to have two peaks at 45 deg. and 15 deg. This complex angular distribution arises from the shape of both the emitting plasma and the surrounding absorbing plasma. This research reveals that the detailed angular distribution can be important to the deduction of conversionmore » efficiency.« less
  • The effect of pulse duration on in-band (2% bandwidth) conversion efficiency (CE) from a CO{sub 2} laser to 13.5 nm extreme ultraviolet (EUV) light was investigated for Sn plasma. It was found that high in-band CE, 2.6%, is consistently obtained using a CO{sub 2} laser with pulse durations from 25 to 110 ns. Employing a long pulse, for example, 110 ns, in a CO{sub 2} laser system used in an EUV lithography source could make the system significantly more efficient, simpler, and cheaper as compared to that using a short pulse of 25 ns or shorter.
  • Temporally resolved imaging of 13.5 nm extreme ultraviolet (EUV) emission from laser-produced Sn plasmas was experimentally investigated with a monochromatic EUV imager. Absorption caused by the surrounding plasma was eliminated by adopting a stripe Sn target laminated on a plastic film so that the CH plasma tamped lateral expansion of the Sn plasma. The experimental results revealed that reabsorption induced by plasma, both in EUV emission-dominant and long scale coronal regions, plays an key role in extracting the EUV light from the plasma efficiently.