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Title: Simplified calculation of nonlocal thermodynamic equilibrium excited state populations contributing to 13.5 nm emission in a tin plasma

Abstract

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 level 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.

Authors:
; ; ; ;  [1]
  1. School of Physics, University College Dublin, Belfield, Dublin 4 (Ireland)
Publication Date:
OSTI Identifier:
20982696
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 101; Journal Issue: 4; Other Information: DOI: 10.1063/1.2434965; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUILIBRIUM; EXCITED STATES; EXTREME ULTRAVIOLET RADIATION; HARTREE-FOCK METHOD; HYDRODYNAMICS; LASER-PRODUCED PLASMA; MULTICHARGED IONS; ONE-DIMENSIONAL CALCULATIONS; PLASMA PRODUCTION; SEMICONDUCTOR MATERIALS; THERMODYNAMICS; TIN; TIN IONS

Citation Formats

White, J., Cummings, A., Dunne, P., Hayden, P., and O'Sullivan, G. Simplified calculation of nonlocal thermodynamic equilibrium excited state populations contributing to 13.5 nm emission in a tin plasma. United States: N. p., 2007. Web. doi:10.1063/1.2434965.
White, J., Cummings, A., Dunne, P., Hayden, P., & O'Sullivan, G. Simplified calculation of nonlocal thermodynamic equilibrium excited state populations contributing to 13.5 nm emission in a tin plasma. United States. doi:10.1063/1.2434965.
White, J., Cummings, A., Dunne, P., Hayden, P., and O'Sullivan, G. Thu . "Simplified calculation of nonlocal thermodynamic equilibrium excited state populations contributing to 13.5 nm emission in a tin plasma". United States. doi:10.1063/1.2434965.
@article{osti_20982696,
title = {Simplified calculation of nonlocal thermodynamic equilibrium excited state populations contributing to 13.5 nm emission in a tin plasma},
author = {White, J. and Cummings, A. and Dunne, P. and Hayden, P. and O'Sullivan, G.},
abstractNote = {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 level 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.},
doi = {10.1063/1.2434965},
journal = {Journal of Applied Physics},
number = 4,
volume = 101,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • 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
  • 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. Themore » results of the model are compared with experimental spectra from tin-based laser-produced plasmas.« less
  • An examination of the influence of target composition and viewing angle on the extreme ultraviolet spectra of laser produced plasmas formed from tin and tin doped planar targets is reported. Spectra have been recorded in the 9-17 nm region from plasmas created by a 700 mJ, 15 ns full width at half maximum intensity, 1064 nm Nd:YAG laser pulse using an absolutely calibrated 0.25 m grazing incidence vacuum spectrograph. The influence of absorption by tin ions (Sn I-Sn X) in the plasma is clearly seen in the shape of the peak feature at 13.5 nm, while the density of tinmore » ions in the target is also seen to influence the level of radiation in the 9-17 nm region.« less
  • Extreme ultraviolet lithography requires a light source at 13.5 nm to match the proposed multilayer optics reflectivity. The impact of wavelength and power density on the ion distribution and electron temperature in a laser-produced plasma is calculated for Nd:YAG and CO{sub 2} lasers. A steady-state figure of merit, calculated to optimize emission as a function of laser wavelength, shows an increase with a CO{sub 2} laser. The influence of reduced electron density in the CO{sub 2} laser-produced plasma is considered in a one-dimensional radiation transport model, where a more than twofold increase in conversion efficiency over that attainable with themore » Nd:YAG is predicted.« less
  • Extreme ultraviolet lithography semiconductor manufacturing requires a 13.5 nm light source. Laser-produced plasma emission from Sn V-Sn XIV ions is one proposed industry solution. The effect of laser pulse width and spatial profile on conversion efficiency is analyzed over a range of power densities using a two-dimensional radiative magnetohydrodynamic code and compared to experiment using a 1.064 {mu}m, neodymium:yttrium aluminium garnet laser on a planar tin target. The calculated and experimental conversion efficiencies and the effects of self-absorption in the plasma edge are compared. Best agreement between theory and experiment is found for an 8.0 ns Gaussian pulse.