Abstract

We present high-accuracy measurements for wavelengths near 157 nm of the absolute index of refraction, the index dispersion, and the temperature dependence of the index for the ultraviolet optical materials with cubic symmetry: CaF2, SrF2, BaF2, and LiF. Accurate values of these quantities for these materials are needed for designs of the lens systems for F2 excimer-laser-based exposure tools for 157-nm photolithography. These tools are expected to use CaF2 as the primary optical material and possibly one of the others to correct for chromatic aberrations. These optical properties were measured by the minimum deviation method. Absolute refractive indices were obtained with an absolute accuracy of 5 × 10-6 to 6 × 10-6.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1998), Vols. 1–3.
  4. B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (U.S. Government Printing Office, Washington, D.C., 1994).
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    [CrossRef]
  7. E. C. Y. Inn, “Vacuum ultraviolet spectroscopy,” Spectrochim. Acta 7, 65–87 (1955).
    [CrossRef]
  8. D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).
  9. U. Griesmann, R. Kling, J. H. Burnett, L. Bratasz, R. A. Gietzen, “The NIST FT700 vacuum ultraviolet Fourier transform spectrometer: applications in ultraviolet spectrometry and radiometry,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymonds, eds., Proc. SPIE3818, 180–188 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. U. Griesmann, J. H. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699–1701 (1999).
    [CrossRef]
  13. C. J. Sansonetti, J. Reader, K. Vogler, “Precision measurement of wavelengths emitted by a molecular fluorine laser at 157 nm,” Appl. Opt. 40, 1974–1978 (2001).
    [CrossRef]
  14. J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
    [CrossRef]
  15. V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, New York, 1984).
    [CrossRef]
  16. J. H. Burnett, Z. H. Levine, E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
    [CrossRef]
  17. G. Ghosh, ed., Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, San Diego, Calif., 1998).

2001

C. J. Sansonetti, J. Reader, K. Vogler, “Precision measurement of wavelengths emitted by a molecular fluorine laser at 157 nm,” Appl. Opt. 40, 1974–1978 (2001).
[CrossRef]

J. H. Burnett, Z. H. Levine, E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[CrossRef]

1999

1998

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt 37, 5964–5968 (1998).
[CrossRef]

1997

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

1993

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

1990

D. Tentori, J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[CrossRef]

1971

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

1966

1963

1955

E. C. Y. Inn, “Vacuum ultraviolet spectroscopy,” Spectrochim. Acta 7, 65–87 (1955).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, New York, 1984).
[CrossRef]

Birch, K. P.

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), pp. 190–193.

Boucarut, R. A.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Bratasz, L.

U. Griesmann, R. Kling, J. H. Burnett, L. Bratasz, R. A. Gietzen, “The NIST FT700 vacuum ultraviolet Fourier transform spectrometer: applications in ultraviolet spectrometry and radiometry,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymonds, eds., Proc. SPIE3818, 180–188 (1999).
[CrossRef]

Burnett, J. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[CrossRef]

U. Griesmann, J. H. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699–1701 (1999).
[CrossRef]

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt 37, 5964–5968 (1998).
[CrossRef]

U. Griesmann, R. Kling, J. H. Burnett, L. Bratasz, R. A. Gietzen, “The NIST FT700 vacuum ultraviolet Fourier transform spectrometer: applications in ultraviolet spectrometry and radiometry,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymonds, eds., Proc. SPIE3818, 180–188 (1999).
[CrossRef]

Downs, M. J.

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

French, T. A.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Gardner, L. D.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Geithner, P. H.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Gietzen, R. A.

U. Griesmann, R. Kling, J. H. Burnett, L. Bratasz, R. A. Gietzen, “The NIST FT700 vacuum ultraviolet Fourier transform spectrometer: applications in ultraviolet spectrometry and radiometry,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymonds, eds., Proc. SPIE3818, 180–188 (1999).
[CrossRef]

Ginzburg, V. L.

V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, New York, 1984).
[CrossRef]

Griesmann, U.

U. Griesmann, J. H. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699–1701 (1999).
[CrossRef]

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt 37, 5964–5968 (1998).
[CrossRef]

U. Griesmann, R. Kling, J. H. Burnett, L. Bratasz, R. A. Gietzen, “The NIST FT700 vacuum ultraviolet Fourier transform spectrometer: applications in ultraviolet spectrometry and radiometry,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymonds, eds., Proc. SPIE3818, 180–188 (1999).
[CrossRef]

Gupta, R.

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt 37, 5964–5968 (1998).
[CrossRef]

Hagopian, J. G.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Hartig, G.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Inn, E. C. Y.

E. C. Y. Inn, “Vacuum ultraviolet spectroscopy,” Spectrochim. Acta 7, 65–87 (1955).
[CrossRef]

Keski-Kuha, R. A. M.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Khanna, B. N.

Kling, R.

U. Griesmann, R. Kling, J. H. Burnett, L. Bratasz, R. A. Gietzen, “The NIST FT700 vacuum ultraviolet Fourier transform spectrometer: applications in ultraviolet spectrometry and radiometry,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymonds, eds., Proc. SPIE3818, 180–188 (1999).
[CrossRef]

Kuyatt, C. E.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (U.S. Government Printing Office, Washington, D.C., 1994).

Lerma, J. R.

D. Tentori, J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[CrossRef]

Levine, Z. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[CrossRef]

Leviton, D. B.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Madison, T. J.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Malitson, I. H.

Pastrnak, J.

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

Peck, E. R.

Reader, J.

Sansonetti, C. J.

Shirley, E. L.

J. H. Burnett, Z. H. Levine, E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[CrossRef]

Taylor, B. N.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (U.S. Government Printing Office, Washington, D.C., 1994).

Tentori, D.

D. Tentori, J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[CrossRef]

Vedam, K.

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

Vogler, K.

Walhout, M.

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt 37, 5964–5968 (1998).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), pp. 190–193.

Appl. Opt

R. Gupta, J. H. Burnett, U. Griesmann, M. Walhout, “Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm,” Appl. Opt 37, 5964–5968 (1998).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Metrologia

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Opt. Eng.

D. Tentori, J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[CrossRef]

Opt. Lett.

Opt. Photon. News Suppl.

D. B. Leviton, J. G. Hagopian, P. H. Geithner, R. A. Boucarut, T. J. Madison, R. A. M. Keski-Kuha, G. Hartig, L. D. Gardner, T. A. French, “Measuring efficiency of far ultraviolet optical systems in gaseous nitrogen,” Opt. Photon. News Suppl. 8, 1–2 (1997).

Phys. Rev. B

J. Pastrnak, K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

J. H. Burnett, Z. H. Levine, E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[CrossRef]

Spectrochim. Acta

E. C. Y. Inn, “Vacuum ultraviolet spectroscopy,” Spectrochim. Acta 7, 65–87 (1955).
[CrossRef]

Other

U. Griesmann, R. Kling, J. H. Burnett, L. Bratasz, R. A. Gietzen, “The NIST FT700 vacuum ultraviolet Fourier transform spectrometer: applications in ultraviolet spectrometry and radiometry,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymonds, eds., Proc. SPIE3818, 180–188 (1999).
[CrossRef]

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1998), Vols. 1–3.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (U.S. Government Printing Office, Washington, D.C., 1994).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), pp. 190–193.

G. Ghosh, ed., Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, San Diego, Calif., 1998).

V. M. Agranovich, V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Springer-Verlag, New York, 1984).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the UV goniometric spectrometer with reflective optics. S1 and S2 are the entrance and exit slits, respectively; M1 is a collimating mirror and M2 a focusing mirror.

Fig. 2
Fig. 2

Schematic of the UV goniometric spectrometer enclosed in a temperature-controlled N2 gas purge housing for index measurements near 157 nm.

Fig. 3
Fig. 3

Deuterium lamp spectrum near 157 nm taken with the NIST FT700 VUV Fourier-transform spectrometer. The wavelength accuracy is 0.02 pm; the instrumental resolution is 0.1 pm.

Fig. 4
Fig. 4

Absolute refractive index of the CaF2 sample C at 20.00(5) °C at eight deuterium lamp spectral line wavelengths in the range 156.8–158.6 nm. The curve is a quadratic least-squares fit to the data and is given by the inset formula. The first two coefficients give the index and dispersion at 157.63094 nm.

Fig. 5
Fig. 5

Absolute refractive index of three samples of CaF2 from three different suppliers at 20.00(5) °C and at 157.63094 nm. Sample A was measured twice independently. The error bars correspond to standard uncertainties of 6 × 10-6 for sample A and 5 × 10-6 for samples B and C. The results for sample C are included in Table 1.

Fig. 6
Fig. 6

Absolute refractive index of three samples of BaF2 from three different suppliers at 20.00(5) °C and at 157.63094 nm. The error bars correspond to standard uncertainties of 6 × 10-6 for all samples. The results for sample D are included in Table 1.

Tables (2)

Tables Icon

Table 1 Absolute Index, Dispersion, and Temperature Dependence of LiF, CaF2, SrF2, and BaF2 near 157 nma

Tables Icon

Table 2 Uncertainty Budget for Refractive-Index Measurement

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

nmatλ=sinA+Dλ2sinA2 ngasλ.
nλ-1T, P=nλ-10×P1.01325273.15273.15+T×0.9995555Z×1+nλ-1061-P1.01325273.15273.15+T-1,
nλ-10=nλ-10 °C, 1.01325bars =1.966273122086.66-1000/λ2+0.027450825133.85688-1000/λ2, Z=1-P1.0132544.45-T×10-5.

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