Abstract

We have performed angle-dependent reflectance measurements of in situ magnetron sputtered films of B4C, C, Mo, Si, and W. The Fresnel relations were used to determine the complex index of refraction from the reflectance data in the region of approximately 35–150 eV. In the cases of Si, C, and B4C we found excellent agreement with published data. However, for Mo and W we found that the optical properties from 35 to 60 eV differed significantly from those in the literature.

© 1998 Optical Society of America

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References

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  1. See the data tables in E. R. Palik, ed., The Handbook of Optical Constants (Academic, Orlando, Fla., 1985 and 1991), Vols. I and II.
  2. B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993); these data are also available in electronic form at http://www-cxro.lbl.gov .
  3. D. L. Windt, J. W. C. Cash, M. Scott, P. Arendt, B. Newman, R. F. Fisher, A. B. Swartzlander, “Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 Å to 1216 Å,” Appl. Opt. 27, 246–278 (1988);D. L. Windt, “Optical constants for thin films of C, diamond, Al, Si, and CVD SiC from 24 Å to 1216 Å,” Appl. Opt. 27, 279–295 (1988);D. L. Windt, “XUV optical constants of single-crystal GaAs and sputtered C, Si, Cr3C2, Mo, and W,” Appl. Opt. 30, 15–25 (1991).
    [CrossRef] [PubMed]
  4. C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
    [CrossRef]
  5. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1965), Chap. 7.
  6. L. Névot, P. Croce, “Caracterisation des surfaces par reflexion rasante de rayons. X. Application a l’etude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
    [CrossRef]
  7. M. Lampton, B. Margon, S. Bowyer, “Parameter estimation in x-ray astronomy,” Astrophys. J. 208, 177–190 (1976).
    [CrossRef]
  8. R. Soufli, E. M. Gullikson, “Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet–soft-x-ray region,” Appl. Opt. 36, 5499–5507 (1997).
    [CrossRef] [PubMed]
  9. C. Tarrio, S. E. Schnatterly, “Optical properties of silicon and its oxides,” J. Opt. Soc. Am. B 10, 952–957 (1993).
    [CrossRef]
  10. R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. (to be published).

1997 (1)

1994 (1)

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

1993 (2)

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993); these data are also available in electronic form at http://www-cxro.lbl.gov .

C. Tarrio, S. E. Schnatterly, “Optical properties of silicon and its oxides,” J. Opt. Soc. Am. B 10, 952–957 (1993).
[CrossRef]

1988 (1)

1980 (1)

L. Névot, P. Croce, “Caracterisation des surfaces par reflexion rasante de rayons. X. Application a l’etude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

1976 (1)

M. Lampton, B. Margon, S. Bowyer, “Parameter estimation in x-ray astronomy,” Astrophys. J. 208, 177–190 (1976).
[CrossRef]

Arendt, P.

Bowyer, S.

M. Lampton, B. Margon, S. Bowyer, “Parameter estimation in x-ray astronomy,” Astrophys. J. 208, 177–190 (1976).
[CrossRef]

Calcott, T. A.

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

Cash, J. W. C.

Croce, P.

L. Névot, P. Croce, “Caracterisation des surfaces par reflexion rasante de rayons. X. Application a l’etude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

Davis, J. C.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993); these data are also available in electronic form at http://www-cxro.lbl.gov .

Fisher, R. F.

Gullikson, E. M.

R. Soufli, E. M. Gullikson, “Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet–soft-x-ray region,” Appl. Opt. 36, 5499–5507 (1997).
[CrossRef] [PubMed]

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993); these data are also available in electronic form at http://www-cxro.lbl.gov .

R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. (to be published).

Haass, M.

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993); these data are also available in electronic form at http://www-cxro.lbl.gov .

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1965), Chap. 7.

Jia, J.

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

Lampton, M.

M. Lampton, B. Margon, S. Bowyer, “Parameter estimation in x-ray astronomy,” Astrophys. J. 208, 177–190 (1976).
[CrossRef]

Lucatorto, T. B.

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

Margon, B.

M. Lampton, B. Margon, S. Bowyer, “Parameter estimation in x-ray astronomy,” Astrophys. J. 208, 177–190 (1976).
[CrossRef]

Névot, L.

L. Névot, P. Croce, “Caracterisation des surfaces par reflexion rasante de rayons. X. Application a l’etude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

Newman, B.

Schnatterly, S. E.

Scott, M.

Soufli, R.

R. Soufli, E. M. Gullikson, “Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet–soft-x-ray region,” Appl. Opt. 36, 5499–5507 (1997).
[CrossRef] [PubMed]

R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. (to be published).

Swartzlander, A. B.

Tarrio, C.

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

C. Tarrio, S. E. Schnatterly, “Optical properties of silicon and its oxides,” J. Opt. Soc. Am. B 10, 952–957 (1993).
[CrossRef]

Watts, R. N.

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

Windt, D. L.

Appl. Opt. (2)

Astrophys. J. (1)

M. Lampton, B. Margon, S. Bowyer, “Parameter estimation in x-ray astronomy,” Astrophys. J. 208, 177–190 (1976).
[CrossRef]

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993); these data are also available in electronic form at http://www-cxro.lbl.gov .

J. Opt. Soc. Am. B (1)

J. X-Ray Sci. Technol. (1)

C. Tarrio, R. N. Watts, T. B. Lucatorto, M. Haass, T. A. Calcott, J. Jia, “New NIST/DARPA national soft x-ray reflectometry facility,” J. X-Ray Sci. Technol. 4, 96–101 (1994).
[CrossRef]

Rev. Phys. Appl. (1)

L. Névot, P. Croce, “Caracterisation des surfaces par reflexion rasante de rayons. X. Application a l’etude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

Other (3)

R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. (to be published).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1965), Chap. 7.

See the data tables in E. R. Palik, ed., The Handbook of Optical Constants (Academic, Orlando, Fla., 1985 and 1991), Vols. I and II.

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Figures (8)

Fig. 1
Fig. 1

Reflectance at 68.9 eV of a 94-nm-thick Si film on float glass as measured (squares) and calculated (solid curve) with parameters δ = 0.0181 and β = 0.0050; rms roughnesses 1.6 nm (top) and 0.4 nm (bottom).

Fig. 2
Fig. 2

Reflectance at 68.1 eV of a 94-nm-nm thick W film on float glass as measured (squares) and calculated (solid curve) with parameters δ = 0.144 and β = 0.093; rms roughnesses 1.0 nm (top) and 0.6 nm (bottom).

Fig. 3
Fig. 3

χ2 contours from fitting of W data at 68.1 eV. The numbers on the contours are the values of χ2 calculated from Eq. (6); each contour corresponds to an increase of 1.

Fig. 4
Fig. 4

δ and β of in situ-deposited Si films with solid curves to guide the eye. Also shown are data from Ref. 2 (dashed curves).

Fig. 5
Fig. 5

δ and β of in situ-deposited Mo films with solid curves to guide the eye. Also shown are data from Ref. 2 (dashed curves).

Fig. 6
Fig. 6

δ and β of in situ-deposited W films with solid curves to guide the eye. Also shown are data from Ref. 2 (dashed curves).

Fig. 7
Fig. 7

δ and β of in situ-deposited C films with solid curves to guide the eye. Also shown are data from Ref. 2 (dashed curves).

Fig. 8
Fig. 8

δ and β of in situ-deposited B4C films with solid curves to guide the eye. Also shown are data from Ref. 2 (dashed curves).

Equations (6)

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

r = sin   θ - N 2 - cos 2   θ sin   θ + N 2 - cos 2   θ ,
t = 2   sin   θ sin   θ + N 2 - cos 2   θ ,
R = R 0 exp - 4 q 1 q 2 σ 2 ,
r = r t + r b exp 2 i Δ 1 + r t r b exp 2 i Δ ,
Δ = 2 π Nt   sin   θ i λ
χ 2 = i R θ i - R fit θ i Δ R θ i 2 ,

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