Abstract

In the vacuum-ultraviolet region of the spectrum, the optical constants of vacuum-deposited absorbing films can be determined by measuring their specular reflectances at a number of angles of incidence. These reflectance values are then used to solve the generalized Fresnel reflection equations to obtain n and k. If the film is thin enough so that interference occurs between the wave fronts reflected from the film–vacuum and film–substrate interfaces, the errors in determining n and k may be large. Previously an opaque film, one that would transmit only 0.1% of the incident radiant flux at normal incidence if it were free-standing, was considered necessary if the n, k values of the film were to be determined with an accuracy of 1%. This paper presents the results of calculations demonstrating that the film thickness necessary to reduce the errors in n and k to 1% is dependent on n and k and is generally less than the opaque thickness.

© 1974 Optical Society of America

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References

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    [Crossref]
  2. I. Simon, J. Opt. Soc. Am. 41, 336 (1951).
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    [Crossref]
  4. G. F. Jacobus, R. P. Madden, and L. R. Canfield, J. Opt. Soc. Am. 53, 1084 (1963).
    [Crossref]
  5. J. T. Cox, G. Hass, J. B. Ramsey, and W. R. Hunter, J. Opt. Soc. Am. 63, 435 (1973).
    [Crossref]
  6. W. R. Hunter, U. S. Naval Research Laboratory, Washington, D. C.; (unpublished data).
  7. G. Hass, C. F. Jacobus, and W. R. Hunter, J. Opt. Soc. Am. 57, 758 (1967).
    [Crossref]
  8. S. Robin, C. R. Acad. Sci. (Paris) 236, 674 (1953).
  9. J. K. Coulter, G. Hass, and J. B. Ramsey, J. Opt. Soc. Am. 63, 1149 (1973).
    [Crossref]
  10. J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), p. 281.
  11. J. T. Cox, G. Hass, J. B. Ramsey, and W. R. Hunter, J. Opt. Soc. Am. 64, 423 (1974).
    [Crossref]
  12. K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).
  13. W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964).
    [Crossref]
  14. W. R. Hunter, J. Phys. (Paris) 25, 154 (1964).
    [Crossref]
  15. U. S. Whang, R. N. Hamm, E. T. Arakawa, and M. W. Williams, J. Opt. Soc. Am. 63, 305 (1973).
    [Crossref]

1974 (1)

1973 (3)

1967 (1)

1965 (1)

1964 (2)

W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964).
[Crossref]

W. R. Hunter, J. Phys. (Paris) 25, 154 (1964).
[Crossref]

1963 (1)

1953 (1)

S. Robin, C. R. Acad. Sci. (Paris) 236, 674 (1953).

1951 (1)

1939 (1)

Arakawa, E. T.

Bergmark, T.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Canfield, L. R.

Coulter, J. K.

Cox, J. T.

Fahlman, A.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Hamm, R. N.

Hamrin, K.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Hass, G.

Hedman, J.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Hunter, W. R.

Jacobus, C. F.

Jacobus, G. F.

Johansson, G.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Karlsson, S-E.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Lindberg, B.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Lindgren, I.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Madden, R. P.

Nordberg, R.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Nordling, C.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Ramsey, J. B.

Robin, S.

S. Robin, C. R. Acad. Sci. (Paris) 236, 674 (1953).

Siegbahn, K.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

Simon, I.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), p. 281.

Tousey, R.

Whang, U. S.

Williams, M. W.

C. R. Acad. Sci. (Paris) (1)

S. Robin, C. R. Acad. Sci. (Paris) 236, 674 (1953).

J. Opt. Soc. Am. (10)

J. Phys. (Paris) (1)

W. R. Hunter, J. Phys. (Paris) 25, 154 (1964).
[Crossref]

Other (3)

W. R. Hunter, U. S. Naval Research Laboratory, Washington, D. C.; (unpublished data).

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), p. 281.

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S-E. Karlsson, I. Lindgren, and B. Lindberg, ESCA: Atomic, Molecular and Solid State Structure studied by means of Electron Spectroscopy (Almquist and Wiksells, Uppsala, Sweden, 1967).

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Figures (2)

Fig. 1
Fig. 1

Calculated reflectance vs thickness at normal and 40° angle of incidence (upper left) and the relative errors in determining n and k as a function of thickness for iridium on a fused quartz substrate at 300 Å. The error calculations were made for nonpolarized flux, RA, and for perpendicularly and parallel polarized fluxes, RS and RP, respectively. The solid lines show the errors calculated using the angles of incidence 10° through 80° inclusive. The dashed lines show the errors calculated using angles of incidence of 40° through 80° inclusive.

Fig. 2
Fig. 2

Calculated reflectance vs thickness at normal and 40° angle of incidence (upper left) and the relative errors in determining n and k as a function of thickness for iridium on a glass substrate at 1200 Å. The error calculations were made for nonpolarized flux, RA, and for perpendicularly and parallel polarized fluxes, RS and RP, respectively. The solid lines show the errors calculated using the angles of incidence 10° through 80° inclusive. The dashed lines show the errors calculated using angles of incidence of 40° through 80° inclusive.

Tables (1)

Tables Icon

Table I Results of calculations showing the film thickness t, necessary to reduce errors of determining n and k by the reflectance-vs-angle-of-incidence method to 1% or less. The thicknesses were determined for nonpolarized n, and parallel-polarized p, light. T is the normal-incidence transmittance of a free-standing film of the corresponding thickness, and Th is the thickness necessary to reduce the transmittance of a free-standing film to 0.1% at normal incidence. β is the ratio of T/Th. Thicknesses are given in decimal parts of the incident wavelength, and transmittances in percent.