Abstract

We present a method of determining optical constants n and k of a thin film using only the reflectance R(ω) curve (normal incidence reflectance spectroscopy). The method is based on the simultaneous use of Fresnel laws and dispersion relations between n and k of the film, via an iterative process. To illustrate the method, optical constants in the VUV of a film grown on InP were determined. A second example with a SnO2 film shows how the method can reduce the effect of experimental errors when two sets of spectroscopic data are available.

© 1990 Optical Society of America

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  1. P. Drude, “Ueber die Phasenanderung des Lichtes bei der Reflexion an Metallen,” Wied. Ann. 51, 77–104 (1894).
  2. D. D. Heavens, Optical Properties of Thin Solid Films (Butter-worth, London, 1955).
  3. S. G. Tomlin, “Optical reflexion and transmission formulae for thin films,” J. Phys. D1, 1667–1671(1968).
  4. H. Murmann, “Optical constants of transparent silver,” Z. fur Phys. 80, 161–177 (1933).
    [CrossRef]
  5. F. Abeles, M. L. Theye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir de mesures de réflexion et de transmission,” Surface Sci. 5, 325–331 (1966).
    [CrossRef]
  6. R. E. Denton, R. D. Campbell, S. G. Tomlin, “The determination of optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D5, 852–863 (1972).
  7. K. Truszkowska, T. Borowicz, C. Weseolowska, “Algorithm for Determining the Optical Constants of Thin Films,” Appl. Opt. 17, 1579–1581 (1978).
    [CrossRef] [PubMed]
  8. R. T. Phillips, “A numerical method for determining the complex refractive index from reflectance and transmittance of supported thin films,” J. Phys. D16, 489–497 (1983).
  9. W. E. Case, “Algebraic Method for Extracting Thin-Film Optical Parameters from Spectrophotometric Measurements,” Appl. Opt. 22, 1832–1836 (1983).
    [CrossRef] [PubMed]
  10. T. C. Paulick, “Inversion of Normal-Incidence (R,T) Measurements to Obtain n + ik for Thin Films,” Appl. Opt. 25, 562–564 (1986).
    [CrossRef] [PubMed]
  11. F. Demichelis, G. Kaniadakis, A. Tagliaferro, E. Tresso, “New Approach to Optical Analysis of Absorbing Thin Solid Films,” Appl. Opt. 26, 1737–1740 (1987).
    [CrossRef] [PubMed]
  12. W. R. Hunter, G. Hass, “Thickness of Absorbing Films Necessary to Measure Their Optical Constants Using the Reflectance-vs-Angle-of-Incidence Method,” J. Opt. Soc. Amer. 64, 429–433 (1974).
    [CrossRef]
  13. L. Ward, “The accuracy of some mixed photometric and polarization functions in the determination of the optical constants of the films,” J. Phys. D15, 1781–1790 (1982); “A survey of the accuracies of some methods for the determination of the optical constants of thin films,” Optica Acta 32, 155–167 (1985).
  14. A. Hjortzberg, “Determination of Optical Constants of Absorbing Materials Using Transmission and Reflection of Thin Films on Partially Metallized Substrates,” Appl. Opt. 20, 1254–1263 (1981).
    [CrossRef]
  15. C. L. Nagendra, G. K. M. Thutupallis, “Optical Constants of Absorbing Materials: A New Approach,” Appl. Opt. 20, 2747–2753 (1981).
    [CrossRef] [PubMed]
  16. L. Vriens, W. Rippens, “Optical Constants of Absorbing Films on a Substrate,” Appl. Opt. 22, 4105–4110 (1983).
    [CrossRef] [PubMed]
  17. R. M. Azzam, N. Baskara, Ellipsometry and Polarized light (North-Holland, Amsterdam, 1977).
  18. K. Kozima, W. Suetaka, P. N. Schatz, “Optical Constants of Thin Films by Kramers-Kronig Method,” J. Opt. Soc. Amer. 56, 181–184 (1966).
    [CrossRef]
  19. P. O. Nilsson, “Determination of Optical Constants from Intensity Measurements at Normal Incidence,” Appl. Opt. 7, 435–442 (1968).
    [CrossRef] [PubMed]
  20. R. D. Bringans, “The determination of optical constants of thin films from measurements of normal incidence reflectance and transmittance,” J. Phys. D 10, 1855–1861 (1977).
    [CrossRef]
  21. K. F. Palmer, M. Z. Williams, “Determination of the Optical Constants of a Thin Film from Transmittance Measurements of a Single Film Thickness,” Appl. Opt. 24, 1788–1798 (1985).
    [CrossRef] [PubMed]
  22. J. S. Plaskett, P. N. Schatz, “On the Kramers-Kronig method of interpreting reflection data taken through a transparent window,” J. Opt. Chem. Physics 38, 612–617 (1963).
  23. H. W. Verleur, “Determination of Optical Constants From Reflectance or Transmittance Measurements on Bulk Crystals of Thin Films,” J. Opt. Soc. Amer. 58, 1356–1364 (1968).
    [CrossRef]
  24. H. M. Liddell, “Theoretical determination of the optical constants of weakly absorbing thin films,” J. Phys. D 7, 1588–1596 (1974).
    [CrossRef]
  25. J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of Optical Constants of Thin Film Coating Materials Based on Inverse Synthesis,” Appl. Opt. 22, 3191–3200 (1983).
    [CrossRef] [PubMed]
  26. M. Moskovitz, P. J. Ostrowski, “Application of classical oscillator Functions to the Simultaneous Determination of Substrate Optical Constants of Film Thickness from ellipsometric Measurements,” J. Chem. Soc.-Far. Trans. II 71, 387–392 (1975).
  27. J. Roth, B. Rao, M. J. Dignam, “Application to the causality condition to thin film spectroscopy,” J. Chem. Soc.-Far. Trans. II 71, 86–94 (1975).
  28. W. J. Plieth, K. Naegele, “Kramers-Kronig analysis for the determination of the optical constants of thin surface film: theory and application to platinium oxyde film,” Surf. Sci. 50, 53–76 (1976).
    [CrossRef]
  29. L. I. Alperovich, V. N. Pushkarev, “Determination of thin film optical constants using reflection spectra by Kramers-Kronig method,” Opt. and Spectrosc. 47, 516–518 (1979).
  30. Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
    [CrossRef]
  31. G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).
  32. G. Lévêque, C. G. Olson, D. W. Lynch, “Optical anisotropy in the VUV range,” J. de Phys. 45, 1699–1706 (1984).

1987 (2)

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

F. Demichelis, G. Kaniadakis, A. Tagliaferro, E. Tresso, “New Approach to Optical Analysis of Absorbing Thin Solid Films,” Appl. Opt. 26, 1737–1740 (1987).
[CrossRef] [PubMed]

1986 (2)

T. C. Paulick, “Inversion of Normal-Incidence (R,T) Measurements to Obtain n + ik for Thin Films,” Appl. Opt. 25, 562–564 (1986).
[CrossRef] [PubMed]

Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
[CrossRef]

1985 (1)

1984 (1)

G. Lévêque, C. G. Olson, D. W. Lynch, “Optical anisotropy in the VUV range,” J. de Phys. 45, 1699–1706 (1984).

1983 (4)

1982 (1)

L. Ward, “The accuracy of some mixed photometric and polarization functions in the determination of the optical constants of the films,” J. Phys. D15, 1781–1790 (1982); “A survey of the accuracies of some methods for the determination of the optical constants of thin films,” Optica Acta 32, 155–167 (1985).

1981 (2)

1979 (1)

L. I. Alperovich, V. N. Pushkarev, “Determination of thin film optical constants using reflection spectra by Kramers-Kronig method,” Opt. and Spectrosc. 47, 516–518 (1979).

1978 (1)

1977 (1)

R. D. Bringans, “The determination of optical constants of thin films from measurements of normal incidence reflectance and transmittance,” J. Phys. D 10, 1855–1861 (1977).
[CrossRef]

1976 (1)

W. J. Plieth, K. Naegele, “Kramers-Kronig analysis for the determination of the optical constants of thin surface film: theory and application to platinium oxyde film,” Surf. Sci. 50, 53–76 (1976).
[CrossRef]

1975 (2)

M. Moskovitz, P. J. Ostrowski, “Application of classical oscillator Functions to the Simultaneous Determination of Substrate Optical Constants of Film Thickness from ellipsometric Measurements,” J. Chem. Soc.-Far. Trans. II 71, 387–392 (1975).

J. Roth, B. Rao, M. J. Dignam, “Application to the causality condition to thin film spectroscopy,” J. Chem. Soc.-Far. Trans. II 71, 86–94 (1975).

1974 (2)

H. M. Liddell, “Theoretical determination of the optical constants of weakly absorbing thin films,” J. Phys. D 7, 1588–1596 (1974).
[CrossRef]

W. R. Hunter, G. Hass, “Thickness of Absorbing Films Necessary to Measure Their Optical Constants Using the Reflectance-vs-Angle-of-Incidence Method,” J. Opt. Soc. Amer. 64, 429–433 (1974).
[CrossRef]

1972 (1)

R. E. Denton, R. D. Campbell, S. G. Tomlin, “The determination of optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D5, 852–863 (1972).

1968 (3)

H. W. Verleur, “Determination of Optical Constants From Reflectance or Transmittance Measurements on Bulk Crystals of Thin Films,” J. Opt. Soc. Amer. 58, 1356–1364 (1968).
[CrossRef]

S. G. Tomlin, “Optical reflexion and transmission formulae for thin films,” J. Phys. D1, 1667–1671(1968).

P. O. Nilsson, “Determination of Optical Constants from Intensity Measurements at Normal Incidence,” Appl. Opt. 7, 435–442 (1968).
[CrossRef] [PubMed]

1966 (2)

F. Abeles, M. L. Theye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir de mesures de réflexion et de transmission,” Surface Sci. 5, 325–331 (1966).
[CrossRef]

K. Kozima, W. Suetaka, P. N. Schatz, “Optical Constants of Thin Films by Kramers-Kronig Method,” J. Opt. Soc. Amer. 56, 181–184 (1966).
[CrossRef]

1963 (1)

J. S. Plaskett, P. N. Schatz, “On the Kramers-Kronig method of interpreting reflection data taken through a transparent window,” J. Opt. Chem. Physics 38, 612–617 (1963).

1933 (1)

H. Murmann, “Optical constants of transparent silver,” Z. fur Phys. 80, 161–177 (1933).
[CrossRef]

1894 (1)

P. Drude, “Ueber die Phasenanderung des Lichtes bei der Reflexion an Metallen,” Wied. Ann. 51, 77–104 (1894).

Abeles, F.

F. Abeles, M. L. Theye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir de mesures de réflexion et de transmission,” Surface Sci. 5, 325–331 (1966).
[CrossRef]

Alperovich, L. I.

L. I. Alperovich, V. N. Pushkarev, “Determination of thin film optical constants using reflection spectra by Kramers-Kronig method,” Opt. and Spectrosc. 47, 516–518 (1979).

Azzam, R. M.

R. M. Azzam, N. Baskara, Ellipsometry and Polarized light (North-Holland, Amsterdam, 1977).

Baskara, N.

R. M. Azzam, N. Baskara, Ellipsometry and Polarized light (North-Holland, Amsterdam, 1977).

Bergignat, E.

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
[CrossRef]

Borowicz, T.

Bringans, R. D.

R. D. Bringans, “The determination of optical constants of thin films from measurements of normal incidence reflectance and transmittance,” J. Phys. D 10, 1855–1861 (1977).
[CrossRef]

Campbell, R. D.

R. E. Denton, R. D. Campbell, S. G. Tomlin, “The determination of optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D5, 852–863 (1972).

Case, W. E.

Commerce, B.

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
[CrossRef]

Demichelis, F.

Denton, R. E.

R. E. Denton, R. D. Campbell, S. G. Tomlin, “The determination of optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D5, 852–863 (1972).

Dignam, M. J.

J. Roth, B. Rao, M. J. Dignam, “Application to the causality condition to thin film spectroscopy,” J. Chem. Soc.-Far. Trans. II 71, 86–94 (1975).

Dobrowolski, J. A.

Drude, P.

P. Drude, “Ueber die Phasenanderung des Lichtes bei der Reflexion an Metallen,” Wied. Ann. 51, 77–104 (1894).

Froment, M.

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Hass, G.

W. R. Hunter, G. Hass, “Thickness of Absorbing Films Necessary to Measure Their Optical Constants Using the Reflectance-vs-Angle-of-Incidence Method,” J. Opt. Soc. Amer. 64, 429–433 (1974).
[CrossRef]

Heavens, D. D.

D. D. Heavens, Optical Properties of Thin Solid Films (Butter-worth, London, 1955).

Hjortzberg, A.

Ho, F. C.

Hollinger, G.

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
[CrossRef]

Hunter, W. R.

W. R. Hunter, G. Hass, “Thickness of Absorbing Films Necessary to Measure Their Optical Constants Using the Reflectance-vs-Angle-of-Incidence Method,” J. Opt. Soc. Amer. 64, 429–433 (1974).
[CrossRef]

Joseph, J.

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
[CrossRef]

Kaniadakis, G.

Kozima, K.

K. Kozima, W. Suetaka, P. N. Schatz, “Optical Constants of Thin Films by Kramers-Kronig Method,” J. Opt. Soc. Amer. 56, 181–184 (1966).
[CrossRef]

Lévêque, G.

G. Lévêque, C. G. Olson, D. W. Lynch, “Optical anisotropy in the VUV range,” J. de Phys. 45, 1699–1706 (1984).

Liddell, H. M.

H. M. Liddell, “Theoretical determination of the optical constants of weakly absorbing thin films,” J. Phys. D 7, 1588–1596 (1974).
[CrossRef]

Lynch, D. W.

G. Lévêque, C. G. Olson, D. W. Lynch, “Optical anisotropy in the VUV range,” J. de Phys. 45, 1699–1706 (1984).

Moskovitz, M.

M. Moskovitz, P. J. Ostrowski, “Application of classical oscillator Functions to the Simultaneous Determination of Substrate Optical Constants of Film Thickness from ellipsometric Measurements,” J. Chem. Soc.-Far. Trans. II 71, 387–392 (1975).

Murmann, H.

H. Murmann, “Optical constants of transparent silver,” Z. fur Phys. 80, 161–177 (1933).
[CrossRef]

Naegele, K.

W. J. Plieth, K. Naegele, “Kramers-Kronig analysis for the determination of the optical constants of thin surface film: theory and application to platinium oxyde film,” Surf. Sci. 50, 53–76 (1976).
[CrossRef]

Nagendra, C. L.

Nilsson, P. O.

Olson, C. G.

G. Lévêque, C. G. Olson, D. W. Lynch, “Optical anisotropy in the VUV range,” J. de Phys. 45, 1699–1706 (1984).

Ostrowski, P. J.

M. Moskovitz, P. J. Ostrowski, “Application of classical oscillator Functions to the Simultaneous Determination of Substrate Optical Constants of Film Thickness from ellipsometric Measurements,” J. Chem. Soc.-Far. Trans. II 71, 387–392 (1975).

Palmer, K. F.

Paulick, T. C.

Phillips, R. T.

R. T. Phillips, “A numerical method for determining the complex refractive index from reflectance and transmittance of supported thin films,” J. Phys. D16, 489–497 (1983).

Plaskett, J. S.

J. S. Plaskett, P. N. Schatz, “On the Kramers-Kronig method of interpreting reflection data taken through a transparent window,” J. Opt. Chem. Physics 38, 612–617 (1963).

Plieth, W. J.

W. J. Plieth, K. Naegele, “Kramers-Kronig analysis for the determination of the optical constants of thin surface film: theory and application to platinium oxyde film,” Surf. Sci. 50, 53–76 (1976).
[CrossRef]

Pushkarev, V. N.

L. I. Alperovich, V. N. Pushkarev, “Determination of thin film optical constants using reflection spectra by Kramers-Kronig method,” Opt. and Spectrosc. 47, 516–518 (1979).

Rao, B.

J. Roth, B. Rao, M. J. Dignam, “Application to the causality condition to thin film spectroscopy,” J. Chem. Soc.-Far. Trans. II 71, 86–94 (1975).

Rippens, W.

Robach, Y.

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
[CrossRef]

Roth, J.

J. Roth, B. Rao, M. J. Dignam, “Application to the causality condition to thin film spectroscopy,” J. Chem. Soc.-Far. Trans. II 71, 86–94 (1975).

Schatz, P. N.

K. Kozima, W. Suetaka, P. N. Schatz, “Optical Constants of Thin Films by Kramers-Kronig Method,” J. Opt. Soc. Amer. 56, 181–184 (1966).
[CrossRef]

J. S. Plaskett, P. N. Schatz, “On the Kramers-Kronig method of interpreting reflection data taken through a transparent window,” J. Opt. Chem. Physics 38, 612–617 (1963).

Suetaka, W.

K. Kozima, W. Suetaka, P. N. Schatz, “Optical Constants of Thin Films by Kramers-Kronig Method,” J. Opt. Soc. Amer. 56, 181–184 (1966).
[CrossRef]

Tagliaferro, A.

Theye, M. L.

F. Abeles, M. L. Theye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir de mesures de réflexion et de transmission,” Surface Sci. 5, 325–331 (1966).
[CrossRef]

Thutupallis, G. K. M.

Tomlin, S. G.

R. E. Denton, R. D. Campbell, S. G. Tomlin, “The determination of optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D5, 852–863 (1972).

S. G. Tomlin, “Optical reflexion and transmission formulae for thin films,” J. Phys. D1, 1667–1671(1968).

Tresso, E.

Truszkowska, K.

Verleur, H. W.

H. W. Verleur, “Determination of Optical Constants From Reflectance or Transmittance Measurements on Bulk Crystals of Thin Films,” J. Opt. Soc. Amer. 58, 1356–1364 (1968).
[CrossRef]

Viktorovitch, P.

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Vriens, L.

Waldorf, A.

Ward, L.

L. Ward, “The accuracy of some mixed photometric and polarization functions in the determination of the optical constants of the films,” J. Phys. D15, 1781–1790 (1982); “A survey of the accuracies of some methods for the determination of the optical constants of thin films,” Optica Acta 32, 155–167 (1985).

Weseolowska, C.

Williams, M. Z.

Appl. Opt. (10)

P. O. Nilsson, “Determination of Optical Constants from Intensity Measurements at Normal Incidence,” Appl. Opt. 7, 435–442 (1968).
[CrossRef] [PubMed]

K. Truszkowska, T. Borowicz, C. Weseolowska, “Algorithm for Determining the Optical Constants of Thin Films,” Appl. Opt. 17, 1579–1581 (1978).
[CrossRef] [PubMed]

A. Hjortzberg, “Determination of Optical Constants of Absorbing Materials Using Transmission and Reflection of Thin Films on Partially Metallized Substrates,” Appl. Opt. 20, 1254–1263 (1981).
[CrossRef]

C. L. Nagendra, G. K. M. Thutupallis, “Optical Constants of Absorbing Materials: A New Approach,” Appl. Opt. 20, 2747–2753 (1981).
[CrossRef] [PubMed]

W. E. Case, “Algebraic Method for Extracting Thin-Film Optical Parameters from Spectrophotometric Measurements,” Appl. Opt. 22, 1832–1836 (1983).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of Optical Constants of Thin Film Coating Materials Based on Inverse Synthesis,” Appl. Opt. 22, 3191–3200 (1983).
[CrossRef] [PubMed]

L. Vriens, W. Rippens, “Optical Constants of Absorbing Films on a Substrate,” Appl. Opt. 22, 4105–4110 (1983).
[CrossRef] [PubMed]

K. F. Palmer, M. Z. Williams, “Determination of the Optical Constants of a Thin Film from Transmittance Measurements of a Single Film Thickness,” Appl. Opt. 24, 1788–1798 (1985).
[CrossRef] [PubMed]

T. C. Paulick, “Inversion of Normal-Incidence (R,T) Measurements to Obtain n + ik for Thin Films,” Appl. Opt. 25, 562–564 (1986).
[CrossRef] [PubMed]

F. Demichelis, G. Kaniadakis, A. Tagliaferro, E. Tresso, “New Approach to Optical Analysis of Absorbing Thin Solid Films,” Appl. Opt. 26, 1737–1740 (1987).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Y. Robach, J. Joseph, E. Bergignat, B. Commerce, G. Hollinger, “New native oxyde of InP with improved electrical interface properties,” Appl. Phys. Lett. 49, 1281–1283 (1986).
[CrossRef]

J. Chem. Soc.-Far. Trans. II (2)

M. Moskovitz, P. J. Ostrowski, “Application of classical oscillator Functions to the Simultaneous Determination of Substrate Optical Constants of Film Thickness from ellipsometric Measurements,” J. Chem. Soc.-Far. Trans. II 71, 387–392 (1975).

J. Roth, B. Rao, M. J. Dignam, “Application to the causality condition to thin film spectroscopy,” J. Chem. Soc.-Far. Trans. II 71, 86–94 (1975).

J. de Phys. (1)

G. Lévêque, C. G. Olson, D. W. Lynch, “Optical anisotropy in the VUV range,” J. de Phys. 45, 1699–1706 (1984).

J. Opt. Chem. Physics (1)

J. S. Plaskett, P. N. Schatz, “On the Kramers-Kronig method of interpreting reflection data taken through a transparent window,” J. Opt. Chem. Physics 38, 612–617 (1963).

J. Opt. Soc. Amer. (3)

H. W. Verleur, “Determination of Optical Constants From Reflectance or Transmittance Measurements on Bulk Crystals of Thin Films,” J. Opt. Soc. Amer. 58, 1356–1364 (1968).
[CrossRef]

K. Kozima, W. Suetaka, P. N. Schatz, “Optical Constants of Thin Films by Kramers-Kronig Method,” J. Opt. Soc. Amer. 56, 181–184 (1966).
[CrossRef]

W. R. Hunter, G. Hass, “Thickness of Absorbing Films Necessary to Measure Their Optical Constants Using the Reflectance-vs-Angle-of-Incidence Method,” J. Opt. Soc. Amer. 64, 429–433 (1974).
[CrossRef]

J. Phys (1)

R. T. Phillips, “A numerical method for determining the complex refractive index from reflectance and transmittance of supported thin films,” J. Phys. D16, 489–497 (1983).

J. Phys. (3)

L. Ward, “The accuracy of some mixed photometric and polarization functions in the determination of the optical constants of the films,” J. Phys. D15, 1781–1790 (1982); “A survey of the accuracies of some methods for the determination of the optical constants of thin films,” Optica Acta 32, 155–167 (1985).

R. E. Denton, R. D. Campbell, S. G. Tomlin, “The determination of optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D5, 852–863 (1972).

S. G. Tomlin, “Optical reflexion and transmission formulae for thin films,” J. Phys. D1, 1667–1671(1968).

J. Phys. D (2)

R. D. Bringans, “The determination of optical constants of thin films from measurements of normal incidence reflectance and transmittance,” J. Phys. D 10, 1855–1861 (1977).
[CrossRef]

H. M. Liddell, “Theoretical determination of the optical constants of weakly absorbing thin films,” J. Phys. D 7, 1588–1596 (1974).
[CrossRef]

J. Vac. Sci. Technol. (1)

G. Hollinger, J. Joseph, Y. Robach, E. Bergignat, B. Commerce, P. Viktorovitch, M. Froment, “On the chemistry of passivated oxide-InP interface,” J. Vac. Sci. Technol. B5, 1108–1112 (1987).

Opt. and Spectrosc. (1)

L. I. Alperovich, V. N. Pushkarev, “Determination of thin film optical constants using reflection spectra by Kramers-Kronig method,” Opt. and Spectrosc. 47, 516–518 (1979).

Surf. Sci. (1)

W. J. Plieth, K. Naegele, “Kramers-Kronig analysis for the determination of the optical constants of thin surface film: theory and application to platinium oxyde film,” Surf. Sci. 50, 53–76 (1976).
[CrossRef]

Surface Sci. (1)

F. Abeles, M. L. Theye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir de mesures de réflexion et de transmission,” Surface Sci. 5, 325–331 (1966).
[CrossRef]

Wied. Ann. (1)

P. Drude, “Ueber die Phasenanderung des Lichtes bei der Reflexion an Metallen,” Wied. Ann. 51, 77–104 (1894).

Z. fur Phys. (1)

H. Murmann, “Optical constants of transparent silver,” Z. fur Phys. 80, 161–177 (1933).
[CrossRef]

Other (2)

D. D. Heavens, Optical Properties of Thin Solid Films (Butter-worth, London, 1955).

R. M. Azzam, N. Baskara, Ellipsometry and Polarized light (North-Holland, Amsterdam, 1977).

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Figures (8)

Fig. 1
Fig. 1

Representation of the film-substrate system. Definition of the symbols used in Eqs. (1) and (2).

Fig. 2
Fig. 2

Vector diagram corresponding to a transparent film of index N on a transparent substrate of index Ns in the two cases N < N s ( i . e . , r 1 2 < r 2 2 ), and N > N s, with 2δ = 4πNd = 2ω/c Nd.

Fig. 3
Fig. 3

Plot of the contours of constant normal incidence reflectance R(n,k) (solid lines) and constant phase shift θR (dashed lines) of a thin film (index Ñ = n + ik, thickness d = 220 Å) on a substrate (ns = 0.742, ks = 1.015) at hv = 9.5 eV).

Fig. 4
Fig. 4

Example of surface representing the normal incidence reflectance solutions R(n,k,ω) = Rexp(ω). The dotted line represents the solution obtained when the dispersion relations kn are introduced.

Fig. 5
Fig. 5

Normal incidence reflectance of InP and InP + InPO4 film (thickness d = 220 Å).

Fig. 6
Fig. 6

Real part n and imaginary part k of the refractive index Ñ of the InPO4 film as deduced from our iterative calculation.

Fig. 7
Fig. 7

Normal incidence reflectance R and transmittance T of a SnO2 film (thickness d = 4200 Å) on silica. The heavy lines represent the experimental data; the thinner lines represent the best fit by our iterative method. Interference order 1 = (2Nd/λ) are indicated, X refers to the point where r1 = r2.

Fig. 8
Fig. 8

Real part n and imaginary part k of the refractive index Ñ of the SnO2 film. Thin lines are deduced from Rexp and Texp data by simple inversion of the Fresnel laws. Dots represent values of n deduced from the positions of the interference extrema of R. The heavy lines are the result of our one-way iterative treatment.

Equations (13)

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θ T ( ω ) = - ω π 0 ln T ( ω ) d ω ω 2 - ω 2 ,
R = ρ ˜ 2 , ρ ˜ = r ˜ 1 + r ˜ 2 e ˜ 2 1 + r ˜ 1 r ˜ 2 e 2
T = n s τ ˜ 2 , τ ˜ = t ˜ 1 t ˜ 2 e ˜ 1 + r ˜ 1 r ˜ 2 e ˜ 2
r ˜ 1 = 1 - N ˜ 1 + N ˜             t ˜ 1 = 2 1 + N ˜ r ˜ 2 = N ˜ - N ˜ s N ˜ + N ˜ s             t ˜ 2 = 2 N ˜ N ˜ + N ˜ s e ˜ = exp ( i 2 π λ N ˜ d ) ,
θ R ( ω ) = - ω π 0 ln R ( ω ) d ω ω 2 - ω 2 + 2 j arctan ω - a j b j ,
θ R = θ B - θ A .
{ n = 1 + 2 π 0 ω k ( ω ) d ω ω 2 - ω 2 k = - 2 ω π 0 n ( ω ) d ω ω 2 - ω 2 .
{ n = 1 + 1 π ω 0 d [ ω k ( ω ) ] d ω ln | ω + ω ω - ω | d ω k = - 1 π 0 d [ n ( ω ) ] d ω ln | ω + ω ω - ω | d ω ,
δ n = ( R exp - R calc ) R n ( R n ) 2 + ( R k ) 2 δ k = ( R exp - R calc ) R k ( R n ) 2 + ( R k ) 2
{ n 1 k 2 k 1 n 2
N ˜ 3 = ½ [ ( n 1 + n 2 ) + i ( k 1 + k 2 ) ]
n = l λ m 2 d ,
k 1 = k 0 + δ k n 2 .

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