Abstract

We describe a computational method of determining the optical constants n(λ),k(λ) and the film thickness d from photometric R(λ),T(λ) and ellipsometric Ψ(λ),Δ(λ) data. Combinations of three or four of the measured quantities are compared using Newton-Raphson and Simplex techniques. The method is applied to thin films of gold and amorphous metallic alloys. The results are discussed.

© 1986 Optical Society of America

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  1. F. Abelès, M. L. Thèye, “Mèthode de Calcul des Constants Optiques des Couches Minces Absorbantes à partir de Measures de Rèflexion et de Transmission,” Surf. Sci. 325, 5 (1966).
  2. L. Ward, A. Nag, “A Theoretical Study of the Sensitivities of Some Normal Incidence Methods for Measuring the Optical Constants and Thicknesses of Thin Films,” Br. J. Appl. Phys. 18, 277 (1967).
    [CrossRef]
  3. P. O. Nilsson, “Determination of Optical Constants From Intensity Measurements at Normal Incidence,” Appl. Opt. 7, 435 (1968).
    [CrossRef] [PubMed]
  4. J. E. Nestell, R. W. Christy, “Derivation of Optical Constants of Metals From Thin-Film Measurements at Oblique Incidence,” Appl. Opt. 11, 643 (1972).
    [CrossRef] [PubMed]
  5. P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  6. L. Ward, A. Nag, L. C. Dixon, “Hill-Climbing Techniques as a Method of Calculating the Optical Constants and Thickness of a Thin Metallic Film,” J. Phys. D 2, 301 (1969).
    [CrossRef]
  7. A. Hjortsberg, “Determination of Optical Constants of Absorbing Materials Using Transmission and Reflection of Thin Films on Partially Metallized Substrates: Analysis of the New (T,Rm) Technique,” Appl. Opt. 20, 1254 (1981).
    [CrossRef] [PubMed]
  8. E. Elizalde, F. Rueda, “On the Determination of the Optical Constants n(λ) and k(λ) of Thin Supported Films,” Thin Solid Films 122, 45 (1984).
    [CrossRef]
  9. B. D. Cahan, R. F. Spanier, “A High Speed Precision Automatic Ellipsometer,” Surf. Sci. 16, 166 (1969).
    [CrossRef]
  10. D. E. Aspnes, A. A. Studna, “High Precision Scanning Ellipsometer,” Appl. Opt. 14, 220 (1975).
    [PubMed]
  11. R. Greef, “An Automatic Ellipsometer for Use in Electrochemical Investigations,” Rev. Sci. Instrum. 41, 532 (1970).
    [CrossRef]
  12. W. Umrath, “Schichdickenmessung nach Kiessig mit einem automatisch registrierenden Röntgengoniometer,” Z. Angew. Phys. 22, 406 (1967).
  13. D. E. Aspnes, H. G. Craighead, “Multiple Determination of the Optical Constants of Thin-film Coating Materials: a Rh Sequel,” Appl. Opt. 25, 1299 (1986).
    [CrossRef] [PubMed]
  14. J. Rivory, J. M. Frigerio, J. P. Rebouillat, “Contribution à la détermination de las structure électronique d’alliages métalliques amorphes Cu50Ze50 par Spectroscopie Optique,” J. Phys. Paris Lett. 42, L-481 (1981).
  15. F. Abelés, Prog. Opt. 2, 268 (1963); Phys. Thin Films 6, 151 (1971).
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1968).
  17. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955).
  18. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).
  19. H. Margeneau, G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1947).
  20. H. W. Bode, Network Analysis and Feedback Amplifier Design (Van Nostrand, New York, 1945).
  21. D. M. Roessler, “Kramers-Kronig Analysis of Reflection Data,” Br. J. Appl. Phys. 16, 1119 (1965).
    [CrossRef]
  22. M. L. Thèye, “Investigation of the Optical Properties of Au by Means of Thin Semitransparent Films,” Phys. Rev. B 2, 3060 (1970).
    [CrossRef]
  23. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), pp. 55–62.

1986 (1)

1984 (1)

E. Elizalde, F. Rueda, “On the Determination of the Optical Constants n(λ) and k(λ) of Thin Supported Films,” Thin Solid Films 122, 45 (1984).
[CrossRef]

1981 (2)

J. Rivory, J. M. Frigerio, J. P. Rebouillat, “Contribution à la détermination de las structure électronique d’alliages métalliques amorphes Cu50Ze50 par Spectroscopie Optique,” J. Phys. Paris Lett. 42, L-481 (1981).

A. Hjortsberg, “Determination of Optical Constants of Absorbing Materials Using Transmission and Reflection of Thin Films on Partially Metallized Substrates: Analysis of the New (T,Rm) Technique,” Appl. Opt. 20, 1254 (1981).
[CrossRef] [PubMed]

1975 (1)

1972 (2)

1970 (2)

M. L. Thèye, “Investigation of the Optical Properties of Au by Means of Thin Semitransparent Films,” Phys. Rev. B 2, 3060 (1970).
[CrossRef]

R. Greef, “An Automatic Ellipsometer for Use in Electrochemical Investigations,” Rev. Sci. Instrum. 41, 532 (1970).
[CrossRef]

1969 (2)

L. Ward, A. Nag, L. C. Dixon, “Hill-Climbing Techniques as a Method of Calculating the Optical Constants and Thickness of a Thin Metallic Film,” J. Phys. D 2, 301 (1969).
[CrossRef]

B. D. Cahan, R. F. Spanier, “A High Speed Precision Automatic Ellipsometer,” Surf. Sci. 16, 166 (1969).
[CrossRef]

1968 (1)

1967 (2)

W. Umrath, “Schichdickenmessung nach Kiessig mit einem automatisch registrierenden Röntgengoniometer,” Z. Angew. Phys. 22, 406 (1967).

L. Ward, A. Nag, “A Theoretical Study of the Sensitivities of Some Normal Incidence Methods for Measuring the Optical Constants and Thicknesses of Thin Films,” Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

1966 (1)

F. Abelès, M. L. Thèye, “Mèthode de Calcul des Constants Optiques des Couches Minces Absorbantes à partir de Measures de Rèflexion et de Transmission,” Surf. Sci. 325, 5 (1966).

1965 (1)

D. M. Roessler, “Kramers-Kronig Analysis of Reflection Data,” Br. J. Appl. Phys. 16, 1119 (1965).
[CrossRef]

1963 (1)

F. Abelés, Prog. Opt. 2, 268 (1963); Phys. Thin Films 6, 151 (1971).

Abelés, F.

F. Abelés, Prog. Opt. 2, 268 (1963); Phys. Thin Films 6, 151 (1971).

Abelès, F.

F. Abelès, M. L. Thèye, “Mèthode de Calcul des Constants Optiques des Couches Minces Absorbantes à partir de Measures de Rèflexion et de Transmission,” Surf. Sci. 325, 5 (1966).

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

Bode, H. W.

H. W. Bode, Network Analysis and Feedback Amplifier Design (Van Nostrand, New York, 1945).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1968).

Cahan, B. D.

B. D. Cahan, R. F. Spanier, “A High Speed Precision Automatic Ellipsometer,” Surf. Sci. 16, 166 (1969).
[CrossRef]

Christy, R. W.

Craighead, H. G.

Dixon, L. C.

L. Ward, A. Nag, L. C. Dixon, “Hill-Climbing Techniques as a Method of Calculating the Optical Constants and Thickness of a Thin Metallic Film,” J. Phys. D 2, 301 (1969).
[CrossRef]

Elizalde, E.

E. Elizalde, F. Rueda, “On the Determination of the Optical Constants n(λ) and k(λ) of Thin Supported Films,” Thin Solid Films 122, 45 (1984).
[CrossRef]

Frigerio, J. M.

J. Rivory, J. M. Frigerio, J. P. Rebouillat, “Contribution à la détermination de las structure électronique d’alliages métalliques amorphes Cu50Ze50 par Spectroscopie Optique,” J. Phys. Paris Lett. 42, L-481 (1981).

Greef, R.

R. Greef, “An Automatic Ellipsometer for Use in Electrochemical Investigations,” Rev. Sci. Instrum. 41, 532 (1970).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), pp. 55–62.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955).

Hjortsberg, A.

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Margeneau, H.

H. Margeneau, G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1947).

Murphy, G. M.

H. Margeneau, G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1947).

Nag, A.

L. Ward, A. Nag, L. C. Dixon, “Hill-Climbing Techniques as a Method of Calculating the Optical Constants and Thickness of a Thin Metallic Film,” J. Phys. D 2, 301 (1969).
[CrossRef]

L. Ward, A. Nag, “A Theoretical Study of the Sensitivities of Some Normal Incidence Methods for Measuring the Optical Constants and Thicknesses of Thin Films,” Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

Nestell, J. E.

Nilsson, P. O.

Rebouillat, J. P.

J. Rivory, J. M. Frigerio, J. P. Rebouillat, “Contribution à la détermination de las structure électronique d’alliages métalliques amorphes Cu50Ze50 par Spectroscopie Optique,” J. Phys. Paris Lett. 42, L-481 (1981).

Rivory, J.

J. Rivory, J. M. Frigerio, J. P. Rebouillat, “Contribution à la détermination de las structure électronique d’alliages métalliques amorphes Cu50Ze50 par Spectroscopie Optique,” J. Phys. Paris Lett. 42, L-481 (1981).

Roessler, D. M.

D. M. Roessler, “Kramers-Kronig Analysis of Reflection Data,” Br. J. Appl. Phys. 16, 1119 (1965).
[CrossRef]

Rueda, F.

E. Elizalde, F. Rueda, “On the Determination of the Optical Constants n(λ) and k(λ) of Thin Supported Films,” Thin Solid Films 122, 45 (1984).
[CrossRef]

Spanier, R. F.

B. D. Cahan, R. F. Spanier, “A High Speed Precision Automatic Ellipsometer,” Surf. Sci. 16, 166 (1969).
[CrossRef]

Studna, A. A.

Thèye, M. L.

M. L. Thèye, “Investigation of the Optical Properties of Au by Means of Thin Semitransparent Films,” Phys. Rev. B 2, 3060 (1970).
[CrossRef]

F. Abelès, M. L. Thèye, “Mèthode de Calcul des Constants Optiques des Couches Minces Absorbantes à partir de Measures de Rèflexion et de Transmission,” Surf. Sci. 325, 5 (1966).

Umrath, W.

W. Umrath, “Schichdickenmessung nach Kiessig mit einem automatisch registrierenden Röntgengoniometer,” Z. Angew. Phys. 22, 406 (1967).

Ward, L.

L. Ward, A. Nag, L. C. Dixon, “Hill-Climbing Techniques as a Method of Calculating the Optical Constants and Thickness of a Thin Metallic Film,” J. Phys. D 2, 301 (1969).
[CrossRef]

L. Ward, A. Nag, “A Theoretical Study of the Sensitivities of Some Normal Incidence Methods for Measuring the Optical Constants and Thicknesses of Thin Films,” Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1968).

Appl. Opt. (5)

Br. J. Appl. Phys. (2)

D. M. Roessler, “Kramers-Kronig Analysis of Reflection Data,” Br. J. Appl. Phys. 16, 1119 (1965).
[CrossRef]

L. Ward, A. Nag, “A Theoretical Study of the Sensitivities of Some Normal Incidence Methods for Measuring the Optical Constants and Thicknesses of Thin Films,” Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

J. Phys. D (1)

L. Ward, A. Nag, L. C. Dixon, “Hill-Climbing Techniques as a Method of Calculating the Optical Constants and Thickness of a Thin Metallic Film,” J. Phys. D 2, 301 (1969).
[CrossRef]

J. Phys. Paris Lett. (1)

J. Rivory, J. M. Frigerio, J. P. Rebouillat, “Contribution à la détermination de las structure électronique d’alliages métalliques amorphes Cu50Ze50 par Spectroscopie Optique,” J. Phys. Paris Lett. 42, L-481 (1981).

Phys. Rev. B (2)

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[CrossRef]

M. L. Thèye, “Investigation of the Optical Properties of Au by Means of Thin Semitransparent Films,” Phys. Rev. B 2, 3060 (1970).
[CrossRef]

Prog. Opt. (1)

F. Abelés, Prog. Opt. 2, 268 (1963); Phys. Thin Films 6, 151 (1971).

Rev. Sci. Instrum. (1)

R. Greef, “An Automatic Ellipsometer for Use in Electrochemical Investigations,” Rev. Sci. Instrum. 41, 532 (1970).
[CrossRef]

Surf. Sci. (2)

F. Abelès, M. L. Thèye, “Mèthode de Calcul des Constants Optiques des Couches Minces Absorbantes à partir de Measures de Rèflexion et de Transmission,” Surf. Sci. 325, 5 (1966).

B. D. Cahan, R. F. Spanier, “A High Speed Precision Automatic Ellipsometer,” Surf. Sci. 16, 166 (1969).
[CrossRef]

Thin Solid Films (1)

E. Elizalde, F. Rueda, “On the Determination of the Optical Constants n(λ) and k(λ) of Thin Supported Films,” Thin Solid Films 122, 45 (1984).
[CrossRef]

Z. Angew. Phys. (1)

W. Umrath, “Schichdickenmessung nach Kiessig mit einem automatisch registrierenden Röntgengoniometer,” Z. Angew. Phys. 22, 406 (1967).

Other (6)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1968).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

H. Margeneau, G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1947).

H. W. Bode, Network Analysis and Feedback Amplifier Design (Van Nostrand, New York, 1945).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), pp. 55–62.

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