Abstract

A previously presented method of measuring simultaneously both the complex refractive index and thickness of a thin film is shown to work successfully on a variety of thin films. The reliability of the optical constants is shown both by comparing their repeatability with several different methods and by comparison of the calculated and measured reflectance from the film as a function of angle of incidence. The computer-inversion method is used to show that a thin inhomogeneous film can usually be approximated by one homogeneous film. A method of determining the anisotropy of a thin film is presented that compares the complex index determined from perpendicular polarization measurements to that determined from parallel polarization measurements.

© 1977 Optical Society of America

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References

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  1. Handbook of Thin Film Technology, edited by L. I. Maissel and R. Glang (McGraw-Hill, New York, 1970).
  2. H. E. Bennett and J. M. Bennett, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1967), Vol. 4,pp. 1–96.
  3. O. S. Heavens, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1964), Vol. 2, p. 193.
  4. J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 60, 224 (1970).
    [Crossref]
  5. W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
    [Crossref]
  6. P. Rouard and P. Bousquet, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1965), Vol. 5, pp. 161ff.
  7. W. N. Hansen, J. Opt. Soc. Amn. 63, 793 (1973).
    [Crossref]
  8. W. J. Anderson and W. N. Hansen, Appl. Opt. 12, 1038 (1973).
    [Crossref] [PubMed]
  9. H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
    [Crossref]
  10. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [Crossref]
  11. J. E. Davey and T. Pankey, J. Appl. Phys. 9, 359 (1965).
  12. E. David, Z. Phys. 114, 389 (1939).
    [Crossref]
  13. F. Abelès, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1971), Vol. 6, pp. 170 ff.
  14. G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963).
    [Crossref]
  15. N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
    [Crossref]
  16. W. N. Hansen, J. Opt. Soc. Am. 58, 380 (1968).
    [Crossref]
  17. R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
    [Crossref]
  18. T. M. Donovan, W. E. Spicer, J. M. Bennett, and E. J. Ashley, Phys. Rev. B 2, 397 (1970).
    [Crossref]
  19. D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).
    [Crossref]
  20. T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 62, 634 (1972).
    [Crossref]
  21. P. Bousquet, Ann. Phys. (Paris) 2, 163 (1957).

1973 (2)

1972 (2)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 62, 634 (1972).
[Crossref]

1970 (2)

T. M. Donovan, W. E. Spicer, J. M. Bennett, and E. J. Ashley, Phys. Rev. B 2, 397 (1970).
[Crossref]

J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 60, 224 (1970).
[Crossref]

1968 (1)

1967 (1)

N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
[Crossref]

1966 (1)

R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
[Crossref]

1965 (2)

J. E. Davey and T. Pankey, J. Appl. Phys. 9, 359 (1965).

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
[Crossref]

1964 (1)

1963 (1)

1961 (1)

1957 (1)

P. Bousquet, Ann. Phys. (Paris) 2, 163 (1957).

1939 (1)

E. David, Z. Phys. 114, 389 (1939).
[Crossref]

Abelès, F.

F. Abelès, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1971), Vol. 6, pp. 170 ff.

Anderson, W. J.

Ashley, E. J.

J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 60, 224 (1970).
[Crossref]

T. M. Donovan, W. E. Spicer, J. M. Bennett, and E. J. Ashley, Phys. Rev. B 2, 397 (1970).
[Crossref]

Bennett, H. E.

D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).
[Crossref]

H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
[Crossref]

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1967), Vol. 4,pp. 1–96.

Bennett, J. M.

T. M. Donovan, W. E. Spicer, J. M. Bennett, and E. J. Ashley, Phys. Rev. B 2, 397 (1970).
[Crossref]

J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 60, 224 (1970).
[Crossref]

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1967), Vol. 4,pp. 1–96.

Bousquet, P.

P. Bousquet, Ann. Phys. (Paris) 2, 163 (1957).

P. Rouard and P. Bousquet, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1965), Vol. 5, pp. 161ff.

Burge, D. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Davey, J. E.

J. E. Davey and T. Pankey, J. Appl. Phys. 9, 359 (1965).

David, E.

E. David, Z. Phys. 114, 389 (1939).
[Crossref]

Donovan, T. M.

T. M. Donovan, W. E. Spicer, J. M. Bennett, and E. J. Ashley, Phys. Rev. B 2, 397 (1970).
[Crossref]

Doremus, R. H.

R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
[Crossref]

Emeric, A.

N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
[Crossref]

Emeric, N.

N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
[Crossref]

Hansen, W. N.

Heavens, O. S.

O. S. Heavens, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1964), Vol. 2, p. 193.

Hunter, W. R.

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Kinbara, A.

Pankey, T.

J. E. Davey and T. Pankey, J. Appl. Phys. 9, 359 (1965).

Porteus, J. O.

Rasigni, G.

Rouard, P.

G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963).
[Crossref]

P. Rouard and P. Bousquet, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1965), Vol. 5, pp. 161ff.

Spicer, W. E.

T. M. Donovan, W. E. Spicer, J. M. Bennett, and E. J. Ashley, Phys. Rev. B 2, 397 (1970).
[Crossref]

Stanford, J. L.

Yamaguchi, T.

Yoshida, S.

Ann. Phys. (Paris) (1)

P. Bousquet, Ann. Phys. (Paris) 2, 163 (1957).

Appl. Opt. (1)

J. Appl. Phys. (2)

J. E. Davey and T. Pankey, J. Appl. Phys. 9, 359 (1965).

R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
[Crossref]

J. Opt. Soc. Am. (7)

J. Opt. Soc. Amn. (1)

W. N. Hansen, J. Opt. Soc. Amn. 63, 793 (1973).
[Crossref]

Phys. Rev. B (2)

T. M. Donovan, W. E. Spicer, J. M. Bennett, and E. J. Ashley, Phys. Rev. B 2, 397 (1970).
[Crossref]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Thin Solid Films (1)

N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
[Crossref]

Z. Phys. (1)

E. David, Z. Phys. 114, 389 (1939).
[Crossref]

Other (5)

F. Abelès, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1971), Vol. 6, pp. 170 ff.

P. Rouard and P. Bousquet, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1965), Vol. 5, pp. 161ff.

Handbook of Thin Film Technology, edited by L. I. Maissel and R. Glang (McGraw-Hill, New York, 1970).

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1967), Vol. 4,pp. 1–96.

O. S. Heavens, in Physics of Thin Films, edited by Georg Hass and Rudolf E. Thun (Academic, New York, 1964), Vol. 2, p. 193.

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Figures (8)

FIG. 1
FIG. 1

The real and imaginary components of the complex index of refraction for a 14. 7-nm-thick gold film determined by several different methods: ○—(T), (R)45°:, ×—(T), (R)45°, (R)45° thickness determined also; +—(R)45°, (R)70°. (R)70° thickness determined with water third phase; ●—optical constants for bulk gold as measured from Ref. 10.

FIG. 2
FIG. 2

The real and imaginary components of the complex index of refraction for a 45.5-nm-thick silver sulfide film determined by several different methods: ×—(R)20°, (R)45°; +— (R)20°, (R⊥)45°. (R)45° thickness determined also; ●—Optical constants for silver sulfide film as measured in Ref. 4.

FIG. 3
FIG. 3

Real part of the refractive index of a 1.05-μm-thick tin oxide film as determined by several different methods: ×— (T), (R)45°; ○—(T), (R)45°; *—(T), (R)45°. (R)45° thickness determined also; +—(R)45°, (R)70°, (R)70° water third-phase thickness determined also.

FIG. 4
FIG. 4

Imaginary part of the refractive index of film in Fig. 3. Symbols are the same as in Fig. 3.

FIG. 5
FIG. 5

Actual structure of thin film broken up into several different layers.

FIG. 6
FIG. 6

Reflectance from a nonhomogeneous gold film (——) compared to the reflectance from a one-film representation (⋯). The optical constants of the nonhomogeneous film are as follows: Substrate: n1 = 1.53. Gold film: n2 = 1.40, k2 = 1.82, h2/λ = 0.06525; n3 = 1.35, k3 = 1.688, h3/λ = 0.00544; n4 = 1.30, k4 = 1.43, h4/λ = 0.00326; n5 = 1.25, k5 = 1.375, h5/λ = 0.00326; n6 = 1.15:k6 = 0.575, h6/λ = 0.00218. Air:n7 = 1.0. The optical constants of the one-film model are n2 = 1.390, k2 = 1.763, h2/λ = 0.07928. The points of inversion are marked by (×).

FIG. 7
FIG. 7

The reflectance from a germanium-gold-germanium film series (——) compared to the reflectance from a one-film representation (⋯). The optical constants of the Ge–Au–Ge series are as follows. Substrate: n1 = 1.53. Ge: n2 = 4.00, k2 = 1.60, h2 = 0.02. Au: n3 = 1.40, k3 = 1.82, h3/λ = 0.02. Ge: n4 = 4.00, k4 = 1.60, h4/λ = 0.02. Air: n5 = 1.0. The optical constants of the one-film model are n2 = 1. 390, k2 = 1.763, h2/λ = 0. 07928. The points of inversion are marked by (×).

FIG. 8
FIG. 8

The internal reflectance (○) from a discontinuous gold film at 480 nm compared to the reflectance (——) from a one-film model with (n2 = 1. 734, k2 = 1.621, h2 = 10. 9 nm). The points of inversion are marked by (×).

Tables (6)

Tables Icon

TABLE I The internal reflectance (Rc) calculated from the measured optical constants compared to the internal reflectance (Rm) measured as a function of angle of incidence. The points of inversion were (T), (R)45°, and (R)45°. The optical constants for the calculated reflectance were n1 = 1. 517, n2 = 4.72, k2 = 1.86, h = 28.85nm, n3 = 1.0, and λ = 550 nm.

Tables Icon

TABLE II The internal reflectance (Rc) calculated from the measured optical constants compared to the reflectance (Rm) measured as a function of angle of incidence. The optical constants for the calculated reflectance were n1 = 1. 523, n2 = 1. 40, k2 = 1.82, h = 37. 03 nm, n3 = 1.0, and λ = 460 nm.

Tables Icon

TABLE III A comparison of two different methods for calculating the thickness of a thin film. The method using water as the third phase was done with three internal-reflection measurements, (R)45°, (R)70°, (R)70°. The method using air as the third phase was done with a transmittance measurement, (T), and two internal-reflectance measurements, (R)45°, (R)45°.

Tables Icon

TABLE IV The optical constants of a discontinuous gold film determined with water and air as the third phase.

Tables Icon

TABLE V The complex index of refraction for a 28. 9-nm-thick Ge film as determined by perpendicular/parallel-polarization measurements.

Tables Icon

TABLE VI The complex index of refraction for a 36.5-nm-thick Au film as determined by perpendicular/parallel-polarization measurements.

Equations (3)

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R i ln R i ( h / λ ) ( h / λ ) R i < 1.2 .
R i ln R i n n R i
R i ln R i k k R i