Abstract

The optical constants of rapidly grown silver sulfide films approximately 400 Å thick have been determined in the wavelength range 0.28–2.5 μ using three independent methods. A fourth method was used to obtain values of n and k for thin (40 Å), naturally grown silver sulfide films on opaque silver in the wavelength range 0.34–0.60 μ. Although these results are probably not representative of bulk silver sulfide, they should be approximately correct for tarnish films on silver. Thus, they can be used to calculate the reflectance as a function of wavelength for silver covered with tarnish films of various thicknesses. The measured reflectances of two such films were in reasonable agreement with the calculations, and the reflectance of heavily tarnished silver was essentially the same as that of fresh silver in the infrared. The measured optical constants of silver sulfide can also be used to calculate the thickness of thin tarnish films from ellipsometric measurements, and to calculate the shift in the surface plasma-resonance frequency when silver is covered with a thin tarnish film.

© 1970 Optical Society of America

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  1. H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
    [CrossRef]
  2. H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
    [CrossRef]
  3. D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, Surface Sci. 16, 303 (1969).
    [CrossRef]
  4. J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).
  5. P. Junod, Helv. Phys. Acta 32, 567 (1959).
  6. R. Bailly, Am. Mineralogist 33, 519 (1948).
  7. F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, Symposium Proceedings, Washington, 1963, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Stds. (U. S.) Misc. Publ. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p. 61.
  8. H. E. Bennett, J. M. Bennett, and E. J. Ashley, J. Opt. Soc. Am. 52, 1245 (1962).
    [CrossRef]
  9. J. M. Bennett and E. J. Ashley, Appl. Opt. 4, 221 (1965).
    [CrossRef]
  10. H. E. Bennett and J. M. Bennett, in Physics of Thin Films, Vol. 4, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), pp. 12–17.
  11. H. E. Bennett and J. F. Roberts, J. Opt. Soc. Am. 54, 568A (1964).
    [CrossRef]
  12. H. E. Bennett and W. F. Koehler, J. Opt. Soc. Am. 50, 1 (1960).
    [CrossRef]
  13. See Ref. 10, pp. 31–37.
  14. J. M. Bennett and M. J. Booty, Appl. Opt. 5, 41 (1966).
    [CrossRef] [PubMed]
  15. See Ref. 10, p. 42.
  16. P. H. Berning, in Physics of Thin Films, Vol. 1, G. Hass, Ed. (Academic Press Inc., New York, 1963), p. 69.
  17. J. A. Horton and W. N. Hansen, Anal. Chem. 39, 1097 (1967).
    [CrossRef]
  18. The Cary 14R spectrophotometer actually measured absorbance [equal to log10(1/R)] and the computer program was set up accordingly, but the method basically deals with internal reflectances.
  19. P.-O. Nilsson, Appl. Opt. 7, 435 (1968).
    [CrossRef] [PubMed]
  20. See Ref. 10, pp. 17–18.
  21. J. M. Bennett and M. J. Booty, Appl. Opt. 8, 2366 (1969).
    [CrossRef] [PubMed]
  22. R. H. Huebner, E. T. Arakawa, R. A. MacRae, and R. N. Hamm, J. Opt. Soc. Am. 54, 1434 (1964).
    [CrossRef]
  23. J. M. Bennett, E. J. Ashley, and H. E. Bennett, Appl. Opt. 4, 961 (1965).
    [CrossRef]
  24. J. L. Stanford, J. Opt. Soc. Am. 60, 49 (1970).
    [CrossRef]
  25. W. F. Koehler, J. Opt. Soc. Am. 45, 934 (1955).
    [CrossRef]

1970 (1)

1969 (4)

J. M. Bennett and M. J. Booty, Appl. Opt. 8, 2366 (1969).
[CrossRef] [PubMed]

H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
[CrossRef]

H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
[CrossRef]

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, Surface Sci. 16, 303 (1969).
[CrossRef]

1968 (2)

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

P.-O. Nilsson, Appl. Opt. 7, 435 (1968).
[CrossRef] [PubMed]

1967 (1)

J. A. Horton and W. N. Hansen, Anal. Chem. 39, 1097 (1967).
[CrossRef]

1966 (1)

1965 (2)

1964 (2)

1962 (1)

1960 (1)

1959 (1)

P. Junod, Helv. Phys. Acta 32, 567 (1959).

1955 (1)

1948 (1)

R. Bailly, Am. Mineralogist 33, 519 (1948).

Arakawa, E. T.

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

R. H. Huebner, E. T. Arakawa, R. A. MacRae, and R. N. Hamm, J. Opt. Soc. Am. 54, 1434 (1964).
[CrossRef]

Ashley, E. J.

Bailly, R.

R. Bailly, Am. Mineralogist 33, 519 (1948).

Bennett, H. E.

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, Surface Sci. 16, 303 (1969).
[CrossRef]

H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
[CrossRef]

H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
[CrossRef]

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

J. M. Bennett, E. J. Ashley, and H. E. Bennett, Appl. Opt. 4, 961 (1965).
[CrossRef]

H. E. Bennett and J. F. Roberts, J. Opt. Soc. Am. 54, 568A (1964).
[CrossRef]

H. E. Bennett, J. M. Bennett, and E. J. Ashley, J. Opt. Soc. Am. 52, 1245 (1962).
[CrossRef]

H. E. Bennett and W. F. Koehler, J. Opt. Soc. Am. 50, 1 (1960).
[CrossRef]

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, Vol. 4, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), pp. 12–17.

Bennett, J. M.

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, Surface Sci. 16, 303 (1969).
[CrossRef]

H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
[CrossRef]

H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
[CrossRef]

J. M. Bennett and M. J. Booty, Appl. Opt. 8, 2366 (1969).
[CrossRef] [PubMed]

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

J. M. Bennett and M. J. Booty, Appl. Opt. 5, 41 (1966).
[CrossRef] [PubMed]

J. M. Bennett and E. J. Ashley, Appl. Opt. 4, 221 (1965).
[CrossRef]

J. M. Bennett, E. J. Ashley, and H. E. Bennett, Appl. Opt. 4, 961 (1965).
[CrossRef]

H. E. Bennett, J. M. Bennett, and E. J. Ashley, J. Opt. Soc. Am. 52, 1245 (1962).
[CrossRef]

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, Vol. 4, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), pp. 12–17.

Berning, P. H.

P. H. Berning, in Physics of Thin Films, Vol. 1, G. Hass, Ed. (Academic Press Inc., New York, 1963), p. 69.

Booty, M. J.

Burge, D. K.

H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
[CrossRef]

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, Surface Sci. 16, 303 (1969).
[CrossRef]

H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
[CrossRef]

Colson, J. P.

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, Symposium Proceedings, Washington, 1963, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Stds. (U. S.) Misc. Publ. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p. 61.

Hamm, R. N.

Hansen, W. N.

J. A. Horton and W. N. Hansen, Anal. Chem. 39, 1097 (1967).
[CrossRef]

Horton, J. A.

J. A. Horton and W. N. Hansen, Anal. Chem. 39, 1097 (1967).
[CrossRef]

Huebner, R. H.

Junod, P.

P. Junod, Helv. Phys. Acta 32, 567 (1959).

Koehler, W. F.

MacRae, R. A.

McCrackin, F. L.

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, Symposium Proceedings, Washington, 1963, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Stds. (U. S.) Misc. Publ. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p. 61.

Nilsson, P.-O.

Peck, R. L.

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, Surface Sci. 16, 303 (1969).
[CrossRef]

H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
[CrossRef]

H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
[CrossRef]

Roberts, J. F.

H. E. Bennett and J. F. Roberts, J. Opt. Soc. Am. 54, 568A (1964).
[CrossRef]

Stanford, J. L.

J. L. Stanford, J. Opt. Soc. Am. 60, 49 (1970).
[CrossRef]

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

Am. Mineralogist (1)

R. Bailly, Am. Mineralogist 33, 519 (1948).

Anal. Chem. (1)

J. A. Horton and W. N. Hansen, Anal. Chem. 39, 1097 (1967).
[CrossRef]

Appl. Opt. (5)

Bull. Am. Phys. Soc. (1)

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

Helv. Phys. Acta (1)

P. Junod, Helv. Phys. Acta 32, 567 (1959).

J. Appl. Phys. (1)

H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
[CrossRef]

J. Opt. Soc. Am. (7)

Surface Sci. (1)

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, Surface Sci. 16, 303 (1969).
[CrossRef]

Other (7)

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, Vol. 4, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), pp. 12–17.

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, Symposium Proceedings, Washington, 1963, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Stds. (U. S.) Misc. Publ. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p. 61.

See Ref. 10, pp. 31–37.

See Ref. 10, p. 42.

P. H. Berning, in Physics of Thin Films, Vol. 1, G. Hass, Ed. (Academic Press Inc., New York, 1963), p. 69.

See Ref. 10, pp. 17–18.

The Cary 14R spectrophotometer actually measured absorbance [equal to log10(1/R)] and the computer program was set up accordingly, but the method basically deals with internal reflectances.

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Figures (11)

Fig. 1
Fig. 1

Apparatus for producing silver sulfide tarnish.

Fig. 2
Fig. 2

Transmittance of an absorbing film on a nonabsorbing substrate measured relative to the transmittance of an identical uncoated substrate. The normal-incidence reflectance of the film is Rf, assuming that the substrate is semi-infinite.

Fig. 3
Fig. 3

The solid curves are differences between the measured normal-incidence reflectances of a freshly evaporated silver film and three tarnished silver films with silver sulfide thicknesses of 13, 21, and 39 Å, respectively, going in the direction of increasing δR. The dashed curves are drawn to separate the effect of the surface plasma resonance in silver from the reflectance decrease caused by the silver sulfide tarnish film.

Fig. 4
Fig. 4

Optical constants of a 383-Å-thick silver sulfide film determined from normal-incidence reflectance and transmittance measurements (n, circles; k, squares), and internal-reflectance measurements (n, primed circles; k, primed squares). The solid and short-dashed curves are reasonable average values of n and k, respectively. The long-dashed curve gives k calculated from reflectance-difference measurements on thin films assuming n values from the solid curve.

Fig. 5
Fig. 5

Optical constants of a 383-Å-thick silver sulfide film determined from normal-incidence reflectance and transmittance measurements (n, circles; k, squares), and Kramers–Kronig analysis of transmittance data (n, triangles; k, diamonds). The n and k values at 1.0 and 2.0 μ, obtained from R and T measurements, were used in the K–K analysis.

Fig. 6
Fig. 6

Refractive index n determined from a Kramers–Kronig analysis of transmittance data for silver sulfide films prepared in the apparatus of Fig. 1. Thicknesses are: circles, 383 Å; squares, 389 Å; and triangles, 449 Å. The first two films were made from silver evaporated in ultrahigh vacuum, the third from silver evaporated in standard vacuum. The n and k values at the points indicated by arrows, obtained from R and T measurements, were used in the K–K analysis.

Fig. 7
Fig. 7

Extinction coefficient k determined from a Kramers–Kronig analysis of transmittance data for the same silver sulfide films shown in Fig. 6. The diamonds are k values obtained from R and T measurements on a 372-Å-thick film prepared from standard vacuum silver which was aged in laboratory air.

Fig. 8
Fig. 8

Range of optical constants determined from reflectance-difference-method calculations that correspond to δR’s within ±0.001 of the assumed values. Assumed δR’s were calculated from n and k values along the solid curves using film thicknesses of 22.5 and 38 Å, respectively. The upper short-dashed n curve goes with the lower short-dashed k curve; the long-dashed n and k curves likewise correspond.

Fig. 9
Fig. 9

Measured (solid curve) and calculated (dashed curve) differences between the reflectance of a freshly evaporated silver film and the reflectance of a silver film covered with a 109-Å-thick tarnish layer. The thin-film constants of silver sulfide in Fig. 4 were used for the calculations.

Fig. 10
Fig. 10

Measured reflectance of fresh silver (solid curve) and calculated reflectances of silver covered with thicknesses of silver sulfide tarnish indicated by the numbers (dashed curves).

Fig. 11
Fig. 11

Measured reflectances of fresh silver (solid curve) and silver covered with thicknesses of silver sulfide tarnish indicated by the numbers (dashed curves).

Tables (2)

Tables Icon

Table I Sample optical data for a 383-Å-thick silver sulfide film.

Tables Icon

Table II Representative optical constants for silver sulfide films, from Fig. 4.

Equations (4)

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T cbs = T f s / T s s = [ T f T s / ( 1 - R f R s ) ] / [ T s 2 / ( 1 - R s 2 ) ] ,
T f = T obs ( 1 - R f R s ) / ( 1 + R s ) .
R obs = R f + T f 2 R s / ( 1 - R f R s ) ,
R f = R obs - T f 2 R s / ( 1 - R f R s ) .