Abstract

The strong coupling between photons and surface plasmons that occur on rough metal surfaces permits optical measurements of the shift of the surface plasma resonance frequency when the metal surface is covered with a thin film. Thin, discontinuous silver sulfide tarnish films on silver shift the resonance to lower frequencies and also damp the resonance, in agreement with surface plasmon dispersion theory. The wavelength of the dominant surface plasma wave is large compared to the size of the discontinuities, so the effect of the thin film should be the same as that of a continuous film whose thickness is the average thickness of the discontinuous film. On this basis, the thicknesses of several silver sulfide films are calculated from the measured frequency shift of the resonance peak and are found to be in excellent agreement with values determined from independent ellipsometric measurements.

© 1970 Optical Society of America

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References

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  1. H. E. Bennett and J. M. Bennett, in Physics of Thin Films, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), Vol. 4, pp. 37–41.
  2. H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
    [Crossref]
  3. H. Raether, Surface Sci. 8, 233 (1967).
    [Crossref]
  4. T. Kloos, Z. Physik 208, 77 (1968).
    [Crossref]
  5. S. N. Jasperson and S. E. Schnatterly, Bull. Am. Phys. Soc. 12, 399 (1967).
  6. J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).
  7. O. Hunderi and D. Beaglehole, Bull. Am. Phys. Soc. 14, 26 (1969).
  8. R. A. Ferrell, Phys. Rev. 111, 1214 (1958).
    [Crossref]
  9. E. A. Stern and R. A. Ferrell, Phys. Rev. 120, 130 (1960).
    [Crossref]
  10. R. H. Ritchie, Surface Sci. 3, 497 (1965).
    [Crossref]
  11. E. A. Stern, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publ. Co., Amsterdam, 1966), p. 396.
  12. Y. Teng and E. A. Stern, Phys. Rev. Letters 19, 511 (1967).
    [Crossref]
  13. P. A. Fedders, Phys. Rev. 165, 580 (1968);R. H. Ritchie and R. E. Wilems, Phys. Rev. 178, 372 (1969).
    [Crossref]
  14. A. Otto, Z. Physik 185, 232 (1965).
    [Crossref]
  15. The values used were obtained from the highest measured reflectance from smooth, freshly evaporated silver films. These values differ only slightly from those of Huebner et al. [R. H. Huebner, E. T. Arakawa, R. A. MacRae, and R. N. Hamm, J. Opt. Soc. Am. 54, 1434 (1964).]
    [Crossref]
  16. Ralph W. Dietz and Jean M. Bennett, Appl. Opt. 5, 881 (1966).
    [PubMed]
  17. H. E. Bennett and J. F. Roberts, J. Opt. Soc. Am. 54, 568A (1964).
    [Crossref]
  18. D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, in Proceedings of the Conference on Recent Developments in Ellipsometry, Surface Sci. 16, 303 (1969).
  19. See Ref. 1, pp. 17–18.
  20. H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
    [Crossref]
  21. J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 59, 499A (1969).
    [Crossref]
  22. H. E. Bennett, R. L. Peck, D. K. Burge, and J. M. Bennett, J. Appl. Phys. 40, 3351 (1969).
    [Crossref]

1969 (5)

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

O. Hunderi and D. Beaglehole, Bull. Am. Phys. Soc. 14, 26 (1969).

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, in Proceedings of the Conference on Recent Developments in Ellipsometry, Surface Sci. 16, 303 (1969).

J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 59, 499A (1969).
[Crossref]

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

1968 (3)

P. A. Fedders, Phys. Rev. 165, 580 (1968);R. H. Ritchie and R. E. Wilems, Phys. Rev. 178, 372 (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).

T. Kloos, Z. Physik 208, 77 (1968).
[Crossref]

1967 (3)

S. N. Jasperson and S. E. Schnatterly, Bull. Am. Phys. Soc. 12, 399 (1967).

H. Raether, Surface Sci. 8, 233 (1967).
[Crossref]

Y. Teng and E. A. Stern, Phys. Rev. Letters 19, 511 (1967).
[Crossref]

1966 (1)

1965 (2)

R. H. Ritchie, Surface Sci. 3, 497 (1965).
[Crossref]

A. Otto, Z. Physik 185, 232 (1965).
[Crossref]

1964 (2)

1961 (1)

1960 (1)

E. A. Stern and R. A. Ferrell, Phys. Rev. 120, 130 (1960).
[Crossref]

1958 (1)

R. A. Ferrell, Phys. Rev. 111, 1214 (1958).
[Crossref]

Arakawa, E. T.

Ashley, E. J.

J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 59, 499A (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).

Beaglehole, D.

O. Hunderi and D. Beaglehole, Bull. Am. Phys. Soc. 14, 26 (1969).

Bennett, H. E.

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, in Proceedings of the Conference on Recent Developments in Ellipsometry, Surface Sci. 16, 303 (1969).

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

H. E. Bennett and J. F. Roberts, J. Opt. Soc. Am. 54, 568A (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, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), Vol. 4, pp. 37–41.

Bennett, J. M.

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, in Proceedings of the Conference on Recent Developments in Ellipsometry, Surface Sci. 16, 303 (1969).

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, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 59, 499A (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).

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), Vol. 4, pp. 37–41.

Bennett, Jean M.

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, in Proceedings of the Conference on Recent Developments in Ellipsometry, Surface Sci. 16, 303 (1969).

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

Dietz, Ralph W.

Fedders, P. A.

P. A. Fedders, Phys. Rev. 165, 580 (1968);R. H. Ritchie and R. E. Wilems, Phys. Rev. 178, 372 (1969).
[Crossref]

Ferrell, R. A.

E. A. Stern and R. A. Ferrell, Phys. Rev. 120, 130 (1960).
[Crossref]

R. A. Ferrell, Phys. Rev. 111, 1214 (1958).
[Crossref]

Hamm, R. N.

Huebner, R. H.

Hunderi, O.

O. Hunderi and D. Beaglehole, Bull. Am. Phys. Soc. 14, 26 (1969).

Jasperson, S. N.

S. N. Jasperson and S. E. Schnatterly, Bull. Am. Phys. Soc. 12, 399 (1967).

Kloos, T.

T. Kloos, Z. Physik 208, 77 (1968).
[Crossref]

MacRae, R. A.

Otto, A.

A. Otto, Z. Physik 185, 232 (1965).
[Crossref]

Peck, R. L.

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, in Proceedings of the Conference on Recent Developments in Ellipsometry, Surface Sci. 16, 303 (1969).

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]

Porteus, J. O.

Raether, H.

H. Raether, Surface Sci. 8, 233 (1967).
[Crossref]

Ritchie, R. H.

R. H. Ritchie, Surface Sci. 3, 497 (1965).
[Crossref]

Roberts, J. F.

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

Schnatterly, S. E.

S. N. Jasperson and S. E. Schnatterly, Bull. Am. Phys. Soc. 12, 399 (1967).

Stanford, J. L.

J. M. Bennett, J. L. Stanford, and E. J. Ashley, J. Opt. Soc. Am. 59, 499A (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).

Stern, E. A.

Y. Teng and E. A. Stern, Phys. Rev. Letters 19, 511 (1967).
[Crossref]

E. A. Stern and R. A. Ferrell, Phys. Rev. 120, 130 (1960).
[Crossref]

E. A. Stern, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publ. Co., Amsterdam, 1966), p. 396.

Teng, Y.

Y. Teng and E. A. Stern, Phys. Rev. Letters 19, 511 (1967).
[Crossref]

Appl. Opt. (1)

Bull. Am. Phys. Soc. (3)

S. N. Jasperson and S. E. Schnatterly, Bull. Am. Phys. Soc. 12, 399 (1967).

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

O. Hunderi and D. Beaglehole, Bull. Am. Phys. Soc. 14, 26 (1969).

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. (5)

Phys. Rev. (3)

R. A. Ferrell, Phys. Rev. 111, 1214 (1958).
[Crossref]

E. A. Stern and R. A. Ferrell, Phys. Rev. 120, 130 (1960).
[Crossref]

P. A. Fedders, Phys. Rev. 165, 580 (1968);R. H. Ritchie and R. E. Wilems, Phys. Rev. 178, 372 (1969).
[Crossref]

Phys. Rev. Letters (1)

Y. Teng and E. A. Stern, Phys. Rev. Letters 19, 511 (1967).
[Crossref]

Proceedings of the Conference on Recent Developments in Ellipsometry (1)

D. K. Burge, J. M. Bennett, R. L. Peck, and H. E. Bennett, in Proceedings of the Conference on Recent Developments in Ellipsometry, Surface Sci. 16, 303 (1969).

Surface Sci. (2)

H. Raether, Surface Sci. 8, 233 (1967).
[Crossref]

R. H. Ritchie, Surface Sci. 3, 497 (1965).
[Crossref]

Z. Physik (2)

T. Kloos, Z. Physik 208, 77 (1968).
[Crossref]

A. Otto, Z. Physik 185, 232 (1965).
[Crossref]

Other (3)

E. A. Stern, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publ. Co., Amsterdam, 1966), p. 396.

See Ref. 1, pp. 17–18.

H. E. Bennett and J. M. Bennett, in Physics of Thin Films, G. Hass and R. E. Thun, Eds. (Academic Press Inc., New York, 1967), Vol. 4, pp. 37–41.

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Figures (2)

Fig. 1
Fig. 1

Dispersion curves for surface plasma waves at silver–vacuum interface (solid curve) and at silver–quartz interface (dashed curve). Straight lines are dispersion curves for light in vacuum (solid line) and in quartz (dashed line).

Fig. 2
Fig. 2

Reflectance change due to optically excited surface plasma resonances on a rough silver surface. Thickness of silver sulfide film on surface as determined from ellipsometric measurements is indicated on each curve.

Tables (1)

Tables Icon

Table I Position of resonance peaks and corresponding film thickness determined ellipsometrically and from resonance shift.

Equations (17)

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+ η [ k 3 / k 2 ] { [ 1 - γ exp ( - 2 k 2 τ ) ] / [ 1 + γ exp ( - 2 k 2 τ ) ] } = 0 ,
γ = ( η k 1 - k 2 ) / ( η k 1 + k 2 ) , k 1 = ( k 2 - ω 2 / c 2 ) 1 2 = ( k 2 - k 0 2 ) 1 2 , k 2 = ( k 2 - η k 0 2 ) 1 2 , k 3 = ( k 2 - k 0 2 ) 1 2 .
+ ( k 2 - k 0 2 ) 1 2 / ( k 2 - k 0 2 ) 1 2 = 0 ,
k = k 0 [ / ( + 1 ) ] 1 2 .
k = k 0 [ ( 1 + i 2 ) / ( 1 + 1 + i 2 ) ] 1 2 k 0 [ 1 / ( 1 + 1 ) ] 1 2 + i k 0 2 / 2 [ 1 ( 1 + 1 ) 3 ] 1 2 .
k r k 0 [ 1 / ( 1 + 1 ) ] 1 2 ,
k i k 0 2 / 2 [ 1 ( 1 + 1 ) 3 ] 1 2 .
k = k 0 [ η / ( + η ) ] 1 2 ,
k r k 0 [ 1 η 1 / ( 1 + η 1 ) ] 1 2
k i k 0 2 [ η 1 3 / 1 ( 1 + η 1 ) 3 ] 1 2 / 2.
= - ( η k 3 / i k 2 ) ( η k 1 tan i k 2 τ + i k 2 ) / ( η k 1 - i k 2 tan i k 2 τ ) .
- ( k 3 / k 1 ) ( 1 + η k 1 τ ) .
k 2 k 0 2 { [ 2 - ( 1 + η k 1 τ ) 2 ] / [ 2 - ( 1 + η k 1 τ ) 2 ] .
k r κ 0 { [ 1 2 - 1 ( 1 + η 1 k 1 τ ) 2 ] / [ 1 2 - ( 1 + η 1 k 1 τ ) 2 ] } 1 2
k i k 0 { 2 ( 1 + η 1 k 1 τ ) 2 [ ( 1 - 1 ) 2 + η 1 k 1 τ ( 2 + η 1 k 1 τ ) ] + 2 1 2 η 2 k 1 τ ( 1 + η 1 k 1 τ ) ( 1 - 1 ) } / { 2 [ 1 2 - 1 ( 1 + η 1 k 1 τ ) 2 ] 1 2 [ 1 2 - ( 1 + η 1 k 1 τ ) 2 ] 3 2 } .
1 - ( k 3 / k 1 ) ( 1 + η 1 k 1 τ ) ,
τ - [ ( k 1 1 / k 3 ) + 1 ] / η 1 k 1 .