Abstract

An aggregated silver film shows absorption bands in the visible and the near-ultraviolet spectral regions caused by the plasma resonances of conduction electrons in the island particles composing the film, for electric fields parallel and perpendicular to the substrate. We derive the relation between the peak wavelengths of absorption bands in terms of the model based on a two-dimensional distribution of island particles and propose the method for the determination of the inter-island dielectric constant ∊<sub><i>a</i></sub>. The method is applied to aggregated silver films and the thickness dependence of ∊<sub><i>a</i></sub> is found.

© 1972 Optical Society of America

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  1. See, for example, G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963); P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North—Holland, Amsterdam, 1965), p. 145.
  2. E. David, Z. Physik 114, 389 (1939).
  3. H. Schopper, Z. Physik 130, 565 (1951).
  4. J. C. Maxwell-Garnett, Phil. Trans. Roy. Soc. London A203, 385 (1940); A205, 237 (1906).
  5. D. Malé, Compt. Rend. 230, 286 (1950).
  6. W. Hampe, Z. Physik 152, 470 (1958); 152, 476 (1958).
  7. R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); 42, 414 (1965); J. Appl. Phys. 37, 2775 (1966).
  8. S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 62 (1971).
  9. S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960).
  10. L. Ward, Brit. J. Appl. Phys. 2, 123 (1969).
  11. See, for example, O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 189.
  12. S. Yamaguchi, J. Phys. Soc. Japan 17, 1172 (1962).
  13. N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
  14. J. Bösenberg, Z. Physik 218, 282 (1969).
  15. T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 62, 634 (1972).
  16. J. P. Marton and J. R. Lemon, Phys. Rev. B 4, 271 (1971).
  17. T. Utagawa and M. Seki, Thesis, University of Tokyo (1972).
  18. For a free electron gas, if we assume ∊a=1, h(λ)=λp22, where λp is the bulk plasma wavelength. Thus, the peak wavelengths λII and λ are obtained as functions of λp and ƒII,┴, λII,┴p/(ƒII,┴)½, which coincide with the results obtained by Emeric and Emeric (Ref. 13) and Bösenberg (Ref. 14), if the contribution from the dipole interaction is ignored, i.e., ƒII,┴0II,┴.
  19. See, for example, L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960).
  20. R. H. Huebner, E. T. Arakawa, R. A. MacRae, and R. N. Hamm, J. Opt. Soc. Am. 54, 1434 (1964).
  21. L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954); L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).
  22. S. Yamaguchi, J. Phys. Soc. Japan 18, 266 (1963); A. McAlister and E. A. Stern, Phys. Rev. 132, 1599 (1963).
  23. U. Kreibig and C. von Fragstein, Z. Physik 224, 307 (1969).
  24. S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).
  25. R. R. Bilboul, Brit. J. Appl. Phys. 2, 921 (1969).

Arakawa, E. T.

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

Bilboul, R. R.

R. R. Bilboul, Brit. J. Appl. Phys. 2, 921 (1969).

Bösenberg, J.

J. Bösenberg, Z. Physik 218, 282 (1969).

David, E.

E. David, Z. Physik 114, 389 (1939).

Doremus, R. H.

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); 42, 414 (1965); J. Appl. Phys. 37, 2775 (1966).

Emeric, A.

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

Emeric, N.

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

Hamm, R. N.

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

Hampe, W.

W. Hampe, Z. Physik 152, 470 (1958); 152, 476 (1958).

Heavens, O. S.

See, for example, O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 189.

Huebner, R. H.

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

Kinbara, A.

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 62 (1971).

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

Kreibig, U.

U. Kreibig and C. von Fragstein, Z. Physik 224, 307 (1969).

Landau, L. D.

See, for example, L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960).

Lemon, J. R.

J. P. Marton and J. R. Lemon, Phys. Rev. B 4, 271 (1971).

Lifshits, E. M.

See, for example, L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960).

MacRae, R. A.

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

Malé, D.

D. Malé, Compt. Rend. 230, 286 (1950).

Marton, J. P.

J. P. Marton and J. R. Lemon, Phys. Rev. B 4, 271 (1971).

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, Phil. Trans. Roy. Soc. London A203, 385 (1940); A205, 237 (1906).

Rasigni, G.

See, for example, G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963); P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North—Holland, Amsterdam, 1965), p. 145.

Rouard, P.

See, for example, G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963); P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North—Holland, Amsterdam, 1965), p. 145.

Schopper, H.

H. Schopper, Z. Physik 130, 565 (1951).

Schulz, L. G.

L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954); L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).

Seki, M.

T. Utagawa and M. Seki, Thesis, University of Tokyo (1972).

Utagawa, T.

T. Utagawa and M. Seki, Thesis, University of Tokyo (1972).

von Fragstein, C.

U. Kreibig and C. von Fragstein, Z. Physik 224, 307 (1969).

Ward, L.

L. Ward, Brit. J. Appl. Phys. 2, 123 (1969).

Yamaguchi, S.

S. Yamaguchi, J. Phys. Soc. Japan 17, 1172 (1962).

S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960).

S. Yamaguchi, J. Phys. Soc. Japan 18, 266 (1963); A. McAlister and E. A. Stern, Phys. Rev. 132, 1599 (1963).

Yamaguchi, T.

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

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 62 (1971).

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

Yoshida, S.

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 62 (1971).

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

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

Other (25)

See, for example, G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963); P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North—Holland, Amsterdam, 1965), p. 145.

E. David, Z. Physik 114, 389 (1939).

H. Schopper, Z. Physik 130, 565 (1951).

J. C. Maxwell-Garnett, Phil. Trans. Roy. Soc. London A203, 385 (1940); A205, 237 (1906).

D. Malé, Compt. Rend. 230, 286 (1950).

W. Hampe, Z. Physik 152, 470 (1958); 152, 476 (1958).

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); 42, 414 (1965); J. Appl. Phys. 37, 2775 (1966).

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 62 (1971).

S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960).

L. Ward, Brit. J. Appl. Phys. 2, 123 (1969).

See, for example, O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 189.

S. Yamaguchi, J. Phys. Soc. Japan 17, 1172 (1962).

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

J. Bösenberg, Z. Physik 218, 282 (1969).

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

J. P. Marton and J. R. Lemon, Phys. Rev. B 4, 271 (1971).

T. Utagawa and M. Seki, Thesis, University of Tokyo (1972).

For a free electron gas, if we assume ∊a=1, h(λ)=λp22, where λp is the bulk plasma wavelength. Thus, the peak wavelengths λII and λ are obtained as functions of λp and ƒII,┴, λII,┴p/(ƒII,┴)½, which coincide with the results obtained by Emeric and Emeric (Ref. 13) and Bösenberg (Ref. 14), if the contribution from the dipole interaction is ignored, i.e., ƒII,┴0II,┴.

See, for example, L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960).

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

L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954); L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).

S. Yamaguchi, J. Phys. Soc. Japan 18, 266 (1963); A. McAlister and E. A. Stern, Phys. Rev. 132, 1599 (1963).

U. Kreibig and C. von Fragstein, Z. Physik 224, 307 (1969).

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

R. R. Bilboul, Brit. J. Appl. Phys. 2, 921 (1969).

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