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 a. The method is applied to aggregated silver films and the thickness dependence of a is found.

© 1972 Optical Society of America

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References

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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.
    [CrossRef]
  2. E. David, Z. Physik 114, 389 (1939).
    [CrossRef]
  3. H. Schopper, Z. Physik 130, 565 (1951).
    [CrossRef]
  4. J. C. Maxwell–Garnett, Phil. Trans. Roy. Soc. London A203, 385 (1940);Phil. Trans. Roy. Soc. London A205, 237 (1906).
  5. D. Malé, Compt. Rend. 230, 286 (1950).
  6. W. Hampe, Z. Physik 152, 470 (1958);Z. Physik 152, 476 (1958).
    [CrossRef]
  7. R. H. Doremus, J. Chem. Phys. 40, 2389 (1964);J. Chem. Phys. 42, 414 (1965);J. Appl. Phys. 37, 2775 (1966).
    [CrossRef]
  8. S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 62 (1971).
    [CrossRef]
  9. S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960).
    [CrossRef]
  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).
    [CrossRef]
  13. N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
    [CrossRef]
  14. J. Bösenberg, Z. Physik 218, 282 (1969).
    [CrossRef]
  15. T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 62, 634 (1972).
    [CrossRef]
  16. J. P. Marton and J. R. Lemon, Phys. Rev. B 4, 271 (1971).
    [CrossRef]
  17. T. Utagawa and M. Seki, Thesis, University of Tokyo (1972).
  18. For a free electron gas, if we assume ∊a = 1, h(λ) = λp2/λ2, where λp is the bulk plasma wavelength. Thus, the peak wavelengths λ⊥ and λ⊥ are obtained as functions of λp and f∥,⊥,λ∥,⊥=λp/(f∥,⊥)12, 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., f∥,⊥ = f0∥,⊥.
  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).
    [CrossRef]
  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).
    [CrossRef]
  22. S. Yamaguchi, J. Phys. Soc. Japan 18, 266 (1963);A. McAlister and E. A. Stern, Phys. Rev. 132, 1599 (1963).
    [CrossRef]
  23. U. Kreibig and C. von Fragstein, Z. Physik 224, 307 (1969).
    [CrossRef]
  24. S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).
    [CrossRef]
  25. R. R. Bilboul, Brit. J. Appl. Phys. 2, 921 (1969).

1972 (1)

1971 (3)

1969 (4)

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

J. Bösenberg, Z. Physik 218, 282 (1969).
[CrossRef]

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

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

1967 (1)

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

1964 (2)

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

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

1963 (2)

1962 (1)

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

1960 (1)

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

1958 (1)

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

1954 (1)

1951 (1)

H. Schopper, Z. Physik 130, 565 (1951).
[CrossRef]

1950 (1)

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

1940 (1)

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

1939 (1)

E. David, Z. Physik 114, 389 (1939).
[CrossRef]

Arakawa, E. T.

Bilboul, R. R.

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

Bösenberg, J.

J. Bösenberg, Z. Physik 218, 282 (1969).
[CrossRef]

David, E.

E. David, Z. Physik 114, 389 (1939).
[CrossRef]

Doremus, R. H.

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964);J. Chem. Phys. 42, 414 (1965);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]

Hamm, R. N.

Hampe, W.

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

Heavens, O. S.

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

Huebner, R. H.

Kinbara, A.

Kreibig, U.

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

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).
[CrossRef]

Lifshits, E. M.

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

MacRae, R. A.

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).
[CrossRef]

Maxwell–Garnett, J. C.

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

Rasigni, G.

Rouard, P.

Schopper, H.

H. Schopper, Z. Physik 130, 565 (1951).
[CrossRef]

Schulz, L. G.

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).
[CrossRef]

Ward, L.

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

Yamaguchi, S.

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

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

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

Yamaguchi, T.

Yoshida, S.

Brit. J. Appl. Phys. (2)

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

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

Compt. Rend. (1)

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

J. Chem. Phys. (1)

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

J. Opt. Soc. Am. (6)

J. Phys. Soc. Japan (3)

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

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

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

Phil. Trans. Roy. Soc. London (1)

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

Phys. Rev. B (1)

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

Thin Solid Films (1)

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

Z. Physik (5)

J. Bösenberg, Z. Physik 218, 282 (1969).
[CrossRef]

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

E. David, Z. Physik 114, 389 (1939).
[CrossRef]

H. Schopper, Z. Physik 130, 565 (1951).
[CrossRef]

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

Other (4)

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

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

For a free electron gas, if we assume ∊a = 1, h(λ) = λp2/λ2, where λp is the bulk plasma wavelength. Thus, the peak wavelengths λ⊥ and λ⊥ are obtained as functions of λp and f∥,⊥,λ∥,⊥=λp/(f∥,⊥)12, 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., f∥,⊥ = f0∥,⊥.

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

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Figures (6)

F. 1
F. 1

Wavelength dependences of h(λ) of silver for various values of a.

F. 2
F. 2

Transmittance spectra observed with p-polarized light at 60° of incidence for films of various thicknesses, deposited at 25°C, 0.5 Å/s.

F. 3
F. 3

Variations of peak wavelengths; (a) λ, and (b) λ, with film thickness dw.

F. 4
F. 4

Variations of the inter-island dielectric constant a with film thickness.

F. 5
F. 5

Wavelength dependences of h(λ) for silver. (a) shows those calculated considering the size effect. R is the linear dimension of a particle. (b) shows those calculated taking into account the effect of the formation of dielectric-pellicle coatings over the spherical particles in the case of adsorption layers. m is the volume ratio of the inner to outer spheres. In these figures, a= 1 is assumed.

F. 6
F. 6

Thickness dependences of the effective depolarizing factors f and f.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

T p 4 n 0 n 2 cos 2 ψ 0 / { [ n 0 cos ψ 2 + n 2 cos ψ 0 ] t [ cos ψ 0 cos ψ 2 Im ( ) n 0 3 n 2 sin 2 ψ 0 Im ( 1 / ) ] } 2 ,
( a ) d 0 E i = E e Σ k υ k α k / ( 1 Σ k A k υ k α k ) ,
α = ( i a ) / [ 1 + f 0 ( i a ) / a ] ,
( a ) d 0 E i = E e α d w / ( 1 d w α Σ k A k ) = E e α d w / ( 1 α β ) ,
a = q α / ( 1 α β ) ,
( a ) / = q α / ( 1 α β ) .
Im ( ) = q a Δ h ( f h ) 2 + ( Δ h ) 2 ,
h = a / ( a 2 + b 2 ) , Δ h = b / ( a 2 + b 2 ) ,
f = h ( λ )
Im ( 1 / ) = q Δ h ( f h ) 2 + ( Δ h ) 2 ,
f = h ( λ ) ,
f 0 x + f 0 y + f 0 z = 1
2 f 0 + f 0 = 1 .
A k x + A k y + A k z = 0 ,
2 β + β = 0 ,
2 f + f = 1 .
H = 2 h ( λ ) + h ( λ ) 1 ,
H = 0