Abstract

The optical properties of the composite systems Ag–SiO2, Si–SiC, and Ge–A12O3 are compared with the predictions of the Maxwell-Garnett and the effective medium theories. Only the Maxwell-Garnett theory predicts the characteristic optical features of granular metals—a red shift relative to the pure metal in the plasma resonance and a dielectric anomaly. In the case of Si-SiC, the observed red shift in the transverse optical phonon frequency is too small to allow one to discriminate between the two theories. In the case of the Ge–A12O3 films, both theories are in good agreement with the experimental results for the optical constants near the absorption edge. The use of composite films for photothermal conversion and other optical applications is discussed.

© 1976 Optical Society of America

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  1. Granular metals are reviewed by B. Abeles, P. Sheng, M. D. Coutts, Y. Arie, Adv. Phys. 24, 407 (1975); and B. Abeles, Applied Solid State Science, Vol. 6, R. Wolfe, Ed. (Academic Press, New York, 1976), in press.
  2. J. I. Gittleman, Appl. Phys. Lett. 28, 370 (1976).
  3. E. B. Priestley, B. Abeles, R. W. Cohen, Phys. Rev. B 12, 2121 (1975).
  4. J. P. Marton, J. R. Lemon, J. Appl. Phys. 44, 3953 (1973).
  5. A. Kawabata, R. Kubo, J. Phys. Soc. Jpn. 21, 1765 (1966).
  6. R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).
  7. J. P. Marton, J. R. Lemon, Phys. Rev. B 4, 271 (1971).
  8. D. Stroud, Phys. Rev. B 12, 3368 (1975).
  9. R. Landauer, J. Appl. Phys. 23, 779 (1952).
  10. J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904); Philos. Trans. R. Soc. London 205, 237 (1906).
  11. R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3051 (1974).
  12. G. Rasigni, J. P. Palmari, M. Rasigni, Phys. Rev. B 12, 1121 (1975); R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3047 (1974); J. P. Marton, M. Schlesinger, J. Appl. Phys. 40, 4529 (1969).
  13. R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); J. Chem. Phys. 42, 414 (1965).
  14. P. W. Baumeister, G. Borak, L. Strensland, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, New-Castle-Upon-Tyne, U.K., 1969), p. 147.
  15. H. R. Zeller, D. Kuse, J. Appl. Phys. 44, 2763 (1973).
  16. J. I. Gittleman, B. Abeles, Phys. Rev. in press. 1976.
  17. H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).
  18. I. Webman, J. Jortner, M. H. Cohen, Phys. Rev. in press.
  19. J. I. Gittleman, B. Abeles, H. A. Weakliem, P. J. Zanzucchi, unpublished data.
  20. W. G. Spitzer, D. Kleinman, D. Walsh, Phys. Rev. 113, 127, 133 (1959); E. A. Fagen, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 16.
  21. H. R. Philipp, E. A. Taft, Phys. Rev. 120, 37 (1960); P. A. Schumann, W. A. Keenan, A. W. Tong, H. H. Gegenwarton, C. P. Schneider, J. Electrochem. Soc. 118, 145 (1971).
  22. R. J. Tempkin, G. A. N. Cornell, W. Paul, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 533.
  23. B. O. Seraphin, A. B. Meinel, in Optical Properties of Solids—New DevelopmentsB. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), p. 928.
  24. R. W. Tokarsky, J. P. Marton, J. Vac. Sci. Technol. 12, 643 (1975).
  25. D. Flint, P. Baumeister, Opt. Acta 21, 839 (1974).

1976 (1)

J. I. Gittleman, Appl. Phys. Lett. 28, 370 (1976).

1975 (5)

E. B. Priestley, B. Abeles, R. W. Cohen, Phys. Rev. B 12, 2121 (1975).

D. Stroud, Phys. Rev. B 12, 3368 (1975).

Granular metals are reviewed by B. Abeles, P. Sheng, M. D. Coutts, Y. Arie, Adv. Phys. 24, 407 (1975); and B. Abeles, Applied Solid State Science, Vol. 6, R. Wolfe, Ed. (Academic Press, New York, 1976), in press.

G. Rasigni, J. P. Palmari, M. Rasigni, Phys. Rev. B 12, 1121 (1975); R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3047 (1974); J. P. Marton, M. Schlesinger, J. Appl. Phys. 40, 4529 (1969).

R. W. Tokarsky, J. P. Marton, J. Vac. Sci. Technol. 12, 643 (1975).

1974 (2)

D. Flint, P. Baumeister, Opt. Acta 21, 839 (1974).

R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3051 (1974).

1973 (3)

H. R. Zeller, D. Kuse, J. Appl. Phys. 44, 2763 (1973).

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).

J. P. Marton, J. R. Lemon, J. Appl. Phys. 44, 3953 (1973).

1971 (1)

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

1966 (1)

A. Kawabata, R. Kubo, J. Phys. Soc. Jpn. 21, 1765 (1966).

1964 (1)

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

1962 (1)

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).

1960 (1)

H. R. Philipp, E. A. Taft, Phys. Rev. 120, 37 (1960); P. A. Schumann, W. A. Keenan, A. W. Tong, H. H. Gegenwarton, C. P. Schneider, J. Electrochem. Soc. 118, 145 (1971).

1959 (1)

W. G. Spitzer, D. Kleinman, D. Walsh, Phys. Rev. 113, 127, 133 (1959); E. A. Fagen, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 16.

1952 (1)

R. Landauer, J. Appl. Phys. 23, 779 (1952).

1904 (1)

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904); Philos. Trans. R. Soc. London 205, 237 (1906).

Abeles, B.

Granular metals are reviewed by B. Abeles, P. Sheng, M. D. Coutts, Y. Arie, Adv. Phys. 24, 407 (1975); and B. Abeles, Applied Solid State Science, Vol. 6, R. Wolfe, Ed. (Academic Press, New York, 1976), in press.

E. B. Priestley, B. Abeles, R. W. Cohen, Phys. Rev. B 12, 2121 (1975).

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).

J. I. Gittleman, B. Abeles, Phys. Rev. in press. 1976.

J. I. Gittleman, B. Abeles, H. A. Weakliem, P. J. Zanzucchi, unpublished data.

Arie, Y.

Granular metals are reviewed by B. Abeles, P. Sheng, M. D. Coutts, Y. Arie, Adv. Phys. 24, 407 (1975); and B. Abeles, Applied Solid State Science, Vol. 6, R. Wolfe, Ed. (Academic Press, New York, 1976), in press.

Baumeister, P.

D. Flint, P. Baumeister, Opt. Acta 21, 839 (1974).

Baumeister, P. W.

P. W. Baumeister, G. Borak, L. Strensland, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, New-Castle-Upon-Tyne, U.K., 1969), p. 147.

Borak, G.

P. W. Baumeister, G. Borak, L. Strensland, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, New-Castle-Upon-Tyne, U.K., 1969), p. 147.

Cody, G. D.

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).

Cohen, M. H.

I. Webman, J. Jortner, M. H. Cohen, Phys. Rev. in press.

Cohen, R. W.

E. B. Priestley, B. Abeles, R. W. Cohen, Phys. Rev. B 12, 2121 (1975).

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).

Cornell, G. A. N.

R. J. Tempkin, G. A. N. Cornell, W. Paul, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 533.

Coutts, M. D.

Granular metals are reviewed by B. Abeles, P. Sheng, M. D. Coutts, Y. Arie, Adv. Phys. 24, 407 (1975); and B. Abeles, Applied Solid State Science, Vol. 6, R. Wolfe, Ed. (Academic Press, New York, 1976), in press.

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).

Doremus, R. H.

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

Ehrenreich, H.

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).

Flint, D.

D. Flint, P. Baumeister, Opt. Acta 21, 839 (1974).

Gittleman, J. I.

J. I. Gittleman, Appl. Phys. Lett. 28, 370 (1976).

J. I. Gittleman, B. Abeles, H. A. Weakliem, P. J. Zanzucchi, unpublished data.

J. I. Gittleman, B. Abeles, Phys. Rev. in press. 1976.

Jortner, J.

I. Webman, J. Jortner, M. H. Cohen, Phys. Rev. in press.

Kawabata, A.

A. Kawabata, R. Kubo, J. Phys. Soc. Jpn. 21, 1765 (1966).

Kleinman, D.

W. G. Spitzer, D. Kleinman, D. Walsh, Phys. Rev. 113, 127, 133 (1959); E. A. Fagen, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 16.

Kubo, R.

A. Kawabata, R. Kubo, J. Phys. Soc. Jpn. 21, 1765 (1966).

Kuse, D.

H. R. Zeller, D. Kuse, J. Appl. Phys. 44, 2763 (1973).

Landauer, R.

R. Landauer, J. Appl. Phys. 23, 779 (1952).

Lemon, J. R.

J. P. Marton, J. R. Lemon, J. Appl. Phys. 44, 3953 (1973).

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

Marton, J. P.

R. W. Tokarsky, J. P. Marton, J. Vac. Sci. Technol. 12, 643 (1975).

R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3051 (1974).

J. P. Marton, J. R. Lemon, J. Appl. Phys. 44, 3953 (1973).

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

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904); Philos. Trans. R. Soc. London 205, 237 (1906).

Meinel, A. B.

B. O. Seraphin, A. B. Meinel, in Optical Properties of Solids—New DevelopmentsB. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), p. 928.

Palmari, J. P.

G. Rasigni, J. P. Palmari, M. Rasigni, Phys. Rev. B 12, 1121 (1975); R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3047 (1974); J. P. Marton, M. Schlesinger, J. Appl. Phys. 40, 4529 (1969).

Paul, W.

R. J. Tempkin, G. A. N. Cornell, W. Paul, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 533.

Philipp, H. R.

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).

H. R. Philipp, E. A. Taft, Phys. Rev. 120, 37 (1960); P. A. Schumann, W. A. Keenan, A. W. Tong, H. H. Gegenwarton, C. P. Schneider, J. Electrochem. Soc. 118, 145 (1971).

Priestley, E. B.

E. B. Priestley, B. Abeles, R. W. Cohen, Phys. Rev. B 12, 2121 (1975).

Rasigni, G.

G. Rasigni, J. P. Palmari, M. Rasigni, Phys. Rev. B 12, 1121 (1975); R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3047 (1974); J. P. Marton, M. Schlesinger, J. Appl. Phys. 40, 4529 (1969).

Rasigni, M.

G. Rasigni, J. P. Palmari, M. Rasigni, Phys. Rev. B 12, 1121 (1975); R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3047 (1974); J. P. Marton, M. Schlesinger, J. Appl. Phys. 40, 4529 (1969).

Seraphin, B. O.

B. O. Seraphin, A. B. Meinel, in Optical Properties of Solids—New DevelopmentsB. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), p. 928.

Sheng, P.

Granular metals are reviewed by B. Abeles, P. Sheng, M. D. Coutts, Y. Arie, Adv. Phys. 24, 407 (1975); and B. Abeles, Applied Solid State Science, Vol. 6, R. Wolfe, Ed. (Academic Press, New York, 1976), in press.

Spitzer, W. G.

W. G. Spitzer, D. Kleinman, D. Walsh, Phys. Rev. 113, 127, 133 (1959); E. A. Fagen, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 16.

Strensland, L.

P. W. Baumeister, G. Borak, L. Strensland, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, New-Castle-Upon-Tyne, U.K., 1969), p. 147.

Stroud, D.

D. Stroud, Phys. Rev. B 12, 3368 (1975).

Taft, E. A.

H. R. Philipp, E. A. Taft, Phys. Rev. 120, 37 (1960); P. A. Schumann, W. A. Keenan, A. W. Tong, H. H. Gegenwarton, C. P. Schneider, J. Electrochem. Soc. 118, 145 (1971).

Tempkin, R. J.

R. J. Tempkin, G. A. N. Cornell, W. Paul, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 533.

Tokarsky, R. W.

R. W. Tokarsky, J. P. Marton, J. Vac. Sci. Technol. 12, 643 (1975).

R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3051 (1974).

Walsh, D.

W. G. Spitzer, D. Kleinman, D. Walsh, Phys. Rev. 113, 127, 133 (1959); E. A. Fagen, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 16.

Weakliem, H. A.

J. I. Gittleman, B. Abeles, H. A. Weakliem, P. J. Zanzucchi, unpublished data.

Webman, I.

I. Webman, J. Jortner, M. H. Cohen, Phys. Rev. in press.

Zanzucchi, P. J.

J. I. Gittleman, B. Abeles, H. A. Weakliem, P. J. Zanzucchi, unpublished data.

Zeller, H. R.

H. R. Zeller, D. Kuse, J. Appl. Phys. 44, 2763 (1973).

Adv. Phys. (1)

Granular metals are reviewed by B. Abeles, P. Sheng, M. D. Coutts, Y. Arie, Adv. Phys. 24, 407 (1975); and B. Abeles, Applied Solid State Science, Vol. 6, R. Wolfe, Ed. (Academic Press, New York, 1976), in press.

Appl. Phys. Lett. (1)

J. I. Gittleman, Appl. Phys. Lett. 28, 370 (1976).

J. Appl. Phys. (4)

R. Landauer, J. Appl. Phys. 23, 779 (1952).

J. P. Marton, J. R. Lemon, J. Appl. Phys. 44, 3953 (1973).

R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3051 (1974).

H. R. Zeller, D. Kuse, J. Appl. Phys. 44, 2763 (1973).

J. Chem. Phys. (1)

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

J. Phys. Soc. Jpn. (1)

A. Kawabata, R. Kubo, J. Phys. Soc. Jpn. 21, 1765 (1966).

J. Vac. Sci. Technol. (1)

R. W. Tokarsky, J. P. Marton, J. Vac. Sci. Technol. 12, 643 (1975).

Opt. Acta (1)

D. Flint, P. Baumeister, Opt. Acta 21, 839 (1974).

Philos. Trans. R. Soc. London (1)

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904); Philos. Trans. R. Soc. London 205, 237 (1906).

Phys. Rev. (3)

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).

W. G. Spitzer, D. Kleinman, D. Walsh, Phys. Rev. 113, 127, 133 (1959); E. A. Fagen, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 16.

H. R. Philipp, E. A. Taft, Phys. Rev. 120, 37 (1960); P. A. Schumann, W. A. Keenan, A. W. Tong, H. H. Gegenwarton, C. P. Schneider, J. Electrochem. Soc. 118, 145 (1971).

Phys. Rev. B (5)

G. Rasigni, J. P. Palmari, M. Rasigni, Phys. Rev. B 12, 1121 (1975); R. W. Tokarsky, J. P. Marton, J. Appl. Phys. 45, 3047 (1974); J. P. Marton, M. Schlesinger, J. Appl. Phys. 40, 4529 (1969).

E. B. Priestley, B. Abeles, R. W. Cohen, Phys. Rev. B 12, 2121 (1975).

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).

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

D. Stroud, Phys. Rev. B 12, 3368 (1975).

Other (6)

P. W. Baumeister, G. Borak, L. Strensland, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, New-Castle-Upon-Tyne, U.K., 1969), p. 147.

I. Webman, J. Jortner, M. H. Cohen, Phys. Rev. in press.

J. I. Gittleman, B. Abeles, H. A. Weakliem, P. J. Zanzucchi, unpublished data.

J. I. Gittleman, B. Abeles, Phys. Rev. in press. 1976.

R. J. Tempkin, G. A. N. Cornell, W. Paul, in Amorphous and Liquid Semiconductors, J. Stuke, W. Brenig, Eds. (Taylor and Francis, London, 1974), p. 533.

B. O. Seraphin, A. B. Meinel, in Optical Properties of Solids—New DevelopmentsB. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), p. 928.

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Figures (7)

Fig. 1
Fig. 1

Electron micrographs of sputtered Au–A12O3 films. The vol% of Au and length scale are indicated in the figure. The thicknesses of the films are (a) 110 Å, (b) 140 Å, (c) 110 Å, and (d) 70 Å. (After Abeles et al.1)

Fig. 2
Fig. 2

Log of optical transmission T (measured at normal incidence) vs wavelength λ in sputtered Ag–SiO2 films. The volume fractions x of Ag and the film thicknesses are indicated. (After Cohen et al.6)

Fig. 3
Fig. 3

Optical density of Ag–SiO2 film containing 0.39 volume fraction Ag. Theoretical curves computed from Eqs. (1) and (2); experimental data points are represented by crosses. (After Gittleman and Abeles.16)

Fig. 4
Fig. 4

Plot of the experimental data points for λp and λA as a function of volume fraction of insulator. Full curves calculated from Eq. (2) for spherical (L = ⅓) and cylindrical (L = ½) Ag grains using for A the dielectric constant of bulk Ag and for B the dielectric constant of the insulator. (After Priestley et al.3)

Fig. 5
Fig. 5

Transmission characteristics of sputtered Si–SiC films on Si substrates for various volume fractions of SiC.19 The wavenumber corresponding to the transverse optical phonon in pure SiC is indicated.

Fig. 6
Fig. 6

Wavenumber shift Δν of the reststrahlen absorption peak in Si–SiC as a function of volume fraction of Si–SiC, before and after annealing. The straight line for the annealed samples was computed from Eq. (2).19

Fig. 7
Fig. 7

Reflectance of a 2.8-μm thick film of Ge–A12O3 containing 35 vol% Ge, deposited on Al. Experimental data are given by the solid circles connected by straight lines. The solid curve was computed using Eq. (2). (After Gittleman.2)

Equations (2)

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x A - S A + 2 S + ( 1 - x ) B - S B + 2 S = 0 ,
S - B L S + ( 1 - L ) B = x A - B L A + ( 1 - L ) B ,

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