Abstract

Aluminum–silicon composite films consisting of a mixture of aluminum and silicon particles were produced by electron-beam coevaporation. The reflectivity of samples with ≲33-vol % Si was in good agreement with the Bruggeman theory with no adjustable parameters. No parallel-band absorption peak due to the aluminum was detected analogously to the behavior of microcrystalline aluminum films.

© 1983 Optical Society of America

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  1. R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Phys. Rev. B 8, 3689 (1973).
    [CrossRef]
  2. E. B. Priestley, B. Abeles, R. W. Cohen, Phys. Rev. B 12, 2121 (1975).
    [CrossRef]
  3. C. G. Granquist, O. Hunderi, Phys. Rev. B 18, 2897 (1978).
    [CrossRef]
  4. G. A. Niklasson, C. G. Granquist, Thin Solid Films 74, L5 (1980).
    [CrossRef]
  5. C. G. Granquist, R. A. Buhrman, J. Appl. Phys. 47, 2200 (1976).
    [CrossRef]
  6. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York1982).
  7. D. Stroud, Phys. Rev. B 19, 1783 (1979).
    [CrossRef]
  8. L. G. Bernland, O. Hunderi, H. P. Myers, Phys. Rev. Lett. 31, 363 (1973).
    [CrossRef]
  9. D. A. G. Bruggeman, Ann Phys. (Leipzig) 24, 636 (1935).
  10. P. Sheng, Phys. Rev. Lett. 45, 60 (1980).
    [CrossRef]
  11. J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904); Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  13. G. K. M. Thutupalli, S. G. Tomlin, J. Phys. C 10, 467 (1977).
    [CrossRef]
  14. A. G. Mathewson, H. P. Myers, Phys. Scr. 4, 291 (1971).
    [CrossRef]
  15. U. J. Gibson, H. G. Craighead, R. A. Buhrman, Phys. Rev. B 25, 1449 (1982).
    [CrossRef]
  16. A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
    [CrossRef]
  17. C. G. Granquist, O. Hunderi, J. Appl. Phys. 51, 1751 (1980).
    [CrossRef]
  18. O. Hunderi, Thin Solid Films 37, 275 (1976).
    [CrossRef]
  19. N. W. Ashcroft, K. Sturm, Phys. Rev. B 3, 1898 (1971).
    [CrossRef]
  20. A. G. Mathewson, H. P. Myers, J. Phys. F 2, 403 (1972).
    [CrossRef]

1982 (1)

U. J. Gibson, H. G. Craighead, R. A. Buhrman, Phys. Rev. B 25, 1449 (1982).
[CrossRef]

1980 (4)

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

C. G. Granquist, O. Hunderi, J. Appl. Phys. 51, 1751 (1980).
[CrossRef]

G. A. Niklasson, C. G. Granquist, Thin Solid Films 74, L5 (1980).
[CrossRef]

P. Sheng, Phys. Rev. Lett. 45, 60 (1980).
[CrossRef]

1979 (1)

D. Stroud, Phys. Rev. B 19, 1783 (1979).
[CrossRef]

1978 (1)

C. G. Granquist, O. Hunderi, Phys. Rev. B 18, 2897 (1978).
[CrossRef]

1977 (1)

G. K. M. Thutupalli, S. G. Tomlin, J. Phys. C 10, 467 (1977).
[CrossRef]

1976 (2)

O. Hunderi, Thin Solid Films 37, 275 (1976).
[CrossRef]

C. G. Granquist, R. A. Buhrman, J. Appl. Phys. 47, 2200 (1976).
[CrossRef]

1975 (1)

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

1973 (2)

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

L. G. Bernland, O. Hunderi, H. P. Myers, Phys. Rev. Lett. 31, 363 (1973).
[CrossRef]

1972 (1)

A. G. Mathewson, H. P. Myers, J. Phys. F 2, 403 (1972).
[CrossRef]

1971 (2)

A. G. Mathewson, H. P. Myers, Phys. Scr. 4, 291 (1971).
[CrossRef]

N. W. Ashcroft, K. Sturm, Phys. Rev. B 3, 1898 (1971).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, Ann Phys. (Leipzig) 24, 636 (1935).

1904 (1)

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904); Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
[CrossRef]

Abeles, B.

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

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

Ashcroft, N. W.

N. W. Ashcroft, K. Sturm, Phys. Rev. B 3, 1898 (1971).
[CrossRef]

Bendijk, A.

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

Bernland, L. G.

L. G. Bernland, O. Hunderi, H. P. Myers, Phys. Rev. Lett. 31, 363 (1973).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Bruggeman, D. A. G.

D. A. G. Bruggeman, Ann Phys. (Leipzig) 24, 636 (1935).

Buhrman, R. A.

U. J. Gibson, H. G. Craighead, R. A. Buhrman, Phys. Rev. B 25, 1449 (1982).
[CrossRef]

C. G. Granquist, R. A. Buhrman, J. Appl. Phys. 47, 2200 (1976).
[CrossRef]

Cody, G. D.

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

Cohen, R. W.

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

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

Coutts, M. D.

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

Craighead, H. G.

U. J. Gibson, H. G. Craighead, R. A. Buhrman, Phys. Rev. B 25, 1449 (1982).
[CrossRef]

deKeijser, T. H.

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

Delhez, R.

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

Gibson, U. J.

U. J. Gibson, H. G. Craighead, R. A. Buhrman, Phys. Rev. B 25, 1449 (1982).
[CrossRef]

Granquist, C. G.

C. G. Granquist, O. Hunderi, J. Appl. Phys. 51, 1751 (1980).
[CrossRef]

G. A. Niklasson, C. G. Granquist, Thin Solid Films 74, L5 (1980).
[CrossRef]

C. G. Granquist, O. Hunderi, Phys. Rev. B 18, 2897 (1978).
[CrossRef]

C. G. Granquist, R. A. Buhrman, J. Appl. Phys. 47, 2200 (1976).
[CrossRef]

Hunderi, O.

C. G. Granquist, O. Hunderi, J. Appl. Phys. 51, 1751 (1980).
[CrossRef]

C. G. Granquist, O. Hunderi, Phys. Rev. B 18, 2897 (1978).
[CrossRef]

O. Hunderi, Thin Solid Films 37, 275 (1976).
[CrossRef]

L. G. Bernland, O. Hunderi, H. P. Myers, Phys. Rev. Lett. 31, 363 (1973).
[CrossRef]

Katgerman, L.

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

Mathewson, A. G.

A. G. Mathewson, H. P. Myers, J. Phys. F 2, 403 (1972).
[CrossRef]

A. G. Mathewson, H. P. Myers, Phys. Scr. 4, 291 (1971).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904); Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
[CrossRef]

Mittemeijer, E. J.

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

Myers, H. P.

L. G. Bernland, O. Hunderi, H. P. Myers, Phys. Rev. Lett. 31, 363 (1973).
[CrossRef]

A. G. Mathewson, H. P. Myers, J. Phys. F 2, 403 (1972).
[CrossRef]

A. G. Mathewson, H. P. Myers, Phys. Scr. 4, 291 (1971).
[CrossRef]

Niklasson, G. A.

G. A. Niklasson, C. G. Granquist, Thin Solid Films 74, L5 (1980).
[CrossRef]

Priestley, E. B.

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

Sheng, P.

P. Sheng, Phys. Rev. Lett. 45, 60 (1980).
[CrossRef]

Stroud, D.

D. Stroud, Phys. Rev. B 19, 1783 (1979).
[CrossRef]

Sturm, K.

N. W. Ashcroft, K. Sturm, Phys. Rev. B 3, 1898 (1971).
[CrossRef]

Thutupalli, G. K. M.

G. K. M. Thutupalli, S. G. Tomlin, J. Phys. C 10, 467 (1977).
[CrossRef]

Tomlin, S. G.

G. K. M. Thutupalli, S. G. Tomlin, J. Phys. C 10, 467 (1977).
[CrossRef]

van der Pers, N. M.

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Ann Phys. (Leipzig) (1)

D. A. G. Bruggeman, Ann Phys. (Leipzig) 24, 636 (1935).

J. Appl. Phys. (2)

C. G. Granquist, R. A. Buhrman, J. Appl. Phys. 47, 2200 (1976).
[CrossRef]

C. G. Granquist, O. Hunderi, J. Appl. Phys. 51, 1751 (1980).
[CrossRef]

J. Mater. Sci. (1)

A. Bendijk, R. Delhez, L. Katgerman, T. H. deKeijser, E. J. Mittemeijer, N. M. van der Pers, J. Mater. Sci. 15, 2803 (1980).
[CrossRef]

J. Phys. C (1)

G. K. M. Thutupalli, S. G. Tomlin, J. Phys. C 10, 467 (1977).
[CrossRef]

J. Phys. F (1)

A. G. Mathewson, H. P. Myers, J. Phys. F 2, 403 (1972).
[CrossRef]

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

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904); Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
[CrossRef]

Phys. Rev. B (6)

U. J. Gibson, H. G. Craighead, R. A. Buhrman, Phys. Rev. B 25, 1449 (1982).
[CrossRef]

D. Stroud, Phys. Rev. B 19, 1783 (1979).
[CrossRef]

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

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

C. G. Granquist, O. Hunderi, Phys. Rev. B 18, 2897 (1978).
[CrossRef]

N. W. Ashcroft, K. Sturm, Phys. Rev. B 3, 1898 (1971).
[CrossRef]

Phys. Rev. Lett. (2)

L. G. Bernland, O. Hunderi, H. P. Myers, Phys. Rev. Lett. 31, 363 (1973).
[CrossRef]

P. Sheng, Phys. Rev. Lett. 45, 60 (1980).
[CrossRef]

Phys. Scr. (1)

A. G. Mathewson, H. P. Myers, Phys. Scr. 4, 291 (1971).
[CrossRef]

Thin Solid Films (2)

G. A. Niklasson, C. G. Granquist, Thin Solid Films 74, L5 (1980).
[CrossRef]

O. Hunderi, Thin Solid Films 37, 275 (1976).
[CrossRef]

Other (2)

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York1982).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Bright-field transmission electron micrographs of the Al–Si films obtained by the Philips EM 400 instrument. The volume fractions of silicon were (a) fSi = 0.07 and (b) fSi = 0.33. The bar on the micrograph denotes 100 nm.

Fig. 2
Fig. 2

Experimental reflectance spectra of an aluminum film and four Al–Si films with different silicon filling factors.

Fig. 3
Fig. 3

Comparison between experimental and theoretical reflectances for Al–Si composites. The straight curves denote the experimental data. The dashed curves denote theoretical results obtained from Ping Sheng’s theory, and the dash–dot curves were obtained from Bruggeman’s theory. The filling factors and average Al particle radii were (a) fSi = 0.07, R ¯ = 8.0 nm; (b) fSi = 0.17, R ¯ = 5.6 nm; (c) fSi = 0.33, R ¯ = 3.8 nm; and (d) fSi = 0.46, R ¯ = 3.7 nm.

Equations (3)

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f Al Al ¯ Br Al + 2 ¯ Br + f Si Si ¯ Br Si + 2 ¯ Br = 0 ,
( 1 f Al 1 / 3 ) 3 ( Si ¯ PS ) ( Al + 2 Si ) + f Al ( 2 Si + ¯ PS ) ( Al Si ) ( Si + 2 ¯ PS ) ( Al + 2 Si ) + 2 f Al ( Si ¯ PS ) ( Al Si ) + ( 1 f Si 1 / 3 ) 3 ( Al ¯ PS ) ( Si + 2 Al ) + f Si ( 2 Al + ¯ PS ) ( Si Al ) ( Al + 2 ¯ PS ) ( Si + 2 Al ) + 2 f Si ( Al ¯ PS ) ( Si Al ) = 0.
1 τ p = 1 τ b + V F L .

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