Abstract

The physical mechanism whereby adsorbed layers of transparent material cause a visual darkening of thin indium films is investigated. The indium is observed to be in the form of discrete islands. The wavelength of minimum optical transmission through the indium film does not vary proportionately with the size of the indium island size, as would be expected if Mie scattering were the dominant optical effect. Instead, this wavelength depends on the fractional volume of the indium film occupied by the indium islands themselves, in the manner predicted by Maxwell Garnett theory.

© 1976 Optical Society of America

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References

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  1. I. J. Giaever, Immunol. 110, 1424 (1973).
  2. J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38350 (1974); see also EM File 39662, E. F. Koch (1975).
  3. The structure of evaporated films has been studied by various authors, for example, J. F. Pocza et al., J. Vacuum Sci. Technol. 6, 472 (1969) and R. S. Sennett et al., J. Op. Soc. Am. 40, 203 (1950). Indium, in particular, was studied by H. P. Singh et al., Philos. Mag. 26, 649 (1972).
    [CrossRef]
  4. J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38723 (1975).
  5. H. Scharfman, J. Appl. Phys. 25, 1352 (1954).
    [CrossRef]
  6. G. Mie, Ann. Phys. 25, 377 (1908).
    [CrossRef]
  7. A. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
    [CrossRef]
  8. R. Y. Koyama, Phys. Rev. B 8, 2426 (1973).
    [CrossRef]
  9. J. C. Maxwell Garnett, Philos. Trans. R. Soc. 203, 385 (1904).
    [CrossRef]
  10. E. David, Z. Phys. 114, 389 (1939).
    [CrossRef]
  11. R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
    [CrossRef]
  12. T. Yamaguchi, Thin Solid Films 13, 261 (1972).
    [CrossRef]
  13. P. Bousquet, C. R. Acad. Sci. Ser. 266, 505 (1968).
  14. R. E. Hetrick, J. Lambe, Phys. Rev. B 11, 1273 (1975).
    [CrossRef]
  15. G. Rasigni, P. Rouard, J. Opt. Soc. Am. 53, 604 (1963).
    [CrossRef]
  16. H. C. Van de Hulst; Light Scattering by Small Particles (Wiley, New York, 1957), p. 70.
  17. I. Giaever, private communication. This effect sets in when the protein film is thicker than about 100 Å, based on ellipsometric measurements of metal surfaces under similar conditions.

1975 (2)

J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38723 (1975).

R. E. Hetrick, J. Lambe, Phys. Rev. B 11, 1273 (1975).
[CrossRef]

1974 (1)

J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38350 (1974); see also EM File 39662, E. F. Koch (1975).

1973 (2)

I. J. Giaever, Immunol. 110, 1424 (1973).

R. Y. Koyama, Phys. Rev. B 8, 2426 (1973).
[CrossRef]

1972 (1)

T. Yamaguchi, Thin Solid Films 13, 261 (1972).
[CrossRef]

1969 (1)

The structure of evaporated films has been studied by various authors, for example, J. F. Pocza et al., J. Vacuum Sci. Technol. 6, 472 (1969) and R. S. Sennett et al., J. Op. Soc. Am. 40, 203 (1950). Indium, in particular, was studied by H. P. Singh et al., Philos. Mag. 26, 649 (1972).
[CrossRef]

1968 (1)

P. Bousquet, C. R. Acad. Sci. Ser. 266, 505 (1968).

1966 (1)

R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
[CrossRef]

1963 (1)

1954 (1)

H. Scharfman, J. Appl. Phys. 25, 1352 (1954).
[CrossRef]

1951 (1)

A. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

1939 (1)

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

1908 (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

1904 (1)

J. C. Maxwell Garnett, Philos. Trans. R. Soc. 203, 385 (1904).
[CrossRef]

Aden, A.

A. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Bousquet, P.

P. Bousquet, C. R. Acad. Sci. Ser. 266, 505 (1968).

David, E.

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

Doremus, R. H.

R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
[CrossRef]

Giaever, I.

I. Giaever, private communication. This effect sets in when the protein film is thicker than about 100 Å, based on ellipsometric measurements of metal surfaces under similar conditions.

Giaever, I. J.

I. J. Giaever, Immunol. 110, 1424 (1973).

Hetrick, R. E.

R. E. Hetrick, J. Lambe, Phys. Rev. B 11, 1273 (1975).
[CrossRef]

Kerker, M.

A. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Koyama, R. Y.

R. Y. Koyama, Phys. Rev. B 8, 2426 (1973).
[CrossRef]

Lambe, J.

R. E. Hetrick, J. Lambe, Phys. Rev. B 11, 1273 (1975).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, Philos. Trans. R. Soc. 203, 385 (1904).
[CrossRef]

Mie, G.

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Pocza, J. F.

The structure of evaporated films has been studied by various authors, for example, J. F. Pocza et al., J. Vacuum Sci. Technol. 6, 472 (1969) and R. S. Sennett et al., J. Op. Soc. Am. 40, 203 (1950). Indium, in particular, was studied by H. P. Singh et al., Philos. Mag. 26, 649 (1972).
[CrossRef]

Rasigni, G.

Rouard, P.

Scharfman, H.

H. Scharfman, J. Appl. Phys. 25, 1352 (1954).
[CrossRef]

Vacca, J. G.

J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38723 (1975).

J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38350 (1974); see also EM File 39662, E. F. Koch (1975).

Van de Hulst, H. C.

H. C. Van de Hulst; Light Scattering by Small Particles (Wiley, New York, 1957), p. 70.

Yamaguchi, T.

T. Yamaguchi, Thin Solid Films 13, 261 (1972).
[CrossRef]

Ann. Phys. (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

C. R. Acad. Sci. Ser. (1)

P. Bousquet, C. R. Acad. Sci. Ser. 266, 505 (1968).

Immunol. (1)

I. J. Giaever, Immunol. 110, 1424 (1973).

J. Appl. Phys. (3)

A. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

R. H. Doremus, J. Appl. Phys. 37, 2775 (1966).
[CrossRef]

H. Scharfman, J. Appl. Phys. 25, 1352 (1954).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Vacuum Sci. Technol. (1)

The structure of evaporated films has been studied by various authors, for example, J. F. Pocza et al., J. Vacuum Sci. Technol. 6, 472 (1969) and R. S. Sennett et al., J. Op. Soc. Am. 40, 203 (1950). Indium, in particular, was studied by H. P. Singh et al., Philos. Mag. 26, 649 (1972).
[CrossRef]

Materials Characterization Operation, Electron Microscope File 38350 (1)

J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38350 (1974); see also EM File 39662, E. F. Koch (1975).

Materials Characterization Operation, Electron Microscope File 38723 (1)

J. G. Vacca, General Electric Research & Development Center, Materials Characterization Operation, Electron Microscope File 38723 (1975).

Philos. Trans. R. Soc. (1)

J. C. Maxwell Garnett, Philos. Trans. R. Soc. 203, 385 (1904).
[CrossRef]

Phys. Rev. B (2)

R. Y. Koyama, Phys. Rev. B 8, 2426 (1973).
[CrossRef]

R. E. Hetrick, J. Lambe, Phys. Rev. B 11, 1273 (1975).
[CrossRef]

Thin Solid Films (1)

T. Yamaguchi, Thin Solid Films 13, 261 (1972).
[CrossRef]

Z. Phys. (1)

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

Other (2)

H. C. Van de Hulst; Light Scattering by Small Particles (Wiley, New York, 1957), p. 70.

I. Giaever, private communication. This effect sets in when the protein film is thicker than about 100 Å, based on ellipsometric measurements of metal surfaces under similar conditions.

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Figures (10)

Fig. 1
Fig. 1

Measured optical density (O.D.) vs wavelength for an indium immunology slide with 250-Å mass thickness of indium. The solid curve corresponds to the uncoated slide and the dashed curve to the same slide after it was coated with 40 Å of MgF2.

Fig. 2
Fig. 2

Transmission electron micrograph of the slide from Fig. 1. The glass substrate had been coated with fornvar before the indium was put on. This formvar was teased free from the glass and used for this micrograph. Microscopy was performed by Vacca.

Fig. 3
Fig. 3

Transmission electron micrograph by Vacca of a replicated indium immunology slide (not the same slide as in Fig. 2). Platinum was first shadow cast at an angle of 30° to the surface. Then, carbon was deposited normal to the surface. The carbon replicas were dissolved free in concentrated nitric acid and used for the micrograph. A stereoscope indicates 290 Å as the height of the islands.

Fig. 4
Fig. 4

Theoretical optical density vs wavelength for a film of indium spheres, 1390 Å in diameter. Single scattering only is considered. O.D. is taken as tot/2.303, where σtot is the total scattering cross section, and N is the number of particles per unit area. N is taken to be 4.5 × 109/cm2, corresponding to 68% fractional area coverage. The solid curve is for uncoated spheres, and the dashed curve represents spheres coated with 40 Å of MgF2 (index of refraction = 1.4).

Fig. 5
Fig. 5

Measured O.D. vs wavelength for an indium immunology slide with 200-Å mass thickness of indium. The solid (dashed) curve represents the slide before (after) coating with 40 Å of MgF2.

Fig. 6
Fig. 6

Theoretical O.D. vs wavelength for film of indium spheres 700 Å in diameter. O.D. is taken as tot/2.303, where tot is the total scattering cross section, and N is the number of particles per unit area. N is set equal to 1.6 × 1010/cm2, corresponding to a fractional coverage of 62%. The solid (dashed) curve corresponds to the spheres before (after) coating with 40 Å of MgF2.

Fig. 7
Fig. 7

Relative scattered light intensity vs scattering angle θ for an indium immunology slide before (solid curve) and after (dashed) coating with bovine serum albumin. Zero scattering angle is defined as forward scattering. The slide was held normal to the incident beam of light, which had a wavelength of 5460 Å. The scattering at all angles seems to be less for the slide after coating with BSA than before. The scattering from a plain glass plate is shown as the dotted line. These are the results obtained for both polarizations of light.

Fig. 8
Fig. 8

Plot of λm2p2 vs (2 + Q)/(1 − Q) for the various samples measured. λm is the wavelength of maximum O.D., λp is the plasma wavelength (1080 Å for indium), and Q is the fractional coverage of the islands. According to Eq. (1), a straight line with intercept 1 should be obtained, and the slope should equal the square of the effective index of refraction ns2 of the surrounding medium. From this graph, ns equals 1.31.

Fig. 9
Fig. 9

Theoretical O.D. vs wavelength for a 368-Å thick Maxwell Garnett film of indium, based on the predicted optical constants of Eq. (2). The parameters were chosen to correspond to the film of Figs. 1 and 2. To obtain the observed λm, ns was set equal to 1.5.

Fig. 10
Fig. 10

Plot of the theoretical O.D. peak wavelength λm vs the fractional coverage of the islands Q for various values of the surrounding index of refraction ns. The actual specimens observed are shown here as ○ and follow the expected general behavior as a function of Q. The effective surrounding index ns is higher than expected and corresponds to approximately 1.5.

Tables (2)

Tables Icon

Table I Comparison of the Effective Surrounding Index of Refraction ns Calculated from the Observed O.D. Peak Wavelength λm and the Observed Fractional Coverage of the Islands Q

Tables Icon

Table II Calculation of Effective Index of Refraction of Surrounding Medium n0 Based on Eq. (1) for Two Samples Coated with 40 Å of MgF2

Equations (5)

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λ m = λ p [ 1 + ( 2 + Q 1 - Q ) n s 2 ] 1 / 2 .
( ^ c - 1 ) / ( ^ c + 2 ) = N α ,
α = r 3 [ ^ - s ) / ( ^ + 2 s ) ] ,
^ c - 1 ^ c + 2 = Q ( ^ - s ^ + 2 s ) .
^ c = 2 Q ( ^ - s ) + ^ + 2 s ^ ( 1 - Q ) + s ( 2 + Q ) .

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