Abstract

The optical properties of globular Sn films on Al2O3 substrates are analyzed. These films are composed of Sn particles with sizes of the order of the wavelength of visible light, and are of interest because of their solar-selective properties. The experimental data show interference-film properties at long wavelengths, and a large diffracted component at short wavelengths superimposed on a Lambertian angular distribution. The calculated properties of finite-conductivity wire gratings in general agree well with the observed film properties; however, at short wavelengths a scalar diffraction model describes the angular distribution of the transmitted diffracted light. In this model the globular film appears to have film-thickness variations, and a coherence length of approximately two globule diameters. With an empirical “shadowing” term removed from the experimental data, this scalar model works well even at relatively long wavelengths (λ/4 ≤ globule radius).

© 1978 Optical Society of America

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  1. H. R. Zeller and D. Kuse, J. Appl. Phys. 44, 2763 (1973).
    [Crossref]
  2. E. A. Allen, G. D. Scott, K. T. Thompson, and F. Veas, J. Opt. Soc. Am. 64, 1190 (1974).
    [Crossref]
  3. R. E. Hetrick and J. Lambe, Phys. Rev. B 11, 1273 (1975).
    [Crossref]
  4. C. M. Horwitz, , presented at ISES Conference, Los Angeles, Calif., July 1975. C. M. Horwitz, “Solar selective globular metal films,” J. Opt. Soc. Am. 67, 1032–1038 (1977) (this issue).
  5. H. P. Singh and L. E. Murr, Philos. Mag. 26, 649 (1972).
    [Crossref]
  6. D. J. Stirland, Appl. Phys. Lett. 10, 326 (1966); P. W. Palmberg, T. N. Rhodin, and C. J. Todd, Appl. Phys. Lett. 10, 122 (1967); A. Chambers and M. Prutton, Thin Solid Films 1, 393 (1967).
    [Crossref]
  7. C. G. Granqvist and R. A. Buhrman, Appl. Phys. Lett. 27, 693 (1975); J. G. Skofronick and W. B. Phillips, J. Appl. Phys. 38, 4791 (1967).
    [Crossref]
  8. A. Guinier and G. Fournet, Small Angle Scattering of X Rays (Wiley, New York, 1955), p. 111et seq.
  9. C. M. Horwitz, .
  10. M. Kerker, The Scattering of Light (Academic, New York, (1969).
  11. D. E. Barrick, in Radar Cross-Section Handbook, edited by G. T. Ruck (Plenum, New York, 1970).
  12. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).
  13. A. Guinier, X Ray Diffraction (Wiley, New York, 1963).
  14. R. H. Doremus, J. Appl. Phys. 37, 3775 (1966); T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972); P. H. Lissberger and R. G. Nelson, Thin Solid Films 21, 159 (1974); R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, Phys. Rev. B 8, 3689 (1973).
    [Crossref]
  15. J. I. Treu, Appl. Opt. 15, 2746 (1976).
    [Crossref] [PubMed]
  16. G. W. Stroke, “Diffraction Gratings,” in Handbuch der Physik (Springer-Verlag, Berlin, 1967), Vol. 29, p. 504.
  17. J. A. Beunen, M. Sc. Thesis, University of Sydney (1976).
  18. A. I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 20, 44 (1965).
  19. A. P. Lenham and D. M. Treherne, J. Opt. Soc. Am. 56, 752 (1966).
    [Crossref]
  20. E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
    [Crossref]
  21. R. Bracewell, The Fourier Transform (McGraw-Hill, New York, 1965).

1976 (1)

1975 (3)

C. G. Granqvist and R. A. Buhrman, Appl. Phys. Lett. 27, 693 (1975); J. G. Skofronick and W. B. Phillips, J. Appl. Phys. 38, 4791 (1967).
[Crossref]

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

E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
[Crossref]

1974 (1)

1973 (1)

H. R. Zeller and D. Kuse, J. Appl. Phys. 44, 2763 (1973).
[Crossref]

1972 (1)

H. P. Singh and L. E. Murr, Philos. Mag. 26, 649 (1972).
[Crossref]

1966 (3)

D. J. Stirland, Appl. Phys. Lett. 10, 326 (1966); P. W. Palmberg, T. N. Rhodin, and C. J. Todd, Appl. Phys. Lett. 10, 122 (1967); A. Chambers and M. Prutton, Thin Solid Films 1, 393 (1967).
[Crossref]

R. H. Doremus, J. Appl. Phys. 37, 3775 (1966); T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972); P. H. Lissberger and R. G. Nelson, Thin Solid Films 21, 159 (1974); R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, Phys. Rev. B 8, 3689 (1973).
[Crossref]

A. P. Lenham and D. M. Treherne, J. Opt. Soc. Am. 56, 752 (1966).
[Crossref]

1965 (1)

A. I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 20, 44 (1965).

Allen, E. A.

Barrick, D. E.

D. E. Barrick, in Radar Cross-Section Handbook, edited by G. T. Ruck (Plenum, New York, 1970).

Beunen, J. A.

J. A. Beunen, M. Sc. Thesis, University of Sydney (1976).

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).

Bracewell, R.

R. Bracewell, The Fourier Transform (McGraw-Hill, New York, 1965).

Buhrman, R. A.

C. G. Granqvist and R. A. Buhrman, Appl. Phys. Lett. 27, 693 (1975); J. G. Skofronick and W. B. Phillips, J. Appl. Phys. 38, 4791 (1967).
[Crossref]

Doremus, R. H.

R. H. Doremus, J. Appl. Phys. 37, 3775 (1966); T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972); P. H. Lissberger and R. G. Nelson, Thin Solid Films 21, 159 (1974); R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, Phys. Rev. B 8, 3689 (1973).
[Crossref]

Fournet, G.

A. Guinier and G. Fournet, Small Angle Scattering of X Rays (Wiley, New York, 1955), p. 111et seq.

Franks, A.

E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
[Crossref]

Gale, B.

E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
[Crossref]

Golovashkin, A. I.

A. I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 20, 44 (1965).

Granqvist, C. G.

C. G. Granqvist and R. A. Buhrman, Appl. Phys. Lett. 27, 693 (1975); J. G. Skofronick and W. B. Phillips, J. Appl. Phys. 38, 4791 (1967).
[Crossref]

Guinier, A.

A. Guinier, X Ray Diffraction (Wiley, New York, 1963).

A. Guinier and G. Fournet, Small Angle Scattering of X Rays (Wiley, New York, 1955), p. 111et seq.

Hetrick, R. E.

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

Horwitz, C. M.

C. M. Horwitz, , presented at ISES Conference, Los Angeles, Calif., July 1975. C. M. Horwitz, “Solar selective globular metal films,” J. Opt. Soc. Am. 67, 1032–1038 (1977) (this issue).

C. M. Horwitz, .

Hutley, M. C.

E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
[Crossref]

Kerker, M.

M. Kerker, The Scattering of Light (Academic, New York, (1969).

Kuse, D.

H. R. Zeller and D. Kuse, J. Appl. Phys. 44, 2763 (1973).
[Crossref]

Lambe, J.

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

Lenham, A. P.

Motulevich, G. P.

A. I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 20, 44 (1965).

Murr, L. E.

H. P. Singh and L. E. Murr, Philos. Mag. 26, 649 (1972).
[Crossref]

Palmer, E. W.

E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
[Crossref]

Scott, G. D.

Singh, H. P.

H. P. Singh and L. E. Murr, Philos. Mag. 26, 649 (1972).
[Crossref]

Stirland, D. J.

D. J. Stirland, Appl. Phys. Lett. 10, 326 (1966); P. W. Palmberg, T. N. Rhodin, and C. J. Todd, Appl. Phys. Lett. 10, 122 (1967); A. Chambers and M. Prutton, Thin Solid Films 1, 393 (1967).
[Crossref]

Stroke, G. W.

G. W. Stroke, “Diffraction Gratings,” in Handbuch der Physik (Springer-Verlag, Berlin, 1967), Vol. 29, p. 504.

Thompson, K. T.

Treherne, D. M.

Treu, J. I.

Veas, F.

Verrill, J. F.

E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).

Zeller, H. R.

H. R. Zeller and D. Kuse, J. Appl. Phys. 44, 2763 (1973).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

D. J. Stirland, Appl. Phys. Lett. 10, 326 (1966); P. W. Palmberg, T. N. Rhodin, and C. J. Todd, Appl. Phys. Lett. 10, 122 (1967); A. Chambers and M. Prutton, Thin Solid Films 1, 393 (1967).
[Crossref]

C. G. Granqvist and R. A. Buhrman, Appl. Phys. Lett. 27, 693 (1975); J. G. Skofronick and W. B. Phillips, J. Appl. Phys. 38, 4791 (1967).
[Crossref]

J. Appl. Phys. (2)

R. H. Doremus, J. Appl. Phys. 37, 3775 (1966); T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972); P. H. Lissberger and R. G. Nelson, Thin Solid Films 21, 159 (1974); R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, Phys. Rev. B 8, 3689 (1973).
[Crossref]

H. R. Zeller and D. Kuse, J. Appl. Phys. 44, 2763 (1973).
[Crossref]

J. Opt. Soc. Am. (2)

Philos. Mag. (1)

H. P. Singh and L. E. Murr, Philos. Mag. 26, 649 (1972).
[Crossref]

Phys. Rev. B (1)

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

Rep. Prog. Phys. (1)

E. W. Palmer, M. C. Hutley, A. Franks, J. F. Verrill, and B. Gale, “Diffraction Gratings,” Rep. Prog. Phys. 38, 975 (1975).
[Crossref]

Sov. Phys. JETP (1)

A. I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 20, 44 (1965).

Other (10)

R. Bracewell, The Fourier Transform (McGraw-Hill, New York, 1965).

C. M. Horwitz, , presented at ISES Conference, Los Angeles, Calif., July 1975. C. M. Horwitz, “Solar selective globular metal films,” J. Opt. Soc. Am. 67, 1032–1038 (1977) (this issue).

G. W. Stroke, “Diffraction Gratings,” in Handbuch der Physik (Springer-Verlag, Berlin, 1967), Vol. 29, p. 504.

J. A. Beunen, M. Sc. Thesis, University of Sydney (1976).

A. Guinier and G. Fournet, Small Angle Scattering of X Rays (Wiley, New York, 1955), p. 111et seq.

C. M. Horwitz, .

M. Kerker, The Scattering of Light (Academic, New York, (1969).

D. E. Barrick, in Radar Cross-Section Handbook, edited by G. T. Ruck (Plenum, New York, 1970).

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965).

A. Guinier, X Ray Diffraction (Wiley, New York, 1963).

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Figures (15)

FIG. 1
FIG. 1

Scanning electron micrographs of a typical globular film with 100 nm deposited mass thickness of Sn. (a) plan view; (b) edge view, showing the cross-sectional shape of the particles.

FIG. 2
FIG. 2

(a) Histogram of globule sizes for the film shown in Fig. 1(a). (b) Approximate radius of open areas around the globules, versus globule radius.

FIG. 3
FIG. 3

(a) Total spectral reflectances of globular Sn films with deposited mass thicknesses of (1) 10 nm, (2) 20 nm, (3) 50 nm, and (4) 100 nm. (b) Total spectral transmittance of the above films.

FIG. 4
FIG. 4

(a) Total spectral transmittance and reflectance of a 70 nm mass thickness Sn film on 20 nm of Al2O3, on a glass substrate. (b) The derived refractive indices and film thickness for this film. Dashed lines join points calculated for hemispherically incident radiation, at the two shorter wavelengths. (c) Calculated normal-incidence R and T of an interference film with n = 2.4, k = 0.3, d = 0.16, on a glass substrate.

FIG. 5
FIG. 5

Spectral scattering properties of a 70 nm Sn film on a dielectric substrate (logarithmic scales). (1) Total reflectance, (2) total transmittance, (3) diffuse scatter (reflected), (4) diffuse scatter (transmitted), as ratio of total transmittance.

FIG. 6
FIG. 6

(a) Angular scattered light distribution of a 70 nm Sn film at λ = 0.4 μm. Globules facing the light sources (solid line) and reversed (dotted). 180° corresponds to backscatter. (b) Polar plots of reflected scatter from a 100 nm Sn film at various wavelengths. [Exact circular shapes correspond to a (cosθ) function.] The transmitted scatter at one wavelength is also shown.

FIG. 7
FIG. 7

Transmitted scatter vs angle for a 100 nm film at various wavelengths.

FIG. 8
FIG. 8

Experimental diffracted intensities vs q(=sinθ/λ) for various wavelengths, for a 100 nm Sn film. (a) Plotted directly; (b) cosθ shadowing term removed.

FIG. 9
FIG. 9

Schematic representations of (a) a globular film and (b) its one-dimensional analog, a wire diffraction grating with the E field perpendicular to the wire direction.

FIG. 10
FIG. 10

Theoretical curves for Sn wire gratings giving the total reflected (R) and transmitted (T) energies vs wavelength for normally incident light [E(⊥) polarization]. The grating period is constant at p = 0.9 μm; wire radii are (1) r = 0.35 μm, (2) r = 0.25 μm, (3) r = 0.2 μm.

FIG. 11
FIG. 11

As for Fig. 10, but with p varying while the metal area fraction (2r/p) is held constant at 0.56. (1) p = 0.9 μm, (2) 0.7 μm, (3) p = 0.5 μm.

FIG. 12
FIG. 12

Scattering geometry for an annulus. (a) Plan view: r1 = inner radius, r2 = outer radius; (b) side view: |k| = 2π/λ, θ = scattering angle.

FIG. 13
FIG. 13

Calculated scattering patterns for annulus diffraction, using data from Fig. 2. (a) Plot vs q; (b) plot vs θ, for λ = 0.32 μm.

FIG. 14
FIG. 14

Autocorrelation functions P(r) for (a) The calculated annulus diffraction curve of Fig. 13; (b) the experimental data of Fig. 8(b).

FIG. 15
FIG. 15

Model of a globular film used to account for negative P(r) values. Rays traveling between closely spaced globules (a) experience greater phase shift than those traveling in more open regions (b). The physical film height is d.

Equations (8)

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d = m λ / 4 n ,
d = 3 2 t / f ,
I ( J 1 ( 2 π q r ) ( 2 π q r ) ) 2 ,
r 0.61 q ,
a = 2 π λ ( r 2 2 J 1 ( 2 π q r 2 ) ( 2 π q r 2 ) - r 1 2 J 1 ( 2 π q r 1 ) ( 2 π q r 1 ) ) ,
I diff = n = 1 N p ( n ) a ( n ) 2 ,
P ( r ) = 2 π 0 dq I ( q ) q J 0 ( 2 π r q ) ,
Δ ϕ = k 0 ( n 1 - n 0 ) d 4 rad at λ = 0.32 μ m .