Abstract

Strong scattering, which exhibits a conspicuous wavelength dependence, has been experimentally observed from certain oxidized metals. A model is presented which combines the effects of interface illumination in a new normalization procedure with the scalar scattering reduction of the Fresnel interface reflectance coefficients. The model is used to calculate the specular and the diffuse part of the hemispheric reflectance from the double layer, with oxide thickness and rms roughness as input parameters. The results give a qualitatively correct spectral variation and underline the importance of the substrate reflectance. The results also illustrate an interesting difference in scattering behavior, whether the front surface or the oxide–metal interface is rough.

© 1989 Optical Society of America

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Errata

Arne Roos, Mikael Bergkvist, and Carl G. Ribbing, "Optical scattering from oxidized metals. 1: Model formulation and properties; errata," Appl. Opt. 28, 3795_1-3795_1 (1989)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-28-18-3795_1

References

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  1. J. M. Eastman, “Scattering by All-Dielectric Multilayer Bandpass Filters and Mirrors, for Lasers,” Phys. Thin Films 10, 167 (1978).
  2. C. K. Carniglia, “Scalar Scattering Theory for Multilayer Optical Coatings,” Opt. Eng. 18, 104 (1979).
    [CrossRef]
  3. P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256 (1986).
  4. A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
    [CrossRef]
  5. M. Bergkvist, A. Roos, C-G. Ribbing, “Diffuse Reflectance Measurements of Interface Roughness,” in Semiconductor Technology, IPAT Workshop, Uppsala, June 1986 (CEP Consultants, Edinburgh, 1986), p. 111.
  6. M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
    [CrossRef]
  7. See, for example, O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1954), Chap. 4.
  8. G. Hass, H. H. Schroder, A. F. Turner, “Mirror Coatings for Low Visible and High Infrared Reflectance,” J. Opt. Soc. Am. 46, 31 (1956).
    [CrossRef]
  9. M. Bergkvist, C-G. Ribbing, A. Roos, P. Temple, “Interface Scattering as a Source for Diffuse Interference in Cuprous Oxide on Copper,” Phys. Lett. A 116, 343 (1986).
    [CrossRef]
  10. P. Temple, “Thin-Film Absorptance Measurements Using Laser Calorimetry,” in Handbook of Optical Constants of Solids, E. Palik, Ed. (Academic, New York, 1985), Chap.7.
  11. J. O. Porteus, “Relation Between the Height Distribution of a Rough Surface and the Reflectance at Normal Incidence,” J. Opt. Soc. Am. 53, 1394 (1963).
    [CrossRef]

1987 (1)

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

1986 (2)

M. Bergkvist, C-G. Ribbing, A. Roos, P. Temple, “Interface Scattering as a Source for Diffuse Interference in Cuprous Oxide on Copper,” Phys. Lett. A 116, 343 (1986).
[CrossRef]

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256 (1986).

1985 (1)

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

1979 (1)

C. K. Carniglia, “Scalar Scattering Theory for Multilayer Optical Coatings,” Opt. Eng. 18, 104 (1979).
[CrossRef]

1978 (1)

J. M. Eastman, “Scattering by All-Dielectric Multilayer Bandpass Filters and Mirrors, for Lasers,” Phys. Thin Films 10, 167 (1978).

1963 (1)

1956 (1)

Amra, C.

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256 (1986).

Bergkvist, M.

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

M. Bergkvist, C-G. Ribbing, A. Roos, P. Temple, “Interface Scattering as a Source for Diffuse Interference in Cuprous Oxide on Copper,” Phys. Lett. A 116, 343 (1986).
[CrossRef]

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

M. Bergkvist, A. Roos, C-G. Ribbing, “Diffuse Reflectance Measurements of Interface Roughness,” in Semiconductor Technology, IPAT Workshop, Uppsala, June 1986 (CEP Consultants, Edinburgh, 1986), p. 111.

Carniglia, C. K.

C. K. Carniglia, “Scalar Scattering Theory for Multilayer Optical Coatings,” Opt. Eng. 18, 104 (1979).
[CrossRef]

Eastman, J. M.

J. M. Eastman, “Scattering by All-Dielectric Multilayer Bandpass Filters and Mirrors, for Lasers,” Phys. Thin Films 10, 167 (1978).

Hass, G.

Heavens, O. S.

See, for example, O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1954), Chap. 4.

Pelletier, E.

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256 (1986).

Porteus, J. O.

Ribbing, C-G.

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

M. Bergkvist, C-G. Ribbing, A. Roos, P. Temple, “Interface Scattering as a Source for Diffuse Interference in Cuprous Oxide on Copper,” Phys. Lett. A 116, 343 (1986).
[CrossRef]

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

M. Bergkvist, A. Roos, C-G. Ribbing, “Diffuse Reflectance Measurements of Interface Roughness,” in Semiconductor Technology, IPAT Workshop, Uppsala, June 1986 (CEP Consultants, Edinburgh, 1986), p. 111.

Roche, P.

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256 (1986).

Roos, A.

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

M. Bergkvist, C-G. Ribbing, A. Roos, P. Temple, “Interface Scattering as a Source for Diffuse Interference in Cuprous Oxide on Copper,” Phys. Lett. A 116, 343 (1986).
[CrossRef]

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

M. Bergkvist, A. Roos, C-G. Ribbing, “Diffuse Reflectance Measurements of Interface Roughness,” in Semiconductor Technology, IPAT Workshop, Uppsala, June 1986 (CEP Consultants, Edinburgh, 1986), p. 111.

Schroder, H. H.

Temple, P.

M. Bergkvist, C-G. Ribbing, A. Roos, P. Temple, “Interface Scattering as a Source for Diffuse Interference in Cuprous Oxide on Copper,” Phys. Lett. A 116, 343 (1986).
[CrossRef]

P. Temple, “Thin-Film Absorptance Measurements Using Laser Calorimetry,” in Handbook of Optical Constants of Solids, E. Palik, Ed. (Academic, New York, 1985), Chap.7.

Turner, A. F.

J. Opt. Soc. Am. (2)

J. Vac. Sci. Technol. A (1)

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

Opt. Eng. (1)

C. K. Carniglia, “Scalar Scattering Theory for Multilayer Optical Coatings,” Opt. Eng. 18, 104 (1979).
[CrossRef]

Phys. Lett. A (1)

M. Bergkvist, C-G. Ribbing, A. Roos, P. Temple, “Interface Scattering as a Source for Diffuse Interference in Cuprous Oxide on Copper,” Phys. Lett. A 116, 343 (1986).
[CrossRef]

Phys. Thin Films (1)

J. M. Eastman, “Scattering by All-Dielectric Multilayer Bandpass Filters and Mirrors, for Lasers,” Phys. Thin Films 10, 167 (1978).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. Roche, C. Amra, E. Pelletier, “Measurement of Scattering Distribution for Characterization of the Roughness of Coated or Uncoated Substrates,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 256 (1986).

Thin Solid Films (1)

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

Other (3)

M. Bergkvist, A. Roos, C-G. Ribbing, “Diffuse Reflectance Measurements of Interface Roughness,” in Semiconductor Technology, IPAT Workshop, Uppsala, June 1986 (CEP Consultants, Edinburgh, 1986), p. 111.

P. Temple, “Thin-Film Absorptance Measurements Using Laser Calorimetry,” in Handbook of Optical Constants of Solids, E. Palik, Ed. (Academic, New York, 1985), Chap.7.

See, for example, O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1954), Chap. 4.

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Figures (9)

Fig. 1
Fig. 1

Experimental diffuse reflectance spectra for three different metal–oxide tandems. Approximate oxide thicknesses as indicated.

Fig. 2
Fig. 2

Calculated specular reflectance spectra for a 185-nm thick dielectric film on a nondispersive substrate: a, highly reflecting (noble metallike) and b, moderately reflecting (transition metallike).

Fig. 3
Fig. 3

Schematic representation of the electric field components traveling in the positive and negative z directions for the oxide–metal configuration.

Fig. 4
Fig. 4

Illumination function ɛ(λ,z) vs position in front of and inside the oxide of thickness d = 185 nm: ______, λ = 500 nm; - - - - - -, λ =750 nm.

Fig. 5
Fig. 5

Illumination function ɛ(λ,z) vs wavelength calculated at the air–oxide interface z = −d for a bulk oxide (dash–dot line) and a 185-nm oxide film (dashed line) on a highly reflecting metal.

Fig. 6
Fig. 6

Illumination function ɛ(λ,z) vs wavelength calculated at the oxide–metal interface z = 0 for a bulk oxide (dash–dot line) and a 185-nm oxide film (dashed line) on a highly reflecting metal substrate.

Fig. 7
Fig. 7

Calculated diffuse reflectance spectra for an oxide–metal tandem with oxide extinction coefficients as indicated. Oxide thickness d = 185 nm, σ1 = 0, and σ2 = 5 nm.

Fig. 8
Fig. 8

Calculated diffuse reflectance spectra for an oxide–metal tandem with oxide extinction coefficients as indicated. Oxide thickness d = 185 nm, σ1 = 20, and σ2 = 0 nm.

Fig. 9
Fig. 9

Calculated diffuse reflectance spectra for an oxide–metal tandem using σ2 as a parameter. Oxide thickness d = 185 nm and σ1 = 0.

Equations (12)

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R d E 2
E ( z ) = E + ( z ) + E ( z ) .
E 0 + = A exp [ i ( ω t + ϕ ) ]  ,
E = A r i exp [ i  ​ ( ω t + ϕ ) ]  ,
E + = A ( 1 r i )  exp [ i ( ω t + ϕ ) ] .
ε ( λ , z ) = E 2 E 0 + 2 .
R = r r *  ,
r = r 1 + r 2 exp ( 2 i δ ) 1 + r 1 r 2 exp ( 2 i δ )  ,
r i = r i exp [ 2 ( 2 π n σ i / λ ) 2 ]  ,
R D = R S ,  σ   =   0 R S ,  σ  ,
R D i = { 1 exp [ ( 4 π n σ / λ ) 2 ] } R S i ,  σ   =   0 .
R D ( λ ) = ε ( λ , d ) ε ( oxide ) R D 1 + ε ( λ , 0 ) ε ( metal ) R D 2 exp ( α d ) .

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