Abstract

A model for the calculation of diffuse reflectance spectra for oxidized metals is applied to thermally oxidized copper films and compared with experiments. The model calculations reproduce the spectral structure observed in the experiments. It is demonstrated that the air–oxide interface roughness dominates the scattering for wavelengths shorter than the absorption threshold of the oxide, and the oxide–metal interface roughness dominates for longer wavelengths. Using the model for fitting calculations the rms roughness values for the two interfaces are determined independently. The roughness values agree with the results from high accuracy stylus profiling of the oxide front surface as well as stylus profiling and total integrated scattering of He–Ne light from the bare metal surface, obtained after etching away the oxide. The good overall agreement between the calculated and experimental diffuse reflectance spectra, as well as the rms roughness values determined with different techniques, confirms the applicability of the model.

© 1989 Optical Society of America

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References

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  1. A. Roos, M. Bergkvist, C.-G. Ribbing, “Optical Scattering from Oxidized Metals. 1: Model Formulation and Properties,” Appl. Opt. 28, 1360–1364 (1989).
    [CrossRef] [PubMed]
  2. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).
  3. A. Roos, M. Bergkvist, C.-G. Ribbing, J. M. Bennett, “Quantitative Interface Roughness Studies of Copper Oxide on Copper,” presented at ICTF-7, New Delhi, Dec. 1987;Thin Solid Films 164, 5–17 (1988).
  4. R. D. Pettit, J. M. Freese, “Wavelength Dependent Scattering Caused by Dust Accumulation on Solar Mirrors,” Sol. Energy Mat. 3, 1–20 (1980).
    [CrossRef]
  5. B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
    [CrossRef]
  6. A. Roos, M. Bergkvist, C.-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221–227 (1985).
    [CrossRef]
  7. A. Roos, C.-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225–227 (1985).
    [CrossRef]
  8. A. Roos, M. Bergkvist, C.-G. Ribbing, “Determination of the SiO2/Si Interface Roughness by Diffuse Reflectance Measurements,” Appl. Opt. 27, 4314–4317 (1988).
    [CrossRef] [PubMed]
  9. National Inst. Standards & Technology, Washington, D.C., Reference Materials, Ceramic Diffuse Reflectance Standards, Lg numbers 2019(a) and 2021.
  10. J. M. Bennett, J. H. Dancy, “Stylus Profiling Instrument for Measuring Statistical Properties of Smooth Optical Surfaces,” Appl. Opt. 20, 1785–1802 (1981).
    [CrossRef] [PubMed]
  11. Manufactured by Edge Technologies Indianapolis, IN.
  12. J. M. Bennett, Michelson Laboratory; unpublished data (1988).
  13. S. Tolansky, High Resolution Spectroscopy (Pitman Publishing Corp., New York, 1947), p. 86.
  14. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 133.
  15. J. M. Elson, J. M. Bennett, “Relation Between the Angular Dependence of Scattering and the Statistical Properties of Optical Surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [CrossRef]
  16. G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
    [CrossRef]
  17. L. Mattsson, “Total Integrated Scatter Measurement System for Quality Assessment of Coatings on Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 264–271 (1986).
  18. “Standard Test Method for Measuring the Effective Surface Roughness of Optical Components by Total Integrated Scattering,” ASTM F-1048-87, American Society for Testing and Materials, 1916 Race St., Philadelphia, PA 19103.
  19. A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
    [CrossRef]

1989 (1)

1988 (1)

1987 (2)

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
[CrossRef]

1986 (1)

L. Mattsson, “Total Integrated Scatter Measurement System for Quality Assessment of Coatings on Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 264–271 (1986).

1985 (2)

A. Roos, M. Bergkvist, C.-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221–227 (1985).
[CrossRef]

A. Roos, C.-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225–227 (1985).
[CrossRef]

1982 (1)

B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
[CrossRef]

1981 (1)

1980 (1)

R. D. Pettit, J. M. Freese, “Wavelength Dependent Scattering Caused by Dust Accumulation on Solar Mirrors,” Sol. Energy Mat. 3, 1–20 (1980).
[CrossRef]

1979 (1)

Al-Jumaily, G. A.

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).

Bennett, J. M.

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

J. M. Bennett, J. H. Dancy, “Stylus Profiling Instrument for Measuring Statistical Properties of Smooth Optical Surfaces,” Appl. Opt. 20, 1785–1802 (1981).
[CrossRef] [PubMed]

J. M. Elson, J. M. Bennett, “Relation Between the Angular Dependence of Scattering and the Statistical Properties of Optical Surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
[CrossRef]

J. M. Bennett, Michelson Laboratory; unpublished data (1988).

A. Roos, M. Bergkvist, C.-G. Ribbing, J. M. Bennett, “Quantitative Interface Roughness Studies of Copper Oxide on Copper,” presented at ICTF-7, New Delhi, Dec. 1987;Thin Solid Films 164, 5–17 (1988).

Bergkvist, M.

A. Roos, M. Bergkvist, C.-G. Ribbing, “Optical Scattering from Oxidized Metals. 1: Model Formulation and Properties,” Appl. Opt. 28, 1360–1364 (1989).
[CrossRef] [PubMed]

A. Roos, M. Bergkvist, C.-G. Ribbing, “Determination of the SiO2/Si Interface Roughness by Diffuse Reflectance Measurements,” Appl. Opt. 27, 4314–4317 (1988).
[CrossRef] [PubMed]

A. Roos, M. Bergkvist, C.-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221–227 (1985).
[CrossRef]

A. Roos, M. Bergkvist, C.-G. Ribbing, J. M. Bennett, “Quantitative Interface Roughness Studies of Copper Oxide on Copper,” presented at ICTF-7, New Delhi, Dec. 1987;Thin Solid Films 164, 5–17 (1988).

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 133.

Dancy, J. H.

Duparre, A.

A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
[CrossRef]

Elson, J. M.

Freese, J. M.

R. D. Pettit, J. M. Freese, “Wavelength Dependent Scattering Caused by Dust Accumulation on Solar Mirrors,” Sol. Energy Mat. 3, 1–20 (1980).
[CrossRef]

Jungling, K. C.

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

Karlsson, B.

B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
[CrossRef]

Karlsson, T.

B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
[CrossRef]

Kuhn, H. J.

A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
[CrossRef]

Mattsson, L.

L. Mattsson, “Total Integrated Scatter Measurement System for Quality Assessment of Coatings on Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 264–271 (1986).

McNeil, J. R.

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

Pettit, R. D.

R. D. Pettit, J. M. Freese, “Wavelength Dependent Scattering Caused by Dust Accumulation on Solar Mirrors,” Sol. Energy Mat. 3, 1–20 (1980).
[CrossRef]

Ribbing, C.-G.

A. Roos, M. Bergkvist, C.-G. Ribbing, “Optical Scattering from Oxidized Metals. 1: Model Formulation and Properties,” Appl. Opt. 28, 1360–1364 (1989).
[CrossRef] [PubMed]

A. Roos, M. Bergkvist, C.-G. Ribbing, “Determination of the SiO2/Si Interface Roughness by Diffuse Reflectance Measurements,” Appl. Opt. 27, 4314–4317 (1988).
[CrossRef] [PubMed]

A. Roos, M. Bergkvist, C.-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221–227 (1985).
[CrossRef]

A. Roos, C.-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225–227 (1985).
[CrossRef]

B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
[CrossRef]

A. Roos, M. Bergkvist, C.-G. Ribbing, J. M. Bennett, “Quantitative Interface Roughness Studies of Copper Oxide on Copper,” presented at ICTF-7, New Delhi, Dec. 1987;Thin Solid Films 164, 5–17 (1988).

Roos, A.

A. Roos, M. Bergkvist, C.-G. Ribbing, “Optical Scattering from Oxidized Metals. 1: Model Formulation and Properties,” Appl. Opt. 28, 1360–1364 (1989).
[CrossRef] [PubMed]

A. Roos, M. Bergkvist, C.-G. Ribbing, “Determination of the SiO2/Si Interface Roughness by Diffuse Reflectance Measurements,” Appl. Opt. 27, 4314–4317 (1988).
[CrossRef] [PubMed]

A. Roos, C.-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225–227 (1985).
[CrossRef]

A. Roos, M. Bergkvist, C.-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221–227 (1985).
[CrossRef]

B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
[CrossRef]

A. Roos, M. Bergkvist, C.-G. Ribbing, J. M. Bennett, “Quantitative Interface Roughness Studies of Copper Oxide on Copper,” presented at ICTF-7, New Delhi, Dec. 1987;Thin Solid Films 164, 5–17 (1988).

Schirmer, G.

A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).

Tolansky, S.

S. Tolansky, High Resolution Spectroscopy (Pitman Publishing Corp., New York, 1947), p. 86.

Valkonen, E.

B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
[CrossRef]

Walther, H. G.

A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
[CrossRef]

Welsch, E.

A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
[CrossRef]

Wilson, S. R.

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J. Phys. (Paris) (1)

A. Duparre, E. Welsch, H. G. Walther, H. J. Kuhn, G. Schirmer, “Optical Losses of Sputtered Ta2O5 Films,” J. Phys. (Paris) 48, 1155–1159 (1987).
[CrossRef]

Opt. Eng. (1)

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, J. M. Bennett, “Frequency Response Characteristics of a Mechanical Surface Profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

Phys. Lett. A (1)

A. Roos, C.-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225–227 (1985).
[CrossRef]

Phys. Scr. (1)

B. Karlsson, C.-G. Ribbing, A. Roos, E. Valkonen, T. Karlsson, “Optical Properties of some Metal Oxides in Solar Collectors,” Phys. Scr. 25, 826–831 (1982).
[CrossRef]

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

L. Mattsson, “Total Integrated Scatter Measurement System for Quality Assessment of Coatings on Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 652, 264–271 (1986).

Sol. Energy Mat. (1)

R. D. Pettit, J. M. Freese, “Wavelength Dependent Scattering Caused by Dust Accumulation on Solar Mirrors,” Sol. Energy Mat. 3, 1–20 (1980).
[CrossRef]

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, 221–227 (1985).
[CrossRef]

Other (8)

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).

A. Roos, M. Bergkvist, C.-G. Ribbing, J. M. Bennett, “Quantitative Interface Roughness Studies of Copper Oxide on Copper,” presented at ICTF-7, New Delhi, Dec. 1987;Thin Solid Films 164, 5–17 (1988).

National Inst. Standards & Technology, Washington, D.C., Reference Materials, Ceramic Diffuse Reflectance Standards, Lg numbers 2019(a) and 2021.

“Standard Test Method for Measuring the Effective Surface Roughness of Optical Components by Total Integrated Scattering,” ASTM F-1048-87, American Society for Testing and Materials, 1916 Race St., Philadelphia, PA 19103.

Manufactured by Edge Technologies Indianapolis, IN.

J. M. Bennett, Michelson Laboratory; unpublished data (1988).

S. Tolansky, High Resolution Spectroscopy (Pitman Publishing Corp., New York, 1947), p. 86.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 133.

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Figures (5)

Fig. 1
Fig. 1

Diffuse reflectance spectra illustrating the fitting of σ1 for sample 4. In the short wavelength region the σ2-value is unimportant and is set = 0. Notice the expanded reflectance scale:— — — —, σ1 = 6 nm; · — · — · —, σ1 = 7 nm; ·· — ·· — ·· —, σ1 = 8 nm.

Fig. 2
Fig. 2

Reflectance spectra as in Fig. 1, illustrating the fitting of the σ2-value for sample 3. The experimental and calculated specular spectra are also shown. σ1 = 6.8 nm, obtained as in Fig. 1, was used in the calculations — — —, σ2 = 5.5 nm; — · — · —, σ2 = 6.5 nm; — ·· — ·· —, σ2 = 7.5 nm.

Fig. 3
Fig. 3

Experimental and calculated diffuse reflectance spectra for the four samples as indicated. The σ-values used in the calculations are given in Table I.

Fig. 4
Fig. 4

Talystep profiles of the various interfaces as indicated. The σ-values obtained from the analysis of the profile are indicated. Notice the differences in x- and y-scales.

Fig. 5
Fig. 5

Comparison of σ-values obtained with the three different techniques as discussed in the text. (a) σ1 (model calculation) vs σ1 (Talystep) (b) σ2 (model calculation) and σ2 (TIS) vs σ2 (Talystep).

Tables (1)

Tables Icon

Table I Data on Sample Preparation and Surface Roughness rms-Values as Obtained by Different Techniquesa

Equations (4)

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R D i = { 1 exp [ ( 4 π σ i / λ ) 2 ] } R S i , σ = 0 ,
R D ( λ ) = ( λ , d ) ( oxide ) R D 1 + ( λ , 0 ) ( metal ) R D 2 exp ( α d ) .
d min = 2 π a r .
TIS = R D R S + R D = 1 exp [ ( 4 π σ λ ) 2 ] ,

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