Abstract

It is shown how light scattering provides a powerful tool for thin-film characterization. The introduction of a roughness isotropy degree permits the extraction of structural parameters of the stacks. Replication functions and residual roughnesses are given for TiO2, SiO2, and Ta2O5 materials produced by ion-assisted deposition and ion plating. Additional confirmation is given by measurements of scattering versus wavelength. The sensitivity of design to material and substrate effects is studied. At low-loss levels, surface and bulk phenomena are discussed together. Microstructure is characterized in the frequency bandwidth given by experiment.

© 1993 Optical Society of America

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  1. P. Giacomo, “Les couches réfléchissantes multidiélectriques appliquées à l'interféromètre de Fabry–Perot. Etude théorique et expérimental des couches réelles,” Rev. Opt. 35, 317–354, 442–467 (1956).
  2. J. M. Eastman, “Surface scattering in optical interference coatings,” Ph.D. dissertation (University of Rochester, Rochester, New York, 1974).
  3. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  4. J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation-length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
    [CrossRef] [PubMed]
  5. J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
    [CrossRef] [PubMed]
  6. C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
    [CrossRef] [PubMed]
  7. C. Amra, “From light scattering to the microstructure of thin film multilayers,” in Surface Roughness and Scattering, Vol. 14 of 1992 OSA Technical Digest Series, andOptical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).
  8. C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).
  9. S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
    [CrossRef] [PubMed]
  10. J. M. Elson, “Angle resolved light scattering from composite optical surfaces,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.240, 296–306 (1980).
  11. P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
    [CrossRef]
  12. J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
    [CrossRef]
  13. P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
    [CrossRef]
  14. C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
    [CrossRef]
  15. C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef] [PubMed]
  16. P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
    [CrossRef]
  17. C. Amra, “Minimizing scattering in multilayers: technique for searching optimal realization conditions,” in Optical Technologies for Space Communication Systems, K. B. Bhasin, G. A. Koepf, eds., Proc. Soc. Photo-Opt. Instrum. Eng.756, 265–271 (1987).
  18. C. Amra, P. Roche, E. Pelletier, “Interface roughness cross-correlation laws deduced from scattering diagram measurements on optical multilayers: effect of the material grain size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
    [CrossRef]
  19. C. Amra, D. Torricini, Y. Boucher, L. Bruel, E. Pelletier, “Scattering from optical surfaces and coatings: an easy investigation of microroughness,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 72–81 (1990).
  20. C. Amra, “Calculs et mesures de diffusion appliqués à l'étude de la rugosité dans les traitements optiques multicouches,” J. Opt. (Paris) 21, 83–98 (1990).
    [CrossRef]
  21. C. Amra, “Scattering characterization of materials in thin film form,” in Laser-Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1438, 309–323 (1990).
  22. P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
    [CrossRef]
  23. P. Roche, E. Pelletier, “Characterization of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
    [CrossRef] [PubMed]
  24. C. Amra, “Light scattering from multilayer optics. Part A: Investigation tools. Part B: Application to experiment,” J. Opt. Soc. Am. A (to be published).
  25. R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” Appl. Opt. 31, 1426–1435 (1992).
    [CrossRef] [PubMed]
  26. E. L. Church, “Comments on the correlation length,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 102–111 (1986).
  27. C. Amra, G. Albrand, P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
    [CrossRef] [PubMed]
  28. E. L. Church, “The optical estimator of finish parameters,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 71–85 (1991).
  29. C. Amra, D. Torricini, G. Albrand, P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” submitted to Appl. Opt.
    [PubMed]
  30. C. Amra, L. Bruel, “Comparison of different techniques to characterize surface roughness,” in Surface Roughness and Scattering, Vol. 14 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).
  31. Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

1993

C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
[CrossRef]

C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

1992

1991

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

1990

C. Amra, “Calculs et mesures de diffusion appliqués à l'étude de la rugosité dans les traitements optiques multicouches,” J. Opt. (Paris) 21, 83–98 (1990).
[CrossRef]

1987

C. Amra, P. Roche, E. Pelletier, “Interface roughness cross-correlation laws deduced from scattering diagram measurements on optical multilayers: effect of the material grain size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
[CrossRef]

1986

1985

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[CrossRef]

1984

P. Roche, E. Pelletier, “Characterization of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[CrossRef] [PubMed]

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

1983

1981

P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
[CrossRef]

1980

1956

P. Giacomo, “Les couches réfléchissantes multidiélectriques appliquées à l'interféromètre de Fabry–Perot. Etude théorique et expérimental des couches réelles,” Rev. Opt. 35, 317–354, 442–467 (1956).

Albrand, G.

C. Amra, G. Albrand, P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
[CrossRef] [PubMed]

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

C. Amra, D. Torricini, G. Albrand, P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” submitted to Appl. Opt.
[PubMed]

Al-Jumaily, G. A.

Amra, C.

C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
[CrossRef]

C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

C. Amra, “Calculs et mesures de diffusion appliqués à l'étude de la rugosité dans les traitements optiques multicouches,” J. Opt. (Paris) 21, 83–98 (1990).
[CrossRef]

C. Amra, P. Roche, E. Pelletier, “Interface roughness cross-correlation laws deduced from scattering diagram measurements on optical multilayers: effect of the material grain size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
[CrossRef]

C. Amra, G. Albrand, P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
[CrossRef] [PubMed]

C. Amra, D. Torricini, G. Albrand, P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” submitted to Appl. Opt.
[PubMed]

C. Amra, L. Bruel, “Comparison of different techniques to characterize surface roughness,” in Surface Roughness and Scattering, Vol. 14 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).

C. Amra, “Minimizing scattering in multilayers: technique for searching optimal realization conditions,” in Optical Technologies for Space Communication Systems, K. B. Bhasin, G. A. Koepf, eds., Proc. Soc. Photo-Opt. Instrum. Eng.756, 265–271 (1987).

C. Amra, D. Torricini, Y. Boucher, L. Bruel, E. Pelletier, “Scattering from optical surfaces and coatings: an easy investigation of microroughness,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 72–81 (1990).

C. Amra, “Scattering characterization of materials in thin film form,” in Laser-Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1438, 309–323 (1990).

C. Amra, “Light scattering from multilayer optics. Part A: Investigation tools. Part B: Application to experiment,” J. Opt. Soc. Am. A (to be published).

C. Amra, “From light scattering to the microstructure of thin film multilayers,” in Surface Roughness and Scattering, Vol. 14 of 1992 OSA Technical Digest Series, andOptical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

André, E.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

Apfel, J. H.

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

Bennett, J. M.

Boucher, Y.

C. Amra, D. Torricini, Y. Boucher, L. Bruel, E. Pelletier, “Scattering from optical surfaces and coatings: an easy investigation of microroughness,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 72–81 (1990).

Bouffakhreddine, B.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

Bousquet, P.

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
[CrossRef]

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).

Bruel, L.

C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

C. Amra, D. Torricini, Y. Boucher, L. Bruel, E. Pelletier, “Scattering from optical surfaces and coatings: an easy investigation of microroughness,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 72–81 (1990).

C. Amra, L. Bruel, “Comparison of different techniques to characterize surface roughness,” in Surface Roughness and Scattering, Vol. 14 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).

Bussemer, P.

S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
[CrossRef] [PubMed]

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Church, E. L.

E. L. Church, “The optical estimator of finish parameters,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 71–85 (1991).

E. L. Church, “Comments on the correlation length,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 102–111 (1986).

Croce, P.

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[CrossRef]

Dumas, Ph.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

Duparré, A.

Eastman, J. M.

J. M. Eastman, “Surface scattering in optical interference coatings,” Ph.D. dissertation (University of Rochester, Rochester, New York, 1974).

Elson, J. M.

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation-length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
[CrossRef] [PubMed]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

J. M. Elson, “Angle resolved light scattering from composite optical surfaces,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.240, 296–306 (1980).

Flory, F.

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
[CrossRef]

Galindo, R.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

Garcin, J.

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

Giacomo, P.

P. Giacomo, “Les couches réfléchissantes multidiélectriques appliquées à l'interféromètre de Fabry–Perot. Etude théorique et expérimental des couches réelles,” Rev. Opt. 35, 317–354, 442–467 (1956).

Grèzes-Besset, C.

C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

Hehl, K.

S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
[CrossRef] [PubMed]

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Jacobson, R. D.

Kassam, S.

S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
[CrossRef] [PubMed]

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Mattsson, L.

McNeil, J. R.

Neubert, J.

Pelletier, E.

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

C. Amra, P. Roche, E. Pelletier, “Interface roughness cross-correlation laws deduced from scattering diagram measurements on optical multilayers: effect of the material grain size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
[CrossRef]

P. Roche, E. Pelletier, “Characterization of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[CrossRef] [PubMed]

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

C. Amra, D. Torricini, Y. Boucher, L. Bruel, E. Pelletier, “Scattering from optical surfaces and coatings: an easy investigation of microroughness,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 72–81 (1990).

Prod'homme, L.

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[CrossRef]

Rahn, J. P.

Roche, P.

C. Amra, P. Roche, E. Pelletier, “Interface roughness cross-correlation laws deduced from scattering diagram measurements on optical multilayers: effect of the material grain size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
[CrossRef]

C. Amra, G. Albrand, P. Roche, “Theory and application of antiscattering single layers: antiscattering antireflection coatings,” Appl. Opt. 25, 2695–2702 (1986).
[CrossRef] [PubMed]

P. Roche, E. Pelletier, “Characterization of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[CrossRef] [PubMed]

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
[CrossRef]

C. Amra, D. Torricini, G. Albrand, P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” submitted to Appl. Opt.
[PubMed]

Salvan, F.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

Torricini, D.

C. Amra, D. Torricini, G. Albrand, P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” submitted to Appl. Opt.
[PubMed]

C. Amra, D. Torricini, Y. Boucher, L. Bruel, E. Pelletier, “Scattering from optical surfaces and coatings: an easy investigation of microroughness,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 72–81 (1990).

Vatel, O.

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

Wilson, S. R.

Appl. Opt.

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

C. Amra, C. Grèzes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical coatings,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

Appl. Opt.

J. Opt. Soc. Am. A

C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10, 365–374 (1993).
[CrossRef]

J. Opt. Soc. Am. B

C. Amra, P. Roche, E. Pelletier, “Interface roughness cross-correlation laws deduced from scattering diagram measurements on optical multilayers: effect of the material grain size,” J. Opt. Soc. Am. B 4, 1087–1093 (1987).
[CrossRef]

J. Opt. (Paris)

C. Amra, “Calculs et mesures de diffusion appliqués à l'étude de la rugosité dans les traitements optiques multicouches,” J. Opt. (Paris) 21, 83–98 (1990).
[CrossRef]

P. Croce, L. Prod'homme, “Ecarts observés dans l'interprétation des indicatrices de diffusion optique par des théories vectorielles simples,” J. Opt. (Paris) 16, 143–151 (1985).
[CrossRef]

J. Opt. Soc. Am.

P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
[CrossRef]

J. Opt. Soc. Am. A

P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, G. Albrand, “Determination of interface roughness cross-correlation properties of an optical coating from measurements of the angular scattering,” J. Opt. Soc. Am. A 1, 1028–1031 (1984).
[CrossRef]

Phys. Rev. B

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

Rev. Opt.

P. Giacomo, “Les couches réfléchissantes multidiélectriques appliquées à l'interféromètre de Fabry–Perot. Etude théorique et expérimental des couches réelles,” Rev. Opt. 35, 317–354, 442–467 (1956).

Waves Random Media

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Other

C. Amra, “Minimizing scattering in multilayers: technique for searching optimal realization conditions,” in Optical Technologies for Space Communication Systems, K. B. Bhasin, G. A. Koepf, eds., Proc. Soc. Photo-Opt. Instrum. Eng.756, 265–271 (1987).

C. Amra, “Scattering characterization of materials in thin film form,” in Laser-Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guenther, B. E. Newnam, M. J. Soileau, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1438, 309–323 (1990).

C. Amra, D. Torricini, Y. Boucher, L. Bruel, E. Pelletier, “Scattering from optical surfaces and coatings: an easy investigation of microroughness,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 72–81 (1990).

J. M. Eastman, “Surface scattering in optical interference coatings,” Ph.D. dissertation (University of Rochester, Rochester, New York, 1974).

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

J. M. Elson, “Angle resolved light scattering from composite optical surfaces,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.240, 296–306 (1980).

C. Amra, “From light scattering to the microstructure of thin film multilayers,” in Surface Roughness and Scattering, Vol. 14 of 1992 OSA Technical Digest Series, andOptical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988).

C. Amra, “Light scattering from multilayer optics. Part A: Investigation tools. Part B: Application to experiment,” J. Opt. Soc. Am. A (to be published).

E. L. Church, “The optical estimator of finish parameters,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 71–85 (1991).

C. Amra, D. Torricini, G. Albrand, P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” submitted to Appl. Opt.
[PubMed]

C. Amra, L. Bruel, “Comparison of different techniques to characterize surface roughness,” in Surface Roughness and Scattering, Vol. 14 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).

Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. André, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett, (to be published).

E. L. Church, “Comments on the correlation length,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 102–111 (1986).

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Figures (18)

Fig. 1
Fig. 1

Schematic view of surface and bulk phenomena responsible for light scattering.

Fig. 2
Fig. 2

Typical angular scattering from a narrow-band filter at oblique illumination. The energy loss out of the specular directions is the consequence of structural irregularities at interfaces and in the bulk of the multilayer.

Fig. 3
Fig. 3

Mean section of angular scattering by reflection for a black glass sample. The measurement conditions are the following: quasi-normal illumination, i = 1.5°; illumination wavelength, λ = 633 nm; diameter of spot area on the sample, ϕ = 3 mm; angular variation in the receiver solid angle, δθ = 0.5°; minimum angle for measurements, β = 1.8° from specular reflection, that is, θ = 3.3° from the sample normal; angular step for normal angle, Δθ = 2.9°; angular step for polar angle, Δϕ = 1.4°. The curve is relative to 7500 data points in whole space.

Fig. 4
Fig. 4

Surface and bulk scattering calculated for a glass substrate at oblique illumination (i = 65°) and for p-polarized incident light. The angular behavior is strongly different, depending on the origin of scattering.

Fig. 5
Fig. 5

Angular measurements for a black glass substrate under the illumination conditions given in Fig. 4. The decrease of the curve near 50° is characteristic of a surface effect.

Fig. 6
Fig. 6

Roughness spectra measured for two polarization states (s and p) of incident and scattered light. The two curves are quasi-identical.

Fig. 7
Fig. 7

At normal and nonpolarized illumination, angular scattering has the symmetry of revolution around the sample normal, provided that all irregularities are isotropic. This symmetry is studied, at each direction θ, with an angular autocorrelation over polar angle ϕ.

Fig. 8
Fig. 8

Angular correlation FN(θ, α) measured at direction θ = 25° for a glass substrate, before and after deposition of a 2H2L2H stack. The angular extrema reveal privileged directions on the surface. The isotropy degree is given by the minimum of the curve [d(25°) ≈ 0.4 before coating] and characterizes an angular disorder at the spatial frequency σ/2π = sin θ/λ. The two curves before and after coating are strongly similar, which proves that substrate roughness was replicated. In addition, the increase of isotropy degree is characteristic of a material effect. Note the perfect symmetry of the curves with respect to π/2.

Fig. 9
Fig. 9

(a) Calculation and measurement of isotropy degree in the whole θ range (0–90°), before and after deposition of a 2L SiO2 layer (ion-plating process). Measurements concern the curves (before and after) and show an increase of isotropy after coating, which is characteristic of a material effect. Calculation is given for the coating and is relative to the sum of both causal and residual scattering, whose parameters ( α L , γ L g ) are given in the text and are identical to those of Fig. 9(b). Note that calculation of the only causal isotropy degree would be identical to the curve measured before coating (see text), (b) Calculation and measurement of angular scattering from a 2L SiO2 layer. The curve (causal) is calculated for the causal component that is due only to perfect replication [αL(θ) = 1] of substrate roughness. Residual scattering is calculated with a Gaussian spectrum γ L g ( θ ) given in the text and is characteristic of the addition of 0.47-nm residual roughness. The sum (causal + residual) allows us to fit the angular data with good agreement in the whole θ range.

Fig. 10
Fig. 10

Calculation and measurement of angular scattering from a 19-layer mirror with TiO2/SiO2 (IAD process). Substrate is the curve measured before coating. Causal is the substrate effect or causal scattering calculated from this curve from the hypothesis of perfect replication for the two materials [αH(θ) = αL(θ) = 1]. Measured is the measurement after coating, and this last curve is perfectly fitted in the angular range 0–40°. The differences at large angles are attributed to slight errors in the design.24

Fig. 11
Fig. 11

Because of perfect replication and the addition of residual roughness δ r H = δ r L = δ r by each material, the total roughness is increased at each interface of a 19-layer mirror. Under these conditions residual scattering would be expected to be amplified by the number of layers. δs is the substrate roughness.

Fig. 12
Fig. 12

Scattering versus wavelength calculated in the direction θ = 15° for substrate effect (causal) and material effect (residual). The two curves are in phase opposition, which permits an easy detection of the origin of surface scattering. The design is a 12H layer.

Fig. 13
Fig. 13

Calculation and measurement of scattering versus wavelength in the direction θ = 15°. The design is 2H2L2H with materials TiO2/SiO2 produced by the IAD process. Measurements were obtained with a spectrophotometer modified for this application. The surface parameters involved in the calculation were previously obtained from angular measurements at the illumination wavelength λ = 633 nm.6 These parameters permit the fit of both angular and wavelength variations of scattering. Differences at large wavelengths (close to 800 nm) are due to parasitic light from the spectrophotometer.

Fig. 14
Fig. 14

Roughness spectra measured for a 0.5-nm-roughness black glass and for a Si substrate. At the starting angle the two curves are similar because of the poor flatness of the thin (250-μm) Si sample. Otherwise the Si spectrum is 100 times lower than the glass one, and the roughness obtained by integration in the angular range 10–90° is lower than 0.05 nm.

Fig. 15
Fig. 15

Calculation and measurement of angular scattering from a 3H TiO2 layer (IAD process) deposited on a Si substrate. The curve (causal) is the calculation of the substrate effect and can be largely neglected in the range 10–90°. The curve (residual) is the calculation of tho matorial offcct and permits the fit of the experiment in the angular range 10–90°.

Fig. 16
Fig. 16

Angular scattering from a coated Si substrate can be explained oither by a 0.5-nm top interface roughness or by an inhomogeneity of 4 × 10−4 in the bulk.

Fig. 17
Fig. 17

Calculation and measurement of scattering versus wavelength in the directions θ = 15°, 30°, for a coated Si sample. The design is a 6H Ta2O5 layer obtained by ion plating. Calculation is performed for residual surface scattering and shows phase opposition with the measurements. Bulk scattering also cannot explain the measurements.15

Fig. 18
Fig. 18

From the macroscopic to the microscopic: schematic view of irregularity spectrum plotted as a function of spatial frequency. The optical bandwidth depends on illumination wavelength and on angular range for measurements. Nanoprobe instruments are adequate for much higher spatial frequencies.

Tables (1)

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Table 1 Residual Roughness Values Obtained for Different Materials and Deposition Techniquesa

Equations (20)

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I ( θ , ϕ ) = i , j C i j α i j γ j j .
I ¯ ( θ ) = 1 2 π ϕ = 0 2 π I ( θ , ϕ ) d ϕ .
γ s ( θ , ϕ ) = I ( θ , ϕ ) / C 00 ( θ , ϕ ) .
F ( θ , α ) = ϕ = 0 2 π I ( θ , ϕ ) I ( θ , ϕ + α ) d ϕ .
d ( θ ) = min α F N ( θ , α ) 1 .
F N ( θ , α ) = ϕ = 0 2 π γ s ( θ , ϕ ) γ s ( θ , ϕ + α ) d ϕ / ϕ = 0 2 π γ s 2 ( θ , ϕ ) d ϕ ,
h i 1 = h i * a i + g i 1 ,
I ( θ , ϕ ) = I c [ γ s ( θ , ϕ ) , α H ( θ ) , α L ( θ ) ] + I g [ γ H g ( θ ) , γ L g ( θ ) , α H ( θ ) , α L ( θ ) ] .
I ¯ ( θ ) = I c [ γ ¯ s ( θ ) , α ( θ ) ] + I g [ γ g ( θ ) ] .
d ( θ ) = d ( θ ) + B ( θ ) 1 + B ( θ ) ,
B ( θ ) = ξ ( θ ) x ( θ ) [ 2 + x ( θ ) ] ,
x ( θ ) = I g ( θ ) / I ¯ c ( θ ) , ξ ( θ ) = ( γ ¯ s ) 2 ( θ ) / γ ¯ s 2 ( θ ) .
B ( θ ) = d ( θ ) d ( θ ) 1 d ( θ ) .
x ( θ ) = I g ( θ ) / I ¯ c ( θ ) = 1 + [ 1 + B ( θ ) / ξ ( θ ) ] 1 / 2 .
I ¯ ( θ ) = I ¯ c + I g = [ 1 + x ( θ ) ] I c [ γ ¯ s ( θ ) , α ( θ ) ] .
γ L g ( σ ) = 1 4 π δ g 2 L g 2 exp [ ( σ L g / 2 ) 2 ] ,
δ r = δ g { 1 exp [ ( π L g / λ ) 2 ] } 1 / 2 δ r = 0.47 nm .
I ¯ = I ¯ c + I g I g = I g [ γ g ( θ ) ] .
h i 1 = ( h i + g i ) * a i + g i 1 .
B ( λ , θ min , θ max ) = ( sin θ min / λ , sin θ max / λ ) ,

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