Abstract

We present a method of analysis of prism–film coupler spectroscopy based on the use of transfer matrix and genetic algorithm, which allows the simultaneous determination of refractive index, thickness, and optical losses of the measured layer.

© 2008 Optical Society of America

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References

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  1. X. J. Zhang, X. Z. Fan, J. Liao, H. T. Wang, N. B. Ming, L. Qiu, and Y. Q. Shen, “Propagation properties of a light wave in a film quasiwaveguide structure,” J. Appl. Phys. 92, 5647-5657 (2002).
    [CrossRef]
  2. H. Wang, T. Aruga, and P. Ye, “Theory and properties of quasiwaveguide modes,” Appl. Phys. Lett. 69, 611-613 (1996).
    [CrossRef]
  3. F. Abeles, “Methods for determining optical parameters of thin films,” Prog. Opt. 2, 248-288 (1963).
  4. J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,”. J. Phys. E 9, 1002-1004 (1976).
    [CrossRef]
  5. J. C. Martínez-Antón, “Determination of optical parameters in general film substrate systems: a reformulation based on the concepts of envelope extremes and local magnitudes,” Appl. Opt 39, 4557-4568 (2000).
    [CrossRef]
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  9. H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User's Guide (Academic, 1999).
  10. F. Flory, D. Endelema, E. Pelletier, and I. J. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO 2 films,” Appl. Opt 32, 5649-5659 (1993).
    [CrossRef] [PubMed]
  11. H. Rigneault, F. Flory, and S. Monneret, “Nonlinear totally reflecting prism coupler: thermomechanic effects and intensity-dependent refractive index of thin films,” Appl. Opt 34, 4358-4369 (1995).
    [CrossRef] [PubMed]
  12. P. K. Tien and R. Ulrich, “Theory of prism-film coupler and thin-film light guides,” J. Opt. Soc. Am 60, 1325-1337 (1970).
    [CrossRef]
  13. R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,” J. Opt. Soc. Am 60, 1337-1350 (1970).
    [CrossRef]
  14. S. Garcia-Blanco, E. Alfaro-Cid, R. M. De La Rue, and J. S. Aitchison, “Genetic algorithm-based characterization of the optical properties of flame-hydrolysis deposited silica waveguides,” J. Lightwave Technol. 22, 2801-2807 (2004).
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  16. M. Born and E. Wolf, Principles of Optics (Academic, 1980).
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    [CrossRef]
  19. P. Yeh, Optical Waves in Layered Media (Academic, 1988).
  20. A. B. H. Yedder, “Optimisation numerique et controle optimal: (applications en chimie moleculaire),” Ph.D. dissertation (Ecole Nationale des Ponts et Chaussees2002).
  21. Z. Michalewicz, Genetic Algorithms+ Data Structures= Evolution Programs (Academic, 1996).
  22. K. Deb, “Genetic algorithm in search and optimization: the technique and applications,” in Proceedings of International Workshop on Soft Computing and Intelligent Systems (Academic, 1998), pp. 58-87.
  23. K. Deb, Genetic Algorithms for Optimization, KanGAL Report No. 2001002, (KanGal, 2001).
  24. V. S. Gordon and D. Whitley, “Serial and parallel genetic algorithms as function optimizers,” in Proceedings of the Fifth International Conference on Genetic Algorithms (Academic, 1993), pp. 177-183.
  25. S. W. Mahfoud, “Niching methods for genetic algorithms,” Ph.D. dissertation (University of Urbana, 1995).
  26. P. J. B. Hancock, “An empirical comparison of selection methods in evolutionary algorithms,” in Evolutionary Computing: AISB Workshop, Leeds, UK, (Academic, 1994), selected papers.
  27. K. Deb and R. B. Agrawal, “Simulated binary crossover for continuous search space,” in Complex Systems (Academic, 1995), pp. 115-148.
  28. Microchem Corporation, http://www.microchem.com/products/su_eight.htm.
  29. S. Adachi, “Model dielectric constants of Si and Ge ,” Phys. Rev. B 38, 12966-12976 (1988).
  30. Pra¨zisions Glas & Optik GmbH, http://www.pgo-online.com/.
  31. H. E. Bennett and J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am , 51, 123-129 (1961).
    [CrossRef]
  32. H. Davies, “The reflection of electromagnetic waves from a rough surface,” in Proceedings of the Institution of Electrical Engineers (Academic, 1954), 209-214.
  33. E. Dumont, B. Dugnoille, and S. Bienfait, “Simultaneous determination of the optical properties and of the structure of rf-sputtered ZnO thin films,” Thin Solid Films 353, 93-99 (1999).
    [CrossRef]
  34. M. Rebien, W. Henrion, M. Bär, and C. H. Fischer, “Optical properties of ZnO thin films: ion layer gas reaction compared to sputter deposition,” Appl. Phys. Lett. 80, 3518-3520(2002).
    [CrossRef]
  35. S. Laux, N. Kaiser, A. Zöller, R. Götzelmann, H. Lauth, and H. Bernitzki, “Room-temperature deposition of indium tin oxide thin films with plasma ion-assisted evaporation,” Thin Solid Films 335, 1-5 (1998).
    [CrossRef]

2005

J. Cardin, D. Leduc, T. Schneider, C. Lupi, D. Averty, and H. W. Gundel, “Optical characterization of PZT thin films for waveguide applications,” J. Eur. Ceram. Soc. 25, 2913-2916 (2005).
[CrossRef]

2004

2002

M. Rebien, W. Henrion, M. Bär, and C. H. Fischer, “Optical properties of ZnO thin films: ion layer gas reaction compared to sputter deposition,” Appl. Phys. Lett. 80, 3518-3520(2002).
[CrossRef]

X. J. Zhang, X. Z. Fan, J. Liao, H. T. Wang, N. B. Ming, L. Qiu, and Y. Q. Shen, “Propagation properties of a light wave in a film quasiwaveguide structure,” J. Appl. Phys. 92, 5647-5657 (2002).
[CrossRef]

2000

J. C. Martínez-Antón, “Determination of optical parameters in general film substrate systems: a reformulation based on the concepts of envelope extremes and local magnitudes,” Appl. Opt 39, 4557-4568 (2000).
[CrossRef]

1999

E. Dumont, B. Dugnoille, and S. Bienfait, “Simultaneous determination of the optical properties and of the structure of rf-sputtered ZnO thin films,” Thin Solid Films 353, 93-99 (1999).
[CrossRef]

1998

S. Laux, N. Kaiser, A. Zöller, R. Götzelmann, H. Lauth, and H. Bernitzki, “Room-temperature deposition of indium tin oxide thin films with plasma ion-assisted evaporation,” Thin Solid Films 335, 1-5 (1998).
[CrossRef]

1996

H. Wang, T. Aruga, and P. Ye, “Theory and properties of quasiwaveguide modes,” Appl. Phys. Lett. 69, 611-613 (1996).
[CrossRef]

1995

H. Rigneault, F. Flory, and S. Monneret, “Nonlinear totally reflecting prism coupler: thermomechanic effects and intensity-dependent refractive index of thin films,” Appl. Opt 34, 4358-4369 (1995).
[CrossRef] [PubMed]

1993

F. Flory, D. Endelema, E. Pelletier, and I. J. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO 2 films,” Appl. Opt 32, 5649-5659 (1993).
[CrossRef] [PubMed]

1989

1988

S. Adachi, “Model dielectric constants of Si and Ge ,” Phys. Rev. B 38, 12966-12976 (1988).

1984

1977

R. M. A. Azzam, “Return-path ellipsometry and a novel normal-incidence null ellipsometer (NINE),” J. Mod. Opt. 24, 1039-1049 (1977).

1976

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,”. J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

1970

P. K. Tien and R. Ulrich, “Theory of prism-film coupler and thin-film light guides,” J. Opt. Soc. Am 60, 1325-1337 (1970).
[CrossRef]

R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,” J. Opt. Soc. Am 60, 1337-1350 (1970).
[CrossRef]

1963

F. Abeles, “Methods for determining optical parameters of thin films,” Prog. Opt. 2, 248-288 (1963).

1961

H. E. Bennett and J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am , 51, 123-129 (1961).
[CrossRef]

Appl. Opt

F. Flory, D. Endelema, E. Pelletier, and I. J. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO 2 films,” Appl. Opt 32, 5649-5659 (1993).
[CrossRef] [PubMed]

H. Rigneault, F. Flory, and S. Monneret, “Nonlinear totally reflecting prism coupler: thermomechanic effects and intensity-dependent refractive index of thin films,” Appl. Opt 34, 4358-4369 (1995).
[CrossRef] [PubMed]

J. C. Martínez-Antón, “Determination of optical parameters in general film substrate systems: a reformulation based on the concepts of envelope extremes and local magnitudes,” Appl. Opt 39, 4557-4568 (2000).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

H. Wang, T. Aruga, and P. Ye, “Theory and properties of quasiwaveguide modes,” Appl. Phys. Lett. 69, 611-613 (1996).
[CrossRef]

M. Rebien, W. Henrion, M. Bär, and C. H. Fischer, “Optical properties of ZnO thin films: ion layer gas reaction compared to sputter deposition,” Appl. Phys. Lett. 80, 3518-3520(2002).
[CrossRef]

J. Appl. Phys.

X. J. Zhang, X. Z. Fan, J. Liao, H. T. Wang, N. B. Ming, L. Qiu, and Y. Q. Shen, “Propagation properties of a light wave in a film quasiwaveguide structure,” J. Appl. Phys. 92, 5647-5657 (2002).
[CrossRef]

J. Eur. Ceram. Soc.

J. Cardin, D. Leduc, T. Schneider, C. Lupi, D. Averty, and H. W. Gundel, “Optical characterization of PZT thin films for waveguide applications,” J. Eur. Ceram. Soc. 25, 2913-2916 (2005).
[CrossRef]

J. Lightwave Technol.

J. Mod. Opt.

R. M. A. Azzam, “Return-path ellipsometry and a novel normal-incidence null ellipsometer (NINE),” J. Mod. Opt. 24, 1039-1049 (1977).

J. Opt. Soc. Am

P. K. Tien and R. Ulrich, “Theory of prism-film coupler and thin-film light guides,” J. Opt. Soc. Am 60, 1325-1337 (1970).
[CrossRef]

R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,” J. Opt. Soc. Am 60, 1337-1350 (1970).
[CrossRef]

H. E. Bennett and J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am , 51, 123-129 (1961).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. E

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,”. J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Model dielectric constants of Si and Ge

S. Adachi, “Model dielectric constants of Si and Ge ,” Phys. Rev. B 38, 12966-12976 (1988).

Prog. Opt.

F. Abeles, “Methods for determining optical parameters of thin films,” Prog. Opt. 2, 248-288 (1963).

Thin Solid Films

E. Dumont, B. Dugnoille, and S. Bienfait, “Simultaneous determination of the optical properties and of the structure of rf-sputtered ZnO thin films,” Thin Solid Films 353, 93-99 (1999).
[CrossRef]

S. Laux, N. Kaiser, A. Zöller, R. Götzelmann, H. Lauth, and H. Bernitzki, “Room-temperature deposition of indium tin oxide thin films with plasma ion-assisted evaporation,” Thin Solid Films 335, 1-5 (1998).
[CrossRef]

Other

H. Davies, “The reflection of electromagnetic waves from a rough surface,” in Proceedings of the Institution of Electrical Engineers (Academic, 1954), 209-214.

Pra¨zisions Glas & Optik GmbH, http://www.pgo-online.com/.

M. Born and E. Wolf, Principles of Optics (Academic, 1980).

Metricon Corporation, http://www.metricon.com/.

P. Yeh, Optical Waves in Layered Media (Academic, 1988).

A. B. H. Yedder, “Optimisation numerique et controle optimal: (applications en chimie moleculaire),” Ph.D. dissertation (Ecole Nationale des Ponts et Chaussees2002).

Z. Michalewicz, Genetic Algorithms+ Data Structures= Evolution Programs (Academic, 1996).

K. Deb, “Genetic algorithm in search and optimization: the technique and applications,” in Proceedings of International Workshop on Soft Computing and Intelligent Systems (Academic, 1998), pp. 58-87.

K. Deb, Genetic Algorithms for Optimization, KanGAL Report No. 2001002, (KanGal, 2001).

V. S. Gordon and D. Whitley, “Serial and parallel genetic algorithms as function optimizers,” in Proceedings of the Fifth International Conference on Genetic Algorithms (Academic, 1993), pp. 177-183.

S. W. Mahfoud, “Niching methods for genetic algorithms,” Ph.D. dissertation (University of Urbana, 1995).

P. J. B. Hancock, “An empirical comparison of selection methods in evolutionary algorithms,” in Evolutionary Computing: AISB Workshop, Leeds, UK, (Academic, 1994), selected papers.

K. Deb and R. B. Agrawal, “Simulated binary crossover for continuous search space,” in Complex Systems (Academic, 1995), pp. 115-148.

Microchem Corporation, http://www.microchem.com/products/su_eight.htm.

A. Bashara, Ellipsometry and Polarized Light (Academic, 1977).

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User's Guide (Academic, 1999).

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Figures (6)

Fig. 1
Fig. 1

Prism coupler configuration: (a) transmission configuration, and (b) reflection configuration.

Fig. 2
Fig. 2

(a) Transfer function of the Metricon prism-coupler, and (b) m-lines spectrum (TE mode) of a photoresist S1818 film: raw data (—) and corrected spectrum (○).

Fig. 3
Fig. 3

Distribution of experimental noise.

Fig. 4
Fig. 4

Measured (○) and fitted (—) m-lines spectra of an S1818 film on silicon in TE mode.

Fig. 5
Fig. 5

Measured (○) and fitted (—) m-lines spectra of different ZnO film on glass in TE mode.

Fig. 6
Fig. 6

Measured (○) and fitted (—) m-lines spectra of different ITO film on glass in TE mode.

Tables (3)

Tables Icon

Table 1 Errors on Paramaters Retrieved by the Genetic Algorithm for the Simulated Spectra; Subscript th Denotes the Theoretical Values

Tables Icon

Table 2 Characteristics of Different Thin Films Obtained with the GA and a Resolution of the Modal Dispersion Equations (MDE)

Tables Icon

Table 3 Characteristics of Different Thin Films Obtained with the GA and a Resolution of the MDE

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

M j = ( cos ϕ j - i γ j - 1 sin ϕ j - i γ j sin ϕ j cos ϕ j ) ,
R ( θ ) = | ( m 11 + m 12 γ s ) γ p - m 21 - m 22 γ s ( m 11 + m 12 γ s ) γ p + m 21 + m 22 γ s | 2 ,
{ T ( θ ) a / p = n p 2 - n a 2 sin 2 θ n a cos θ | t a p | 2 T ( θ ) p / a = n a cos θ n p 2 - n a 2 sin 2 θ | t p a | 2 ,
R calc ( θ ) = H ( θ ) T ( θ ) a / p R ( θ ) T ( θ ) p / a .
σ m 2 = i = 1 N N 1 [ R calc ( θ i ) - R meas ( θ i ) ] 2 ,

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