Abstract

We propose the use of a pattern search optimization technique in combination with a seed preprocessing procedure to determine the optical constants and thickness of thin films using only the transmittance spectra. The approach is quite flexible, straightforward to implement, and efficient in reaching the best fitting. We demonstrate the effectiveness of the method in extracting optical constants, even when the films are not displaying interference fringes. Comparison to a real-coded genetic algorithm shows that the modified pattern search is fast, almost accurate, and does not need any parameter adjustments. The approach is successfully applied to extract the thickness and optical constants of spray pyrolyzed nanocrystalline CdO thin films.

© 2012 Optical Society of America

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  1. R. G. Gordon, MRS Bull. 25, 52 (2000).
    [CrossRef]
  2. J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.
  3. R. Swanepoel, J. Phys. E 16, 1214 (1983).
    [CrossRef]
  4. M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, Appl. Phys. Lett. 77, 2133 (2000).
    [CrossRef]
  5. T. Ross and G. Cormier, J. Opt. Soc. Am. A 27, 319 (2010).
    [CrossRef]
  6. G. Cormier and R. Boudreau, J. Opt. Soc. Am. A 17, 129 (2000).
    [CrossRef]
  7. G. E. P. Box, Appl. Stat. 681 (1957).
  8. R. Hooke and T. A. Jeeves, J. ACM 8212 (1961).
    [CrossRef]
  9. J. Singh, Optical Properties of Condensed Matter and Applications (Wiley, 2006).
  10. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Kluwer Academic, 1989).
  11. K. Deb and A. Kumar, Complex Syst. 9, 431 (1995).
  12. K. Deb and M. A. Goyal, Comp. Sci. Informatics 26, 30 (1996).
  13. N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
    [CrossRef]
  14. A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
    [CrossRef]
  15. R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
    [CrossRef]
  16. R. Ferro and J. A. Rodríguez, Phys. Status Solidi B 220, 299 (2000).
    [CrossRef]
  17. C. K. Carniglia, Opt. Eng. 18, 104 (1979).

2010 (1)

2002 (1)

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

2000 (5)

R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
[CrossRef]

R. Ferro and J. A. Rodríguez, Phys. Status Solidi B 220, 299 (2000).
[CrossRef]

R. G. Gordon, MRS Bull. 25, 52 (2000).
[CrossRef]

M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, Appl. Phys. Lett. 77, 2133 (2000).
[CrossRef]

G. Cormier and R. Boudreau, J. Opt. Soc. Am. A 17, 129 (2000).
[CrossRef]

1997 (1)

N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
[CrossRef]

1996 (1)

K. Deb and M. A. Goyal, Comp. Sci. Informatics 26, 30 (1996).

1995 (1)

K. Deb and A. Kumar, Complex Syst. 9, 431 (1995).

1983 (1)

R. Swanepoel, J. Phys. E 16, 1214 (1983).
[CrossRef]

1979 (1)

C. K. Carniglia, Opt. Eng. 18, 104 (1979).

1961 (1)

R. Hooke and T. A. Jeeves, J. ACM 8212 (1961).
[CrossRef]

1957 (1)

G. E. P. Box, Appl. Stat. 681 (1957).

Alleman, J. L.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Benramdane, N.

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
[CrossRef]

Birgin, E. G.

M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, Appl. Phys. Lett. 77, 2133 (2000).
[CrossRef]

Boudreau, R.

Bouzidi, A.

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

Box, G. E. P.

G. E. P. Box, Appl. Stat. 681 (1957).

Carniglia, C. K.

C. K. Carniglia, Opt. Eng. 18, 104 (1979).

Chambouleyron, I.

M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, Appl. Phys. Lett. 77, 2133 (2000).
[CrossRef]

Contreras-Puente, G.

R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
[CrossRef]

Cormier, G.

Da Costa, A.

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

Dabney, M. S.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Deb, K.

K. Deb and M. A. Goyal, Comp. Sci. Informatics 26, 30 (1996).

K. Deb and A. Kumar, Complex Syst. 9, 431 (1995).

Delahoy, A. E.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Desfeux, R.

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

Ferro, R.

R. Ferro and J. A. Rodríguez, Phys. Status Solidi B 220, 299 (2000).
[CrossRef]

R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
[CrossRef]

Gedvilas, L. M.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Ginley, D. S.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Kluwer Academic, 1989).

Gordon, R. G.

R. G. Gordon, MRS Bull. 25, 52 (2000).
[CrossRef]

Goyal, M. A.

K. Deb and M. A. Goyal, Comp. Sci. Informatics 26, 30 (1996).

Guo, S.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Hooke, R.

R. Hooke and T. A. Jeeves, J. ACM 8212 (1961).
[CrossRef]

Jeeves, T. A.

R. Hooke and T. A. Jeeves, J. ACM 8212 (1961).
[CrossRef]

Kebbab, Z.

N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
[CrossRef]

Keyes, B. M.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Khelifa, B.

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

Kumar, A.

K. Deb and A. Kumar, Complex Syst. 9, 431 (1995).

Martínez, J. M.

M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, Appl. Phys. Lett. 77, 2133 (2000).
[CrossRef]

Mathieu, C.

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

Misho, R. H.

N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
[CrossRef]

Morales-Acevedo, A.

R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
[CrossRef]

Mulato, M.

M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, Appl. Phys. Lett. 77, 2133 (2000).
[CrossRef]

Murad, W. A.

N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
[CrossRef]

Nekrela, A.

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

Perkins, J. D.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Readey, D. W.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Rodríguez, J. A.

R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
[CrossRef]

R. Ferro and J. A. Rodríguez, Phys. Status Solidi B 220, 299 (2000).
[CrossRef]

Ross, T.

Singh, J.

J. Singh, Optical Properties of Condensed Matter and Applications (Wiley, 2006).

Swanepoel, R.

R. Swanepoel, J. Phys. E 16, 1214 (1983).
[CrossRef]

Taylor, M. P.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Teplin, C. W.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

To, B.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

van Hest, M. F. A. M.

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

Vigil, O.

R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
[CrossRef]

Ziane, M.

N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, Appl. Phys. Lett. 77, 2133 (2000).
[CrossRef]

Appl. Stat. (1)

G. E. P. Box, Appl. Stat. 681 (1957).

Comp. Sci. Informatics (1)

K. Deb and M. A. Goyal, Comp. Sci. Informatics 26, 30 (1996).

Complex Syst. (1)

K. Deb and A. Kumar, Complex Syst. 9, 431 (1995).

J. ACM (1)

R. Hooke and T. A. Jeeves, J. ACM 8212 (1961).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. E (1)

R. Swanepoel, J. Phys. E 16, 1214 (1983).
[CrossRef]

Mater. Chem. Phys. (1)

N. Benramdane, W. A. Murad, R. H. Misho, M. Ziane, and Z. Kebbab, Mater. Chem. Phys. 48119 (1997).
[CrossRef]

Mater. Sci. Eng. B (1)

A. Bouzidi, N. Benramdane, A. Nekrela, C. Mathieu, B. Khelifa, R. Desfeux, and A. Da Costa, Mater. Sci. Eng. B 95141 (2002).
[CrossRef]

MRS Bull. (1)

R. G. Gordon, MRS Bull. 25, 52 (2000).
[CrossRef]

Opt. Eng. (1)

C. K. Carniglia, Opt. Eng. 18, 104 (1979).

Phys. Status Solidi A (1)

R. Ferro, J. A. Rodríguez, O. Vigil, A. Morales-Acevedo, and G. Contreras-Puente, Phys. Status Solidi A 177, 477 (2000).
[CrossRef]

Phys. Status Solidi B (1)

R. Ferro and J. A. Rodríguez, Phys. Status Solidi B 220, 299 (2000).
[CrossRef]

Other (3)

J. Singh, Optical Properties of Condensed Matter and Applications (Wiley, 2006).

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Kluwer Academic, 1989).

J. D. Perkins, M. P. Taylor, M. F. A. M. van Hest, C. W. Teplin, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, B. To, D. W. Readey, A. E. Delahoy, S. Guo, and D. S. Ginley, in 31st IEEE Photovoltaics Specialists Conference and Exhibition (IEEE, 2005), pp. 145–147.

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Figures (2)

Fig. 1.
Fig. 1.

(a) Flowchart of the fitting procedure. (b) Graphical illustration of the exploratory mesh in two dimensions.

Fig. 2.
Fig. 2.

(a) Measured and fitted transmittance data as a function of wavelength. (b) Refractive index and extinction coefficient obtained from fitting of a two-term Lorentz dispersion equation.

Tables (1)

Tables Icon

Table 1. Refractive Indices, Extinction Coefficients, and Thicknesses, Fitted by Pattern Search, Real-Coded Genetic Algorithms, and Seed Preprocessed PSa

Equations (1)

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kk+1

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