Abstract

The applicably of multi-objective optimization to ellipsometric data analysis is presented and a method to handle complex ellipsometric problems such as multi sample or multi angle analysis using multi-objective optimization is described. The performance of a multi-objective genetic algorithm (MOGA) is tested against a single objective common genetic algorithm (CGA). The procedure is applied to the characterization (refractive index and thickness) of planar waveguides intended for the production of optical components prepared sol-gel derived organic-inorganic hybrids, so-called di-ureasils, modified with zirconium tetrapropoxide, Zr(OPrn)4 deposited on silica on silicon substrates. The results show that for the same initial conditions, MOGA performs better than the CGA, showing a higher success rate in the task of finding the best final solution.

© 2010 OSA

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  1. P. Drude, “Über die Gesetze der Reflexion und Brechung des Lichtes an der Grenze absorbierender Kristalle,” Annalen der Physik 32, 584–625 (1887).
  2. A. Rothen, “The Ellipsometer, an Apparatus to Measure Thicknesses of Thin Surface Films,” Rev. Sci. Instrum. 16(2), 26–30 (1945).
    [CrossRef]
  3. M. Land, J. J. Sidorowich, and R. K. Belew, “Using Genetic Algorithms with Local Search for Thin Film Metrology,” in Proceedings of the Seventh International Conference on Genetic Algorithms, T. Bäck, ed., (Morgan Kaufmann Publishers, Inc, 1997), pp. 537–544.
  4. O. Polgár, M. Fried, T. Lohner, and I. Bársony, “Comparison of algorithms used for evaluation of ellipsometric measurements - Random search, genetic algorithms, simulated annealing and hill climbing graph-searches,” Surf. Sci. 457(1-2), 157–177 (2000).
    [CrossRef]
  5. A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455–456, 804–808 (2004).
    [CrossRef]
  6. O. Polgár, P. Petrik, T. Lohner, and M. Fried, “Evaluation strategies for multi-layer, multi-material ellipsometric measurements,” Appl. Surf. Sci. 253(1), 57–64 (2006).
    [CrossRef]
  7. B. Neto, A. L. J. Teixeira, N. Wada, and P. S. André, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15(26), 17520–17528 (2007).
    [CrossRef] [PubMed]
  8. R. A. S. Ferreira, C. M. S. Vicente, V. Fernandes, A. G. Macedo, E. Pecoraro, R. Nogueira, P. S. André, P. V. S. Marques, and L. D. Carlos, “Organic-inorganic hybrids for the new generation of optical networks,” in Proc. of International Conference on Transparent Optical Networks (ICTON 2009) (IEEE, S. Miguel (Portugal), July. 2009), pp. Tu.B4.2–1.
  9. C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
    [CrossRef]
  10. D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
    [CrossRef]
  11. E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
    [CrossRef] [PubMed]
  12. O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60(1), 65–77 (1989).
    [CrossRef]
  13. A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
    [CrossRef]
  14. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
    [CrossRef]
  15. K. Deb and M. Goyal, “A Combined Genetic Adaptive Search (GeneAS) for Engineering Design,” Comput. Sci. Inform.. 26, 30–45 (1996).
  16. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1998).
  17. C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
    [CrossRef]

2010 (1)

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

2008 (2)

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

2007 (1)

B. Neto, A. L. J. Teixeira, N. Wada, and P. S. André, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15(26), 17520–17528 (2007).
[CrossRef] [PubMed]

2006 (2)

O. Polgár, P. Petrik, T. Lohner, and M. Fried, “Evaluation strategies for multi-layer, multi-material ellipsometric measurements,” Appl. Surf. Sci. 253(1), 57–64 (2006).
[CrossRef]

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[CrossRef]

2005 (1)

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

2004 (1)

A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455–456, 804–808 (2004).
[CrossRef]

2002 (1)

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[CrossRef]

2000 (1)

O. Polgár, M. Fried, T. Lohner, and I. Bársony, “Comparison of algorithms used for evaluation of ellipsometric measurements - Random search, genetic algorithms, simulated annealing and hill climbing graph-searches,” Surf. Sci. 457(1-2), 157–177 (2000).
[CrossRef]

1996 (1)

K. Deb and M. Goyal, “A Combined Genetic Adaptive Search (GeneAS) for Engineering Design,” Comput. Sci. Inform.. 26, 30–45 (1996).

1989 (1)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60(1), 65–77 (1989).
[CrossRef]

1945 (1)

A. Rothen, “The Ellipsometer, an Apparatus to Measure Thicknesses of Thin Surface Films,” Rev. Sci. Instrum. 16(2), 26–30 (1945).
[CrossRef]

1887 (1)

P. Drude, “Über die Gesetze der Reflexion und Brechung des Lichtes an der Grenze absorbierender Kristalle,” Annalen der Physik 32, 584–625 (1887).

Acher, O.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60(1), 65–77 (1989).
[CrossRef]

Agarwal, S.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[CrossRef]

Andre, P. S.

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

André, P. S.

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

B. Neto, A. L. J. Teixeira, N. Wada, and P. S. André, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15(26), 17520–17528 (2007).
[CrossRef] [PubMed]

Balda, R.

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

Bársony, I.

O. Polgár, M. Fried, T. Lohner, and I. Bársony, “Comparison of algorithms used for evaluation of ellipsometric measurements - Random search, genetic algorithms, simulated annealing and hill climbing graph-searches,” Surf. Sci. 457(1-2), 157–177 (2000).
[CrossRef]

Bigan, E.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60(1), 65–77 (1989).
[CrossRef]

Carlos, L. D.

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

Carlos, R. R.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Coit, D. W.

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[CrossRef]

Dahmouche, K.

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

de Zea Bermudez, V.

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Deb, K.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[CrossRef]

K. Deb and M. Goyal, “A Combined Genetic Adaptive Search (GeneAS) for Engineering Design,” Comput. Sci. Inform.. 26, 30–45 (1996).

Drévillon, B.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60(1), 65–77 (1989).
[CrossRef]

Drude, P.

P. Drude, “Über die Gesetze der Reflexion und Brechung des Lichtes an der Grenze absorbierender Kristalle,” Annalen der Physik 32, 584–625 (1887).

Fernández, J.

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

Ferreira, .

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

Ferreira, L. D.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Ferreira, R. A. S.

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

Fried, M.

O. Polgár, P. Petrik, T. Lohner, and M. Fried, “Evaluation strategies for multi-layer, multi-material ellipsometric measurements,” Appl. Surf. Sci. 253(1), 57–64 (2006).
[CrossRef]

O. Polgár, M. Fried, T. Lohner, and I. Bársony, “Comparison of algorithms used for evaluation of ellipsometric measurements - Random search, genetic algorithms, simulated annealing and hill climbing graph-searches,” Surf. Sci. 457(1-2), 157–177 (2000).
[CrossRef]

García-Revilla, S.

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

Gonçalves, S. J. L.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Goyal, M.

K. Deb and M. Goyal, “A Combined Genetic Adaptive Search (GeneAS) for Engineering Design,” Comput. Sci. Inform.. 26, 30–45 (1996).

Konak, A.

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[CrossRef]

Kudla, A.

A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455–456, 804–808 (2004).
[CrossRef]

Leite, P. S. V.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Lohner, T.

O. Polgár, P. Petrik, T. Lohner, and M. Fried, “Evaluation strategies for multi-layer, multi-material ellipsometric measurements,” Appl. Surf. Sci. 253(1), 57–64 (2006).
[CrossRef]

O. Polgár, M. Fried, T. Lohner, and I. Bársony, “Comparison of algorithms used for evaluation of ellipsometric measurements - Random search, genetic algorithms, simulated annealing and hill climbing graph-searches,” Surf. Sci. 457(1-2), 157–177 (2000).
[CrossRef]

Macedo, A. G.

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

Marques,

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Messaddeq, P. J.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Messaddeq, Y.

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

Meyarivan, T.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[CrossRef]

Molina, C.

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Moreira, O.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Neto, B.

B. Neto, A. L. J. Teixeira, N. Wada, and P. S. André, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15(26), 17520–17528 (2007).
[CrossRef] [PubMed]

Nogueira, R.

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

Oliveira, D. C.

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

Pecoraro, E.

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

Petrik, P.

O. Polgár, P. Petrik, T. Lohner, and M. Fried, “Evaluation strategies for multi-layer, multi-material ellipsometric measurements,” Appl. Surf. Sci. 253(1), 57–64 (2006).
[CrossRef]

Polgár, O.

O. Polgár, P. Petrik, T. Lohner, and M. Fried, “Evaluation strategies for multi-layer, multi-material ellipsometric measurements,” Appl. Surf. Sci. 253(1), 57–64 (2006).
[CrossRef]

O. Polgár, M. Fried, T. Lohner, and I. Bársony, “Comparison of algorithms used for evaluation of ellipsometric measurements - Random search, genetic algorithms, simulated annealing and hill climbing graph-searches,” Surf. Sci. 457(1-2), 157–177 (2000).
[CrossRef]

Pratap, A.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[CrossRef]

Ribeiro, S. J. L.

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

Ribeiro, Y.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

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A. Rothen, “The Ellipsometer, an Apparatus to Measure Thicknesses of Thin Surface Films,” Rev. Sci. Instrum. 16(2), 26–30 (1945).
[CrossRef]

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D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

Sá, R. A.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

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D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

Smith, A. E.

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[CrossRef]

Soppera, A. P.

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

Teixeira, A. L. J.

B. Neto, A. L. J. Teixeira, N. Wada, and P. S. André, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15(26), 17520–17528 (2007).
[CrossRef] [PubMed]

Vicente, C. M. S.

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

Wada, N.

B. Neto, A. L. J. Teixeira, N. Wada, and P. S. André, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15(26), 17520–17528 (2007).
[CrossRef] [PubMed]

Annalen der Physik (1)

P. Drude, “Über die Gesetze der Reflexion und Brechung des Lichtes an der Grenze absorbierender Kristalle,” Annalen der Physik 32, 584–625 (1887).

Appl. Surf. Sci. (1)

O. Polgár, P. Petrik, T. Lohner, and M. Fried, “Evaluation strategies for multi-layer, multi-material ellipsometric measurements,” Appl. Surf. Sci. 253(1), 57–64 (2006).
[CrossRef]

Chem. Mater. (1)

D. C. Oliveira, A. G. Macedo, N. J. O. Silva, C. Molina, R. A. Sá, . Ferreira, P. S. Andre, K. Dahmouche, V. de Zea Bermudez, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Photopatternable di-ureasil-zirconium oxocluster organic-inorganic hybrids as cost effective integrated optical substrates,” Chem. Mater. 20(11), 3696–3705 (2008).
[CrossRef]

Comput. Sci. Inform.. (1)

K. Deb and M. Goyal, “A Combined Genetic Adaptive Search (GeneAS) for Engineering Design,” Comput. Sci. Inform.. 26, 30–45 (1996).

IEEE Trans. Evol. Comput. (1)

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[CrossRef]

J. Mater. Chem. (1)

C. Molina, R. A. Sá, L. D. Ferreira, R. R. Carlos, S. J. L. Gonçalves, Y. Ribeiro, P. J. Messaddeq, O. Moreira, A. P. Soppera, P. S. V. Leite, Marques, and V. de Zea Bermudez, “Planar and UV written channel optical waveguides prepared with siloxane-poly(oxyethylene)-zirconia organic-inorganic hybrids. Structure and optical properties,” J. Mater. Chem. 15(35-36), 3937–3945 (2005).
[CrossRef]

J. Sol-Gel Sci. Technol. (1)

C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. André, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48(1-2), 80–85 (2008).
[CrossRef]

Opt. Express (2)

E. Pecoraro, S. García-Revilla, R. A. S. Ferreira, R. Balda, L. D. Carlos, and J. Fernández, “Real time random laser properties of Rhodamine-doped di-ureasil hybrids,” Opt. Express 18(7), 7470–7478 (2010).
[CrossRef] [PubMed]

B. Neto, A. L. J. Teixeira, N. Wada, and P. S. André, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15(26), 17520–17528 (2007).
[CrossRef] [PubMed]

Reliab. Eng. Syst. Saf. (1)

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[CrossRef]

Rev. Sci. Instrum. (2)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60(1), 65–77 (1989).
[CrossRef]

A. Rothen, “The Ellipsometer, an Apparatus to Measure Thicknesses of Thin Surface Films,” Rev. Sci. Instrum. 16(2), 26–30 (1945).
[CrossRef]

Surf. Sci. (1)

O. Polgár, M. Fried, T. Lohner, and I. Bársony, “Comparison of algorithms used for evaluation of ellipsometric measurements - Random search, genetic algorithms, simulated annealing and hill climbing graph-searches,” Surf. Sci. 457(1-2), 157–177 (2000).
[CrossRef]

Thin Solid Films (1)

A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455–456, 804–808 (2004).
[CrossRef]

Other (3)

M. Land, J. J. Sidorowich, and R. K. Belew, “Using Genetic Algorithms with Local Search for Thin Film Metrology,” in Proceedings of the Seventh International Conference on Genetic Algorithms, T. Bäck, ed., (Morgan Kaufmann Publishers, Inc, 1997), pp. 537–544.

R. A. S. Ferreira, C. M. S. Vicente, V. Fernandes, A. G. Macedo, E. Pecoraro, R. Nogueira, P. S. André, P. V. S. Marques, and L. D. Carlos, “Organic-inorganic hybrids for the new generation of optical networks,” in Proc. of International Conference on Transparent Optical Networks (ICTON 2009) (IEEE, S. Miguel (Portugal), July. 2009), pp. Tu.B4.2–1.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1998).

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Figures (3)

Fig. 1
Fig. 1

(a) SEM photo of the cross-section and (b) structure model of the dUZ40 planar waveguides.

Fig. 2
Fig. 2

Ellipsometric parameters Is (open circles) and Ic (open triangles) for (a) dUZ40-1 and (b) d-UZ40-2. The solid lines correspond to the data best fit (MSE = 1.52002 × 10−3).

Fig. 3
Fig. 3

(a) Euclidean distance to the final solution (50 runs and population of 400 elements) as function of the generation’s number for CGA and MOGA algorithms (population size of 400 individuals). The lines are visual guides. (b) Convergence rate for 50 iterations as function of the population size for the two considered algorithms.

Tables (1)

Tables Icon

Table 1 Individual (thickness for the SiO2, WSiO2 and dUZ40, WdUZ40 layers) and shared (high frequency relative dielectric constant, ε, static relative dielectric constant, εs, oscillator resonant frequency, ω0, and damping factor, Γ) parameter values determined using MOGA/LO and CGA/LO algorithms for dUZ40 films.

Equations (2)

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M S E I c I s = 1 2 N M 1 j = 1 N { ( I c j mod I c j exp ) 2 + ( I s j mod I s j exp ) 2 }
ε = ε + ( ε s ε ) ω 0 2 ( ω 0 2 ω 2 ) + i Γ ω

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