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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 28 — Oct. 1, 2008
  • pp: 5208–5220

Estimation of the thickness and the optical parameters of several stacked thin films using optimization

Ricardo Andrade, Ernesto G. Birgin, Ivan Chambouleyron, José Mario Martínez, and Sergio D. Ventura  »View Author Affiliations

Applied Optics, Vol. 47, Issue 28, pp. 5208-5220 (2008)

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The reverse engineering problem addressed in the present research consists of estimating the thicknesses and the optical constants of two thin films deposited on a transparent substrate using only transmittance data through the whole stack. No functional dispersion relation assumptions are made on the complex refractive index. Instead, minimal physical constraints are employed, as in previous works of some of the authors where only one film was considered in the retrieval algorithm. To our knowledge this is the first report on the retrieval of the optical constants and the thickness of multiple film structures using only transmittance data that does not make use of dispersion relations. The same methodology may be used if the available data correspond to normal reflectance. The software used in this work is freely available through the PUMA Project web page (http://www.ime.usp.br/~egbirgin/puma/).

© 2008 Optical Society of America

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(310.0310) Thin films : Thin films

ToC Category:
Thin Films

Original Manuscript: August 8, 2008
Manuscript Accepted: August 21, 2008
Published: September 30, 2008

Ricardo Andrade, Ernesto G. Birgin, Ivan Chambouleyron, José Mario Martínez, and Sergio D. Ventura, "Estimation of the thickness and the optical parameters of several stacked thin films using optimization," Appl. Opt. 47, 5208-5220 (2008)

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  1. I. Chambouleyron and J. M. Martínez, “Optical properties of dielectric and semiconductor thin films,” Handbook of Thin Films Materials, H. S. Nalwa ed., (Academic, 2001), Vol. 3, Chap. 12, pp. 593-622
  2. D. Poelman and P. F. Smet, “Methods for the determination of the optical constants of thin films from single transmission measurements: a critical review,” J. Phys. D 36, 1850-1857(2003). [CrossRef]
  3. E. G. Birgin, I. Chambouleyron, and J. M. Martínez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comput. Phys. 151, 862-880 (1999). [CrossRef]
  4. M. Mulato, I. Chambouleyron, E. G. Birgin, and J. M. Martínez, “Determination of thickness and optical constants of amorphous silicon films from transmittance data,” Appl. Phys. Lett. 77, 2133-2135 (2000). [CrossRef]
  5. I. Chambouleyron, S. D. Ventura, E. G. Birgin, and J. M. Martínez, “Optimal constants and thickness determination of very thin amorphous semiconductor films,” J. Appl. Phys. 92, 3093-3102 (2002). [CrossRef]
  6. S. D. Ventura, E. G. Birgin, J. M. Martínez, and I. Chambouleyron, “Optimization techniques for the estimation of the thickness and the optical parameters of thin films using reflectance data,” J. Appl. Phys. 97, 043512 (2005). [CrossRef]
  7. TFCalc, Software Spectra Inc., Portland, Oreg., USA, www.sspectra.com, 2008.
  8. Filmwizard, Scientific Computing Int., Encinitas, Calif., USA, www.sci-soft.com, 2008.
  9. F. A. Jenkins and H. E. White, Fundamentals of Optics, (McGraw-Hill, 1981).
  10. E. G. Birgin, I. Chambouleyron, and J. M. Martínez, “Optimization problems in the estimation or parameters of thin films and the elimination of the influence of the substrate,” J. Comput. Appl. Math. 152, 35-50 (2003). [CrossRef]
  11. M. Born and E. Wolf, Principles of Optics, 1st ed. (Pergamon, 1959).
  12. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths Scientific Publications, 1950).
  13. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214-1222 (1983). [CrossRef]
  14. T. C. Paulick, “Inversion of normal-incidence (R,T) measurements to obtain n + ik for thin films,” Appl. Opt. 25, 562-564 (1986). [CrossRef] [PubMed]
  15. H. M. Liddell, Computer-Aided Techniques for the Design of Multilayer Filters (Adam Hilger, 1980).
  16. S. D. Ventura, “Optimization techniques for film parameter estimation,” Ph.D. thesis (Department of Applied Mathematics, University of Campinas, 2004).
  17. M. Raydan, “The Barzilai and Borwein gradient method for the large unconstrained minimization problem,” SIAM J. Optim. 7, 26-33 (1997). [CrossRef]
  18. E. G. Birgin and J. M. Martínez, “A spectral conjugate gradient method for unconstrained optimization,” Appl. Math. Optim. 43, 117-128 (2001). [CrossRef]
  19. B. Akaoglu, I. Atilgan, and B. Katircioglu, “Thickness and optical constant distributions of PECVD a-SiCx : H thin films along electrode radial direction,” Thin Solid Films 437, 257-265 (2003). [CrossRef]
  20. E. G. Birgin, I. Chambouleyron, J. M. Martínez, and S. D. Ventura, “Estimation of optical parameters of very thin films,” Appl. Numer. Math. 47, 109-119 (2003). [CrossRef]
  21. F. Curiel, W. E. Vargas, and R. G. Barrera, “Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra,” Appl. Opt. 41, 5969-5978 (2002). [CrossRef] [PubMed]
  22. A. Ramirez-Porras and W. E. Vargas-Castro, “Transmission of visible light through oxidized copper films: feasibility of using a spectral projected gradient method,” Appl. Opt. 43, 1508-1514 (2004). [CrossRef] [PubMed]
  23. N. F. Mott and E. A. Davis, Electronic Properties in Non Crystalline Materials (Clarendon, 1979).
  24. G. Dalba, P. Fornasini, R. Grisenti, F. Rocca, I. Chambouleyron, and C. F. O. Graeff, “Local order in hydrogenated amorphous germanium thin films studied by EXAFS,” J. Phys. Condens. Matter 9, 5875-5888 (1997). [CrossRef]
  25. A. R. Zanatta, M. Mulato, and I. Chambouleyron, “Exponential absorption edge and disorder in Column IV amorphous semiconductors,” J. Appl. Phys. 84, 5184-5190 (1998) [CrossRef]
  26. M. H. Brodsky, D. M. Kaplan, and J. F. Ziegler, Proceedings of the 11th International Conference on the Physics of Semiconductors (PWN-Polish Scientific, 1972), p. 529.
  27. W. Paul, G. A. N. Connell, and R. J. Temkin, “Amorphous germanium I. A model for the structural and optical properties,” Adv. Phys. 22, 531-580 (1973). [CrossRef]
  28. T. M. Donovan and K. Heinemann, “High-resolution electron microscope observations of voids in amorphous Ge,” Phys. Rev. Lett. 27, 1794-1796 (1971). [CrossRef]

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