Optimization problems in the estimation of parameters of thin films and the elimination of the influence of the substrate

  • Authors:

  • Ernesto G. Birgin;Ivan E. Chambouleyron;José Mario Martínez

  • Affiliations:

  • Department of Computer Sciences IME-USP, University of São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo, SP 05508-090, Brazil;Department of Applied Physics, Institute of Physics, University of Campinas, CP 6065, Campinas, SP 13083-970, Brazil;Department of Applied Mathematics IMECC-UNICAMP, University of Campinas, CP 6065, Campinas, SP 13081-970, Brazil

  • Venue:
  • Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
  • Year:
  • 2003

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Abstract

In a recent paper, the authors introduced a method to estimate optical parameters of thin films using transmission data. The associated model assumes that the film is deposited on a completely transparent substrate. It has been observed, however, that small absorption of substrates affect in a nonnegligible way the transmitted energy. The question arises of the reliability of the estimation method to retrieve optical parameters in the presence of substrates of different thicknesses and absorption degrees. In this paper, transmission spectra of thin films deposited on non-transparent substrates are generated and, as a first approximation, the method based on transparent substrates is used to estimate the optical parameters. As expected, the method is good when the absorption of the substrate is very small, but fails when one deals with less transparent substrates. To overcome this drawback, an iterative procedure is introduced, that allows one to approximate the transmittance with transparent substrate, given the transmittance with absorbent substrate. The updated method turns out to be almost as efficient in the case of absorbent substrates as it was in the case of transparent ones.