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Applied Optics

Applied Optics


  • Vol. 40, Iss. 16 — Jun. 1, 2001
  • pp: 2675–2681

Photometric Methods for Determining the Optical Constants and the Thicknesses of Thin Absorbing Films: Selection of a Combination of Photometric Quantities on the Basis of Error Analysis

Tzwetanka Babeva, Snejana Kitova, and Ivan Konstantinov  »View Author Affiliations

Applied Optics, Vol. 40, Issue 16, pp. 2675-2681 (2001)

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We select the best combinations of spectrophotometric quantities for the most accurate determination of the optical constants, <i>n</i> (refractive index), <i>k</i> (absorption coefficient), and the thicknesses of thin absorbing films. The basic comparative criteria used are the maximum absolute errors in the determination of <i>n</i>, <i>k</i>, and <i>d</i> that result from experimental errors in photometric measurements and in the optical constants of the substrates. We studied all possible combinations of photometric quantities <i>T</i>, <i>T</i><sub><i>s</i></sub><sup>θ</sup>, <i>T</i><sub><i>p</i></sub><sup>θ</sup>, <i>R</i>, <i>R</i><sub><i>s</i></sub><sup>θ</sup>, <i>R</i><sub><i>p</i></sub><sup>θ</sup>, <i>R</i><sub><i>m</i></sub>, <i>R</i><sub><i>ms</i></sub><sup>θ</sup>, and <i>R</i><sub><i>mp</i></sub><sup>θ</sup> at 0° < θ ≤ 70°, where <i>T</i> denotes transmission; <i>R</i>, reflection; the subscripts <i>s</i> and <i>p</i>, <i>s</i>- and <i>p</i>-polarized light; <i>m</i>, reflection from a thin film coated upon an opaque substrate; and superscript θ, the angle of incidence of light. The absence of the subscripts <i>s</i> and <i>p</i> implies nonpolarized light; that of the subscript <i>m</i>, a nonabsorbing substrate; and that of superscript θ, normally incident light. The error analysis that is made admits the following conclusions: (1) The best double combinations are (<i>TR</i>), (<i>TR<sub>m</sub></i>), (<i>TR<sub>p</sub></i><sup>70</sup>), and (<i>TR<sub>mp</sub></i><sup>70</sup>); (2) the best triple combinations are (<i>TRR<sub>m</sub></i>), (<i>TRR<sub>p</sub></i><sup>70</sup>), (<i>TRR<sub>mp</sub></i><sup>70</sup>), (<i>TR<sub>m</sub></i><i>R<sub>p</sub></i><sup>70</sup>), and (<i>TR<sub>m</sub></i><i>R<sub>mp</sub></i><sup>70</sup>); (3) the methods indicated above, suitably combined, are quite sufficient to provide the maximum accuracy and reliability of <i>n</i>, <i>k</i>, and <i>d</i> for all practical situations; (4) <i>TRR</i> methods based on measurements with obliquely polarized light are more suitable for thin films with <i>n</i> <, such as some metal films; (5) the regions of <i>n</i>, <i>k</i>, and <i>d</i>/λ with the highest and the lowest accuracies do not overlap in either the <i>TR</i> or the <i>TRR</i> methods. Hence more combinations, preferably all, should be applied for the most accurate determination of <i>n</i>, <i>k</i> (and <i>d</i>), and the errors should be evaluated as a criterion for the best combination.

© 2001 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(310.0310) Thin films : Thin films
(310.6860) Thin films : Thin films, optical properties

Tzwetanka Babeva, Snejana Kitova, and Ivan Konstantinov, "Photometric Methods for Determining the Optical Constants and the Thicknesses of Thin Absorbing Films: Selection of a Combination of Photometric Quantities on the Basis of Error Analysis," Appl. Opt. 40, 2675-2681 (2001)

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  1. J. E. Nestell and R. W. Christy, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11, 643–650 (1972).
  2. H. Liddell, Computer-Aided Techniques for Design of Multilayer Filters (Hilger, Bristol, UK, 1981), Chap. 6, pp. 118–133.
  3. V. Panayotov and I. Konstantinov, “Algebraic determination of thin-film optical constants from photometric (T, Rf, Rm) and (T, Rb, Rm) measurements,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE 2253, 1070–1079 (1994).
  4. K. Lamprecht, W. Papousek, and G. Leising, “Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements,” Appl. Opt. 36, 6364–6371 (1997).
  5. J.-J. Chen, J.-D. Lin, and L.-J. Sheu, “Simultaneous measurements of spectral optical properties and thickness of an absorbing thin film on a substrate,” Thin Solid Films 354, 176–186 (1999).
  6. A. B. Djurisic, T. Fritz, and K. Leo, “Determination of optical constants of thin absorbing films from normal incidence reflectance and transmittance measurements,” Opt. Commun. 166, 35–42 (1999).
  7. R. E. Denton, R. D. Campbell, and S. G. Tomlin, “The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D 5, 852–863 (1972).
  8. W. Hansen, “Optical characterization of thin films: theory,” J. Opt. Soc. Am. 63, 793–802 (1973).
  9. J. Pozo and L. Diaz, “Method for determination of optical constants of thin films: dependence on experimental uncertainties,” Appl. Opt. 31, 4474–4482 (1992).
  10. I. Konstantinov, Tz. Babeva, and S. Kitova, “Analysis of errors in thin-film optical parameters derived from spectrophotometric measurements at normal light incidence,” Appl. Opt. 37, 4260–4267 (1998).
  11. O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D 24, 2088–2094 (1991).
  12. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), Chap. 4, pp. 55–57.
  13. P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 435–441 (1968).
  14. A. Hjortsberg, “Determination of optical constants of absorbing materials using transmission and reflection of thin films on partially metallized substrates: analysis of the new (T, Rm) technique,” Appl. Opt. 20, 1254–1262 (1981).
  15. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
  16. D. Smith, E. Shiles, and M. Inokuti, Handbook of Optical constants of Solids, D. Palik, ed. (Academic Orlando, Fla., 1985), Part II, pp. 377–405.

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