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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.40.002675


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Abstract

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

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-16-2675


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