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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 11, Iss. 7 — Jul. 1, 1994
  • pp: 2156–2158

Determination of complex refractive index and thickness of a homogeneous layer by combined reflection and transmission ellipsometry

John Lekner  »View Author Affiliations

JOSA A, Vol. 11, Issue 7, pp. 2156-2158 (1994)

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Analytic inversion of combined reflection and transmission ellipsometric data is demonstrated. When the thickness is eliminated between the equations that give the reflection and transmission ratios ρ = rp/rs and τ = tp/ts, an algebraic equation for the unknown dielectric constant ε of the layer is obtained. After removal of some factors, this reduces to a linear equation in ε. The solution for unsupported films agrees with that previously obtained by Azzam [ J. Phys. (Paris) C10, 67 ( 1993)]; it can be simplified to ε = ε1 sin2θ1/(cos2θ1ρ/τ), where ε1 is the dielectric constant of the ambient medium and θ1 is the angle of incidence. Stability of the solution with respect to noise in the data is analyzed.

© 1994 Optical Society of America

Original Manuscript: September 7, 1993
Revised Manuscript: November 22, 1993
Manuscript Accepted: January 11, 1994
Published: July 1, 1994

John Lekner, "Determination of complex refractive index and thickness of a homogeneous layer by combined reflection and transmission ellipsometry," J. Opt. Soc. Am. A 11, 2156-2158 (1994)

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  1. R. M. A. Azzam, “Ellipsometry of unsupported and embedded thin films,” J. Phys. (Paris) C10, 67–70 (1983).
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  3. J. Lekner, Theory of Reflection (Nijhoff/Kluwer, Dordrecht, The Netherlands, 1987).
  4. M. C. Dorf, J. Lekner, “Reflection and transmission ellipsometry of a uniform layer,” J. Opt. Soc. Am. A 4, 2096–2100 (1987). [CrossRef]
  5. J. Lekner, “Inversion of reflection ellipsometric data,” Appl. Opt. (to be published). [PubMed]
  6. J. Lekner, “Inversion of transmission ellipsometric data for transparent films,” Appl. Opt. (to be published).
  7. J. Lekner, “Ellipsometry of a thin film between similar media,” J. Opt. Soc. Am. A 5, 1041–1043 (1988). [CrossRef]

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