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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 8 — Aug. 1, 2005
  • pp: 1630–1636

Closed-form inversion of the reflection ellipsometric function of a film–substrate system: absorbing-substrate optical constant

M. Elshazly-Zaghloul and A. R.M. Zaghloul  »View Author Affiliations


JOSA A, Vol. 22, Issue 8, pp. 1630-1636 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001630


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Abstract

A closed-form inversion expression for obtaining the optical constant (complex refractive index) of the substrate of an absorbing-film–absorbing-substrate system from one reflection ellipsometry measurement is derived. If, in addition, the film thickness is to be determined, a second measurement at another angle of incidence may or may not be used. The derived formula does not introduce errors itself, and tolerates errors in input variables very well. Random and systematic errors in the measured ellipsometric parameters do not affect the value obtained for the optical constant of the substrate: it is always the true value to two decimal places. Two examples in ellipsometry and in the design of reflection-type optical devices, one each, are presented and discussed. In addition, experimental results for a commercially available wafer are also presented. Two other closed-form inversion expressions for obtaining the optical constant of the substrate from two and three measurements are also presented and briefly discussed.

© 2005 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(230.5440) Optical devices : Polarization-selective devices
(310.6860) Thin films : Thin films, optical properties

History
Original Manuscript: September 16, 2004
Revised Manuscript: January 25, 2005
Manuscript Accepted: February 3, 2005
Published: August 1, 2005

Citation
M. Elshazly-Zaghloul and A. R.M. Zaghloul, "Closed-form inversion of the reflection ellipsometric function of a film–substrate system: absorbing-substrate optical constant," J. Opt. Soc. Am. A 22, 1630-1636 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-8-1630


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References

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