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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 61, Iss. 10 — Oct. 1, 1971
  • pp: 1380–1391

Ellipsometry with Imperfect Components Including Incoherent Effects

R. M. A. AZZAM and N. M. BASHARA  »View Author Affiliations


JOSA, Vol. 61, Issue 10, pp. 1380-1391 (1971)
http://dx.doi.org/10.1364/JOSA.61.001380


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Abstract

The problem of relating the specimen ψ and Δ to the instrument readings and component imperfections is solved by a general technique without any restriction on the nature of the imperfections. Thus, for the first time, small incoherent effects in the ellipsometer can be treated. The solution is explicit and is given in terms of the properties of the ideal ellipsometer and the Mueller imperfection matrices of the optical devices. After deriving the general solution, we consider a conventional ellipsometric arrangement. Arrays of coupling constants are introduced which clearly show the effect of imperfections on ψ and Δ. Also, we indicate in a schematic way the elements that remain effective after averaging over two and four zones. Component depolarization is discussed and the matrix elements contributing to it are found. Besides allowing all previous results to be obtained, some new conclusions of this analysis are: a small depolarization of the polarizer light output affects ψ (0.15° error in ψ for 1% depolarization) and this effect remains after two- and four-zone averaging. The effect of both coherent and incoherent <i>p</i> ↔ <i>s</i> cross scattering by the cell windows cancels if a two-zone average is taken. The same applies for the coherent and incoherent cross scattering by the specimen-surface roughness or by surface optical activity. For the compensator, cross scattering caused by birefringence and optical activity cancels only if a four-zone average is taken.

Citation
R. M. A. AZZAM and N. M. BASHARA, "Ellipsometry with Imperfect Components Including Incoherent Effects," J. Opt. Soc. Am. 61, 1380-1391 (1971)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-61-10-1380


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References

  1. F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970).
  2. W. R. Hunter, D. H. Eaton, and C. T. Sah, Surface Sci. 20, 355 (1970).
  3. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 600 (1971).
  4. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 1118 (1971).
  5. These are simply referred to as the nulling angles.
  6. See, for example, Refs. 1 and 3. The values of ψ and Δ are given by ρ=tanψeiΔ=tanAc tan(P-C)+tanC]/[ρc tanC tan(P-C)-1], for an ideal ellipsometer in which the compensator is assumed to have a complex slow-to-fast relative transmittance ρc and is set at an azimuth C before reflection. Using the simple transformation PA, we obtain the corresponding expression when the compensator is set after reflection.
  7. These quantities are denoted by t1P and t2P, respectively, in Ref. 3. The small azimuth and ellipticity are determined by the polarizer and the source-beam properties, Eq. (20). Thus, in general, the small ellipticity, ½∊3, is a property of the polarizer-source beam combination. The small azimuth, ½∊2, is equivalent to a polarizer-circle calibration error only at a particular wavelength and for a given light source.
  8. A method to account for the effect of optical activity and birefringence in the compensator is found in Ref. 4.
  9. W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, Mass., 1962), p. 165.
  10. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 44.

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