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Applied Optics

Applied Optics


  • Vol. 30, Iss. 23 — Aug. 10, 1991
  • pp: 3354–3360

Use of the biased estimator in the interpretation of spectroscopic ellipsometry data

G. E. Jellison, Jr.  »View Author Affiliations

Applied Optics, Vol. 30, Issue 23, pp. 3354-3360 (1991)

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The use of the biased estimator in the fitting of spectroscopic ellipsometry data is examined and applied to data from two-channel polarization modulation ellipsometry experiments. It is pointed out that the use of the biased estimator, as opposed to the unbiased estimator that is usually found in the literature, allows the experimentalist to weight properly the more accurate parts of the spectrum, to switch among different representations of the data, and to calculate a goodness of fit. The fit to data taken on a 59-nm SiO2 film on Si is examined with both the biased and the unbiased estimators.

© 1991 Optical Society of America

Original Manuscript: October 30, 1990
Published: August 10, 1991

G. E. Jellison, "Use of the biased estimator in the interpretation of spectroscopic ellipsometry data," Appl. Opt. 30, 3354-3360 (1991)

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  1. G. E. Jellison, F. A. Modine, “Optical absorption of silicon between 1.6 and 4.7 eV at elevated temperatures,” Appl. Phys. Lett. 41, 180–182 (1982); “Optical functions of silicon between 1.7 and 4.7 eV at elevated temperatures,” Phys. Rev. B 27, 7466–7472 (1983). [CrossRef]
  2. D. E. Aspnes, A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983). [CrossRef]
  3. D. E. Aspnes, J. B. Theeten “Optical properties of the interface between si and its thermally grown oxide,” Phys. Rev. Lett. 43, 1046–1050 (1979); “Spectroscopic analysis of the interface between Si and its thermally grown oxide,” J. Electrochem. Soc. 127, 1359–1365 (1980). [CrossRef]
  4. P. J. McMarr, K. Vedam, J. Narayan, “Spectroscopic ellipsometry: a new tool for nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986). [CrossRef]
  5. D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979). [CrossRef]
  6. R. W. Collins, J. M. Cavese, “Influence of substrate structure on the growth of hydrogenated amorphous silicon studied by in situ ellipsometry,” J. Appl. Phys. 60, 4169–4176 (1986). [CrossRef]
  7. P. G. Snyder, M. C. Rost, G. H. Bu-Abbud, J. A. Woolam, S. A. Alterovitz, “Variable angle of incidence spectroscopic ellipsometry: application to GaAs–AlxGa1−xAs multiple heterostructures,” J. Appl. Phys. 60, 3293–3301 (1986). [CrossRef]
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  9. S. Y. Kim, K. Vedam, “Proper choice of the error function in modeling spectroellipsometric data,” Appl. Opt. 25, 2013–2021 (1986). [CrossRef] [PubMed]
  10. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1986).
  11. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  12. F. A. Modine, G. E. Jellison, G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892–900 (1983). [CrossRef]
  13. Aspnes, A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975). [PubMed]
  14. S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969); Rev. Sci. Instrum. 41, 152 (1970). [CrossRef]
  15. G. E. Jellison, F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959–974 (1990). [CrossRef] [PubMed]
  16. G. E. Jellison, F. A. Modine, “Accurate calibration of a photoelastic modulator in polarization modulation ellipsometry,” in Polarizaiton Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 231–241 (1989).
  17. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965). [CrossRef]
  18. D. A. G. Bruggeman, “Berechnung verschiedener physikalisher Konstanten vor heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636 (1935).
  19. G. E. Jellison, “Examination of thin SiO2 films on Si using spectroscopic polarization modulation ellipsometry,” J. Appl. Phys.69 (to be published).
  20. C. R. Helms, B. E. Deal, eds., The Physics and Chemistry of SiO2 and the Si-SiO2 Interface (Plenum, New York, 1988).
  21. Ref. 10, p. 499.

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