OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 403–410

Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers

D. E. Aspnes  »View Author Affiliations

JOSA A, Vol. 21, Issue 3, pp. 403-410 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (183 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



I investigate the dependence of shot-noise-limited uncertainties of the ellipsometric parameters ψ and Δ for the rotating-analyzer ellipsometer (RAE) and the rotating-compensator ellipsometer (RCE) of the polarizer–sample–compensator–analyzer type. The development is general and takes into account correlations among the Fourier coefficients of the transmitted intensity, in particular the average intensity, which is necessarily correlated with all other coefficients through normalization. The results are expressed in terms of the traditional uncertainties δψ and δΔ of the ellipsometric parameters ψ and Δ, respectively, although a more appropriate measure of uncertainty is the differential area 2δψ×sin ψδΔ on the unit-radius Poincaré sphere. Numerical results for broadband operation from 1.5 to 6.0 eV with a Si sample show that the optimum measurement conditions for both configurations occur when the intensity of light reflected from the sample is approximately balanced between the TE and the TM modes, and, for the RCE, when the analyzer azimuth is essentially equal to that of the polarizer. Under typical broadband operating conditions in which components cannot be optimized on a wavelength-by-wavelength basis, the RCE is better at determining Δ, whereas the RAE is better at determining ψ. The approach is easily generalized to other configurations and other types of experimental uncertainty, both random and systematic.

© 2004 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry

Original Manuscript: July 31, 2003
Revised Manuscript: October 28, 2003
Manuscript Accepted: November 6, 2003
Published: March 1, 2004

D. E. Aspnes, "Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers," J. Opt. Soc. Am. A 21, 403-410 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973). [CrossRef]
  2. D. E. Aspnes, “Fourier transform detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8, 222–225 (1973). [CrossRef]
  3. J. Lee, P. I. Rovira, I. An, R. W. Collins, “Rotating-compensator multichannel ellipsometry: applications for real-time Stokes vector spectroscopy of thin film growth,” Rev. Sci. Instrum. 69, 1800–1810 (1998). [CrossRef]
  4. J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–62 (1998). [CrossRef]
  5. B. Drevillon, “Phase-modulated ellipsometry from the ultraviolet to the infrared: in situ application to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1–87 (1993). [CrossRef]
  6. G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997). [CrossRef]
  7. D. E. Aspnes, “Optimizing precision of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 639–646 (1974). [CrossRef]
  8. Z. M. Huang, J. H. Chu, “Optimizing precision of fixed-polarizer, rotating-polarizer, sample, and fixed-analyzer spectroscopic ellipsometry,” Appl. Opt. 39, 6390–6395 (2000). [CrossRef]
  9. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  10. C. V. Kent, J. Lawson, “A photoelectric method for the determination of the parameters of elliptically polarized light,” J. Opt. Soc. Am. 27, 117–119 (1937). [CrossRef]
  11. M. J. Dodge, “Refractive properties of magnesium fluoride,” Appl. Opt. 23, 1980–1985 (1984). [CrossRef] [PubMed]
  12. D. E. Aspnes, A. 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited