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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 2 — Feb. 1, 2007
  • pp: 326–338

Error analysis in inverse scatterometry. I. Modeling

Rayan M. Al-Assaad and Dale M. Byrne  »View Author Affiliations

JOSA A, Vol. 24, Issue 2, pp. 326-338 (2007)

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Scatterometry is an optical technique that has been studied and tested in recent years in semiconductor fabrication metrology for critical dimensions. Previous work presented an iterative linearized method to retrieve surface-relief profile parameters from reflectance measurements upon diffraction. With the iterative linear solution model in this work, rigorous models are developed to represent the random and deterministic or offset errors in scatterometric measurements. The propagation of different types of error from the measurement data to the profile parameter estimates is then presented. The improvement in solution accuracies is then demonstrated with theoretical and experimental data by adjusting for the offset errors. In a companion paper (in process) an improved optimization method is presented to account for unknown offset errors in the measurements based on the offset error model.

© 2007 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.5700) Instrumentation, measurement, and metrology : Reflection

ToC Category:
Diffraction and Gratings

Original Manuscript: January 6, 2006
Manuscript Accepted: July 18, 2006

Rayan M. Al-Assaad and Dale M. Byrne, "Error analysis in inverse scatterometry. I. Modeling," J. Opt. Soc. Am. A 24, 326-338 (2007)

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  1. 2004 International Technology Roadmap for Semiconductors, "Metrology 2004 Update," ITRS Web Resources, http://www.itrs.net/Links/2005ITRS/Metrology2005.pdf.
  2. S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, and K. P. Bishop, "Scatterometry and the simulation of diffraction-based metrology," Microlithogr. World 2, 5-16 (1993).
  3. J. Bischoff, J. W. Baumgart, J. J. Bauer, and H. Truckenbrodt, "Light-scattering-based micrometrology," in Proc. SPIE 2775, 251-262 (1996). [CrossRef]
  4. C. J. Raymond, M. Littau, A. Chuprin, and S. Ward, "Comparison of solutions to the scatterometry inverse problem," in Proc. SPIE 5375, 564-575 (2004). [CrossRef]
  5. E. M. Drege and D. M. Byrne, "Lithographic process monitoring using diffraction measurements," in Proc. SPIE 3998, 147-157 (2000). [CrossRef]
  6. E. M. Drege, J. A. Reed, and D. M. Byrne, "Linearized inversion of scatterometric data to obtain surface profile information," Opt. Eng. 41, 225-236 (2002). [CrossRef]
  7. E. M. Drege, R. M. Al-Assaad, and D. M. Byrne, "Mathematical analysis of inverse scatterometry," in Proc. SPIE 4689, 151-162 (2002). [CrossRef]
  8. R. M. Al-Assaad, E. M. Drege, and D. M. Byrne, "Profile parameter accuracy determined from scatterometric measurements," in Proc. SPIE 4692, 17-28 (2002). [CrossRef]
  9. M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 73, 1105-1112 (1983). [CrossRef]
  10. N. Chateau and J. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," J. Opt. Soc. Am. A 11, 1321-1331 (1994). [CrossRef]
  11. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice Hall, 1974).
  12. J. W. Goodman, Statistical Optics (Wiley, 2000).

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