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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 30 — Oct. 20, 2012
  • pp: 7384–7394

Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry

H. Gross, M.-A. Henn, S. Heidenreich, A. Rathsfeld, and M. Bär  »View Author Affiliations


Applied Optics, Vol. 51, Issue 30, pp. 7384-7394 (2012)
http://dx.doi.org/10.1364/AO.51.007384


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Abstract

We investigate the impact of line-edge and line-width roughness (LER, LWR) on the measured diffraction intensities in angular resolved extreme ultraviolet (EUV) scatterometry for a periodic line-space structure designed for EUV lithography. LER and LWR with typical amplitudes of a few nanometers were previously neglected in the course of the profile reconstruction. The two-dimensional (2D) rigorous numerical simulations of the diffraction process for periodic structures are carried out with the finite element method providing a numerical solution of the 2D Helmholtz equation. To model roughness, multiple calculations are performed for domains with large periods, containing many pairs of line and space with stochastically chosen line and space widths. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances is observed and established for different degrees of roughness. In particular, we obtain simple analytical expressions for the bias in the mean efficiencies and the additional uncertainty contribution stemming from the presence of LER and/or LWR. As a consequence this bias can easily be included into the reconstruction model to provide accurate values for the evaluated profile parameters. We resolve the sensitivity of the reconstruction from this bias by using simulated data with LER/LWR perturbed efficiencies for multiple reconstructions. If the scattering efficiencies are bias-corrected, significant improvements are found in the reconstructed bottom and top widths toward the nominal values.

© 2012 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Diffraction and Gratings

History
Original Manuscript: June 11, 2012
Revised Manuscript: August 17, 2012
Manuscript Accepted: September 21, 2012
Published: October 18, 2012

Citation
H. Gross, M.-A. Henn, S. Heidenreich, A. Rathsfeld, and M. Bär, "Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry," Appl. Opt. 51, 7384-7394 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-30-7384


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References

  1. C. Raymond, M. Murnane, S. Prins, S. Sohail, H. Naqvi, J. McNeil, and J. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (2009). [CrossRef]
  2. M.-A. Henn, R. Model, M. Bär, M. Wurm, B. Bodermann, A. Rathsfeld, and H. Gross, “On numerical reconstructions of lithographic masks in DUV scatterometry,” Proc. SPIE 7390, 73900Q (2009). [CrossRef]
  3. M. Wurm, S. Bonifer, B. Bodermann, and J. Richter, “Deep ultraviolet scatterometer for dimensional characterization of nanostructures: system improvements and test measurements,” Meas. Sci. Technol. 22, 094024 (2011). [CrossRef]
  4. J. Perlich, F. Kamm, J. Rau, F. Scholze, and G. Ulm, “Characterization of extreme ultraviolet masks by extreme ultraviolet scatterometry,” J. Vac. Sci. Technol. B 22, 3059–3062 (2004). [CrossRef]
  5. F. Scholze and C. Laubis, “Use of EUV scatterometry for the characterization of line profiles and line roughness on photomasks,” in EMLC 2008, 24th European Mask and Lithography Conference (VDE Verlag, 2008), pp. 374–382.
  6. R. Petit and L. Botten, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
  7. J. Chandezon, G. Raoult, and D. Maystre, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980). [CrossRef]
  8. P. Lalanne and G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996). [CrossRef]
  9. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
  10. M. Moharam, E. Grann, D. Pommet, and T. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
  11. A. Tavrov, M. Totzeck, N. Kerwien, and H. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002). [CrossRef]
  12. J. Elschner, R. Hinder, and G. Schmidt, “Finite element solution of conical diffraction problems,” Adv. Comput. Math. 16, 139–156 (2002). [CrossRef]
  13. H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modelling of indirect measurements in scatterometry,” Measurement 39, 782–794 (2006). [CrossRef]
  14. O. Cessenat and B. Despres, “Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem,” SIAM J. Numer. Anal. 35, 255–299 (1998). [CrossRef]
  15. A. Tarantola, Inverse Problem Theory (Elsevier, 1987).
  16. H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009). [CrossRef]
  17. R. Al-Assaad and D. Byrne, “Error analysis in inverse scatterometry. I. Modeling,” J. Opt. Soc. Am. A 24, 326–338 (2007). [CrossRef]
  18. H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 6995OT (2008).
  19. H. Patrick, T. A. Germer, Y. Ding, H. Ro, L. Richter, and C. Soles, “In situ measurement of annealing-induced line shape evolution in nanoimprinted polymers using scatterometry,” Proc. SPIE 7271, 727128 (2009). [CrossRef]
  20. M. Wurm, “Über die dimensionelle Charakterisierung von Gitterstrukturen auf Fotomasken mit einem neuartigen DUV-Scatterometer,” Ph.D. thesis (Friedrich-Schiller-Universität Jena, 2008).
  21. H. Patrick, T. Germer, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
  22. A. Kato and F. Scholze, “Effect of line roughness on the diffraction intensities in angular resolved scatterometry,” Appl. Opt. 49, 6102–6111 (2010). [CrossRef]
  23. P. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, 1978).
  24. J. Elschner, R. Hinder, A. Rathsfeld, and G. Schmidt, http://www.wias-berlin.de/software/DIPOG .
  25. M.-A. Henn, H. Gross, C. Elster, F. Scholze, M. Wurm, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20, 12771–12786 (2012). [CrossRef]
  26. T. A. Germer, “Effect of line and trench profile variation on specular and diffusive reflectance from periodic structure,” J. Opt. Soc. Am. A 24, 696–701 (2007). [CrossRef]
  27. T. Schuster, S. Rafler, V. F. Paz, F. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009). [CrossRef]

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