OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 46, Iss. 12 — Apr. 20, 2007
  • pp: 2219–2228

Simplified optical scatterometry for periodic nanoarrays in the near-quasi-static limit

I. Abdulhalim  »View Author Affiliations


Applied Optics, Vol. 46, Issue 12, pp. 2219-2228 (2007)
http://dx.doi.org/10.1364/AO.46.002219


View Full Text Article

Enhanced HTML    Acrobat PDF (2667 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Scatterometry is now proven to be a very powerful technique for measurement of subwavelength periodic structures. However it requires heavy numerical calculations of the scattered optical waves from the structure. For periodic nanoarrays with feature size less than 100   nm , it is possible to simplify this using the Rytov near-quasi-static approximation valid for feature periods only few time less than the wavelength. The validity is investigated by way of comparison with exact numerical results obtained with the eigenfunctions approach. It is shown to be adequate for the determination of the structure parameters from the specularly reflected or transmitted waves and their polarization or ellipsometric properties. The validity of this approach is applied to lamellar nanoscale grating photoresist lines on Si substrate. The high sensitivity of the signals to the structure parameters is demonstrated using wavelengths of only few times the period.

© 2007 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: September 18, 2006
Revised Manuscript: December 1, 2006
Manuscript Accepted: December 4, 2006
Published: April 3, 2007

Citation
I. Abdulhalim, "Simplified optical scatterometry for periodic nanoarrays in the near-quasi-static limit," Appl. Opt. 46, 2219-2228 (2007)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-12-2219


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. "International technology roadmap for semiconductors," (ITRS, 1999), www.itrs.net.
  2. "Technology roadmap for nanoelectronics," (European Commission, November 2000), http://cordis.europa.eu/ist/.
  3. Kjell J. Gasvik, Optical Metrology, 3rd ed. (Wiley, 1996).
  4. H. P. Kleinknecht and H. Meier, "Optical monitoring of the etching of SiO2 and Si3N4 by the use of grating test pattern," J. Electrochem. Soc. 125, 798-803 (1978).
  5. G. F. Mendes, L. Cescato, and J. Frejlich, "Gratings for metrology and process control. 2: Thin film thickness measurement," Appl. Opt. 23, 576-583 (1984). [PubMed]
  6. G. F. Mendes, L. Cescato, J. Frejlich, E. S. Braga, and A. P. Mammana, "Continuous optical measurement of the dry etching of silicon using the diffraction of a lamellar grating," J. Electrochem. Soc. 132, 190-193 (1985).
  7. 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).
  8. S. S. H. Naqvi, S. H. Zaidi, S. R. Brueck, and J. R. McNeil, "Diffractive techniques for lithographic process monitoring and control," J. Vac. Sci. Technol. B 12, 3600-3606 (1994).
  9. S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemszyk, D. M. Haaland, R. A. Gottscho, and A. Kornblit, "Etch depth estimation of large-period silicon gratings with mulivariate calibration of rigorously simulated diffraction profiles," J. Opt. Soc. Am. A 11, 2485-2492 (1994).
  10. C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, "Metrology of subwavelength photoresist gratings using optical scatterometry," J. Vacuum Sci. Technol. B 13, 1484-1495 (1995).
  11. B. K. Minhas, S. L. Prins, S. S. H. Naqvi, and J. R. McNeil, "Toward sub-0.1-mm CD measurements using scatterometry," in Integrated Circuit Metrology, Inspection, and Process Control X, S. K. Jones, ed., Proc. SPIE 2725, 729-739 (1996).
  12. C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. W. Hosch, and J. R. McNeil, "Multiparameter grating metrology using optical scatterometry," J. Vacuum Sci. Technol. B 15, 361-368 (1997).
  13. B. K. Minhas, S. A. Coulombe, S. SohailH. Naqvi, and J. R. McNeil, "Ellipsometric scatterometry for the metrology of sub-0.10 μm linewidth structure," Appl. Opt. 37, 5112-5115 (1998).
  14. S. Hava and M. Auslender, "Groove depth dependence of IR transmission spectra through silicon gratings: experiment versus theory," Infrared Phys. Technol. 41, 149-154 (2000).
  15. S. Hava and M. Auslender, "Optical scatterometry evaluation of groove depth in lamellar silicon grating structures," Opt. Eng. 40, 1244-1248 (2001).
  16. Y. Xu and I. Abdulhalim, "Spectroscopic scatterometer system," U.S. patent 6,483,080, 19 November 2002.
  17. I. J. Allgair, D. Benoit, R. Hershey, L. C. Litt, I. Abdulhalim, B. Braymer, M. Faeyrman, J. C. Robinson, U. Whitney, Y. Xu, P. Zalicki, and J. Seligson, "Manufacturing considerations for implementattion of scatterometry for process monitoring," Proc. SPIE 3998, 125-134 (2000).
  18. J. Allgair, R. R. Hershey, L. C. Litt, D. C. Benoit, P. Herrera, A. Levy, Y. Xu, U. K. Whitney, J. C. Robinson, B. Braymer, I. Abdulhalim, and M. Faeyrman, "Spectroscopic CD offers higher precision metrology for sub-0.18 μm linewidth control," KLA-Tencor Magazine on Yield Management Solutions, 8-13 (2002), www.kla-tencor.com/company/magazine/fall01.
  19. I. Abdulhalim, M. Adel, M. Friedmann, and M. Faeyrman, "Periodic patterns and techniques to control misalignment," U.S. Patents Application Publication #2003/0002043 A1 (2 January 2003).
  20. S. Lakkaparagada, K. A. Brown, M. Hankinson, A. Levy, and I. Abdulhalim, "Methods and systems for lithography process control," U.S. patent application no. 2004/0005507 (8 January 2004).
  21. A. Levy, K. A. Brown, R. Smedt, G. Bultman, M. Nikoonahad, D. Wack, J. Fielden, and I. Abdulhalim, "Methods and systems for determining a critical dimension and overlay of a specimen," U.S. patent application no. 2004/0235205 (25 November 2004).
  22. H.-T. Huang, W. Kong, and F. L. Terry, Jr., "Normal incidence spectroscopic ellipsometry for critical dimension monitoring," Appl. Phys. Lett. 78, 3983-3985 (2001).
  23. B. S. Stutzman, H.-T. Huang, and F. L. Terry, Jr., "Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching," J. Vac. Sci. Technol. B 18, 2785-2793 (2000).
  24. H.-T. Huang and F. L. Terry, Jr., "Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring," Thin Solid Films 455-456, 828-836 (2004).
  25. M. G. Moharam, E. B. Grann, and D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995).
  26. P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996).
  27. G. Granet and B. Guizal, "Really efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996).
  28. P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997).
  29. G. Granet, "Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution," J. Opt. Soc. Am. A 16, 2510-2516 (1999).
  30. L. Li and C. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A 10, 1184-1189 (1993).
  31. L. Li, J. Chandezon, G. Granet, and J. P. Plumey, "Rigorous and efficient grating-analysis method made easy for optical engineers," Appl. Opt. 38, 304-313 (1999).
  32. L. Li, "Use of Fourier series in the analysis of the discontinuous structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
  33. E. Popov and M. Neviere, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000).
  34. H. Chu, "Finite difference approach to optical scattering of gratings," in Advanced Characterization Techniques for Optics, Semiconductors, and Nanotechnologies, A. Duparre and B. Singh, eds., Proc. SPIE 5188, 358-370 (2003).
  35. L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40, 553-573 (1993).
  36. L. Li, "Multilayer modal method for diffraction gratings of arbitary profile, depth, and permittivity," J. Opt. Soc. Am. A 10, 2583-2591 (1993).
  37. L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity:addendum," J. Opt. Soc. Am. A 11, 1685 (1994).
  38. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
  39. M. Auslender and S. Hava, "Scattering-matrix propagation algorithm in full-vectorial optics of multilayer grating structures," Opt. Lett. 21, 1765-1767 (1996). [PubMed]
  40. I. Kallioniemi, J. Saarinen, and E. Oja, "Optical scatterometry of subwavelength diffraction gratings: neural-network approach," Appl. Opt. 37, 5830-5834 (1998).
  41. J. Opsal, H. Chu, Y. Wen, Y. C. Chang, and G. Li, "Fundamental solutions for real-time optical CD metrology," in Metrology, Inspection, and Process Control for Lithography XVI, D. J. Herr, ed., Proc. SPIE 4689, 163-176 (2002).
  42. J. Opsal, H. Chu, Y. Wen, G. Li, and Y. C. Chang, "Contact hole inspection by real-time optical CD metrology," in Metrology, Inspection, and Process Control for Lithography XVII,, D. J. Herr, ed., Proc. SPIE 5038, 597-607 (2003).
  43. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  44. F. García-Vidal, J. M. Pitarke, and J. B. Pendry, "Effective medium theory of the optical properties of aligned carbon nanotubes," Phys. Rev. B 78, 4289-4292 (1997).
  45. C.-Y. You, S.-C. Shin, and S.-Y. Kim, "Modified effective-medium theory for magneto-optical spectra of magnetic materials," Phys. Rev. B 55, 5953-5958 (1997).
  46. H. Kikuta, H. Yoshida, and K. Iwata, "Ability and limitation of effective medium theory for subwavelength gratings," Opt. Rev. 2, 92-99 (1995).
  47. C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, "Calculation of the effective dielectric function of composites with periodic geometry," Physica B 293, 16-32 (2000).
  48. D. H. Raguin and G. M. Morris, "Antireflection structured surfaces for the infrared spectral region," J. Opt. Soc. Am. A 32, 1154-1167 (1993).
  49. E. B. Grann, M. G. Moharam, and D. A. Pommet, "Artificial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings," J. Opt. Soc. Am. A 11, 2695-2703 (1994).
  50. S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).
  51. I. Abdulhalim, "Analytic propagation matrix method for linear optics of arbitrary biaxial layered media," J. Opt. A 1, 646-653 (1999).
  52. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1986), Chap. 4.
  53. M. Schubert, "Generalized ellipsometry and complex optical systems," Thin Solid Films 313-314, 323-332 (1998).

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited