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Journal of Nanomaterials
Volume 2013 (2013), Article ID 621531, 10 pages
http://dx.doi.org/10.1155/2013/621531
Review Article

Advances in Optical and Magnetooptical Scatterometry of Periodically Ordered Nanostructured Arrays

Institute of Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 12116 Prague, Czech Republic

Received 26 November 2012; Accepted 27 December 2012

Academic Editor: Yue Li

Copyright © 2013 Martin Veis and Roman Antos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser & Photonics Reviews, vol. 4, no. 4, pp. 568–580, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. S. Brose, S. Danylyuk, L. Juschkin et al., “Broadband transmission masks, gratings and filters for extreme ultraviolet and soft X-ray lithography,” Thin Solid Films, vol. 520, no. 15, pp. 5080–5085, 2012.
  3. H. Liu, M. Klonowski, D. Kneeburg, G. Dahlen, M. Osborn, and T. Bao, “Advanced atomic force microscopy probes: wear resistant designs,” Journal of Vacuum Science and Technology B, vol. 23, no. 6, pp. 3090–3093, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Dahlen, M. Osborn, N. Okulan, W. Foreman, A. Chand, and J. Foucher, “Tip characterization and surface reconstruction of complex structures with critical dimension atomic force microscopy,” Journal of Vacuum Science and Technology B, vol. 23, no. 6, pp. 2297–2303, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” Journal of Vacuum Science and Technology B, vol. 23, no. 6, pp. 3075–3079, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. Ma and F. Cerrina, “Effect of a surface inhibition layer on line edge roughness,” Journal of Vacuum Science and Technology B, vol. 23, no. 3, pp. 1096–1101, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. R. A. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, North Holland Publishing, North-Holland, The Netherlands, 1977.
  8. R. Antos, J. Pistora, J. Mistrik et al., “Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials,” Journal of Applied Physics, vol. 100, no. 5, Article ID 054906, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Antos, J. Mistrik, T. Yamaguchi, S. Visnovsky, S. O. Demokritov, and B. Hillebrands, “Evidence of native oxides on the capping and substrate of permalloy gratings by magneto-optical spectroscopy in the zeroth- and first-diffraction orders,” Applied Physics Letters, vol. 86, no. 23, Article ID 231101, 3 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Antos, J. Mistrik, T. Yamaguchi, S. Visnovsky, S. O. Demokritov, and B. Hillebrands, “Evaluation of the quality of permalloy gratings by diffracted magneto-optical spectroscopy,” Optics Express, vol. 13, no. 12, pp. 4651–4656, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Visnovsky, Optics in Magnetic Multilayers and Nanostructures, CRC Press, Taylor & Francis, Boca Raton, Fla, USA, 2006.
  12. R. Antoš, J. Mistrík, M. Aoyama, T. Yamaguchi, S. Visnovsky, and B. Hillebrands, “Magneto-optical spectroscopy on permalloy wires in 0th and 1st diffraction orders,” Journal of Magnetism and Magnetic Materials, vol. 272, part 3, supplement 1, pp. 1670–1671, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. P. Vincent, “A finite-difference method for dielectric and conducting crossed gratings,” Optics Communications, vol. 26, no. 3, pp. 293–296, 1978. View at Scopus
  14. T. Delort and D. Maystre, “Finite-element method for gratings,” Journal of the Optical Society of America A, vol. 10, no. 12, pp. 2592–2601, 1993. View at Scopus
  15. H. Ichikawa, “Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method,” Journal of the Optical Society of America A, vol. 15, no. 1, pp. 152–157, 1998. View at Scopus
  16. S. D. Wu and E. N. Glytsis, “Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method,” Applied Optics, vol. 43, no. 5, pp. 1009–1023, 2004. View at Scopus
  17. A. Modinos, N. Stefanou, and V. Yannopapas, “Applications of the layer-KKR method to photonic crystals,” Optics Express, vol. 8, no. 3, pp. 197–202, 2001. View at Scopus
  18. F. Zolla and R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical diffraction mounts,” Journal of the Optical Society of America A, vol. 13, no. 4, pp. 796–802, 1996. View at Scopus
  19. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” Journal of the Optical Society of America A, vol. 10, no. 6, pp. 1168–1175, 1993. View at Scopus
  20. R. Petit, Ed., Electromagnetic Theory of Gratings, Springer, Berlin, Germany, 1980.
  21. E. G. Loewen and E. Popov, Diffraction Gratings and Applications, CRC Press, New York, NY, USA, 1997.
  22. L. Li and J. Chandezon, “Improvement of the coordinate transformation method for surface-relief gratings with sharp edges,” Journal of the Optical Society of America A, vol. 13, no. 11, pp. 2247–2255, 1996. View at Scopus
  23. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” Journal of the Optical Society of America, vol. 71, no. 7, pp. 811–818, 1981. View at Scopus
  24. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” The Bell System Technical Journal, vol. 48, no. 9, pp. 2909–2947, 1969. View at Scopus
  25. N. P. K. Cotter, T. W. Preist, and J. R. Sambles, “Scattering-matrix approach to multilayer diffraction,” Journal of the Optical Society of America A, vol. 12, no. 5, pp. 1097–1103, 1995. View at Scopus
  26. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” Journal of the Optical Society of America A, vol. 13, no. 4, pp. 779–784, 1996. View at Scopus
  27. P. Lalanne, “Convergence performance of the coupled-wave and the differential methods for thin gratings,” Journal of the Optical Society of America A, vol. 14, no. 7, pp. 1583–1591, 1997. View at Scopus
  28. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” Journal of the Optical Society of America A, vol. 14, no. 7, pp. 1592–1598, 1997. View at Scopus
  29. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” Journal of the Optical Society of America A, vol. 13, no. 9, pp. 1870–1876, 1996. View at Scopus
  30. R. Antos, “Fourier factorization with complex polarization bases in modeling optics of discontinuous bi-periodic structures,” Optics Express, vol. 17, no. 9, pp. 7269–7274, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. G. Granet, “Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution,” Journal of the Optical Society of America A, vol. 16, no. 10, pp. 2510–2516, 1999. View at Scopus
  32. 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, vol. 455-456, no. 1-2, pp. 828–836, 2004. View at Publisher · View at Google Scholar · View at Scopus
  33. T. H. Ghong, J. S. Byun, S. H. Han, J. M. Chung, and Y. D. Kim, “Analysis of 2D periodic nanostructures with an oxide overlayer via spectroscopic ellipsometry,” Journal of Nanoscience and Nanotechnology, vol. 11, supplement I, no. 7, pp. 6514–6517, 2011.
  34. Z. Yu, J. Hwu, Y. Liu, G. Gauzner, K. Lee, and D. Kuo, “Study of spin-coated resist coverage on nanoscale topography using spectroscopic ellipsometry,” Journal of Applied Physics, vol. 110, no. 1, Article ID 014303, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. R. Antos, I. Ohlidal, J. Mistrik et al., “Spectroscopic ellipsometry on lamellar gratings,” Applied Surface Science, vol. 244, no. 1–4, pp. 225–229, 2005. View at Publisher · View at Google Scholar · View at Scopus
  36. R. Antos, J. Pistora, I. Ohlidal et al., “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” Journal of Applied Physics, vol. 97, no. 5, Article ID 053107, 7 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  37. T. J. Kim, S. H. Han, T. H. Ghong, J. S. Byun, J. M. Chung, and Y. D. Kim, “Study on an asymmetric nanostructure by using a rigorous coupled-wave analysis,” Journal of the Korean Physical Society, vol. 56, no. 41, pp. 1278–1281, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. E. Liu and F. L. Terry Jr., “Immersion scatterometry for improved nano-scale topography measurements,” Physica Status Solidi A, vol. 205, no. 4, pp. 784–788, 2008. View at Publisher · View at Google Scholar · View at Scopus
  39. M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films, vol. 313-314, pp. 323–332, 1998. View at Scopus
  40. L. Halagačka, K. Postava, M. Foldyna, and J. Pištora, “Precise phase-modulation generalized ellipsometry of anisotropic samples,” Physica Status Solidi A, vol. 205, no. 4, pp. 752–755, 2008. View at Publisher · View at Google Scholar · View at Scopus
  41. M. Foldyna, A. De Martino, E. Garcia-Caurel et al., “Monitoring critical dimensions of bidimensional gratings by spectroscopic ellipsometry and mueller polarimetry,” Physica Status Solidi A, vol. 205, no. 4, pp. 806–809, 2008. View at Publisher · View at Google Scholar · View at Scopus
  42. M. Foldyna, A. De Martino, E. Garcia-Caurel et al., “Critical dimension of biperiodic gratings determined by spectral ellipsometry and Mueller matrix polarimetry,” The European Physical Journal of Applied Physics, vol. 42, no. 3, pp. 351–359, 2008. View at Publisher · View at Google Scholar · View at Scopus
  43. M. Foldyna, T. A. Germer, B. C. Bergner, and R. G. Dixson, “Generalized ellipsometry of artificially designed line width roughness,” Thin Solid Films, vol. 519, supplement 1, no. 9, pp. 2633–2636, 2011. View at Publisher · View at Google Scholar · View at Scopus
  44. R. Antos, M. Veis, E. Liskova et al., “Optical metrology of patterned magnetic structures: deep versus shallow gratings,” in Metrology, Inspection, and Process Control for Microlithography XIX, vol. 5752 of Proceedings of SPIE, pp. 1050–1059, San Jose, Calif, USA, March 2005. View at Publisher · View at Google Scholar · View at Scopus
  45. G. Neuber, R. Rauer, J. Kunze et al., “Temperature-dependent spectral generalized magneto-optical ellipsometry,” Applied Physics Letters, vol. 83, no. 22, pp. 4509–4511, 2003. View at Publisher · View at Google Scholar · View at Scopus
  46. J. I. Martin, J. Nogues, K. Liu, J. L. Vicent, and I. K. Schuller, “Ordered magnetic nanostructures: fabrication and properties,” Journal of Magnetism and Magnetic Materials, vol. 256, no. 1–3, pp. 449–501, 2003. View at Publisher · View at Google Scholar
  47. M. Grimsditch and P. Vavassori, “The diffracted magneto-optic Kerr effect: what does it tell you?” Journal of Physics Condensed Matter, vol. 16, no. 9, pp. R275–R294, 2004. View at Publisher · View at Google Scholar · View at Scopus
  48. W. K. Hiebert, A. Stankiewicz, and M. R. Freeman, “Direct observation of magnetic relaxation in a small permalloy disk by time-resolved scanning Kerr microscopy,” Physical Review Letters, vol. 79, no. 6, pp. 1134–1137, 1997. View at Scopus
  49. T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science, vol. 289, no. 5481, pp. 930–932, 2000. View at Publisher · View at Google Scholar · View at Scopus
  50. A. Wachowiak, J. Wiebe, M. Bode, O. Pietzsch, M. Morgenstern, and R. Wiesendanger, “Direct observation of internal spin structure of magnetic vortex cores,” Science, vol. 298, no. 5593, pp. 577–580, 2002. View at Publisher · View at Google Scholar · View at Scopus
  51. J. B. Kim, Y. H. Lu, M. H. Cho et al., “Diffracted magneto-optical Kerr effect of a Ni magnetic grating,” Journal of Applied Physics, vol. 106, no. 9, Article ID 093103, 2009. View at Publisher · View at Google Scholar · View at Scopus
  52. A. Neudert, J. McCord, R. Schäfer, and L. Schultz, “Subnanosecond vortex transformation in ferromagnetic film elements observed by stroboscopic wide-field Kerr microscopy,” Journal of Applied Physics, vol. 97, no. 10, part 2, Article ID 10E701, 3 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  53. K. Rokushima and J. Yamakita, “Analysis of anisotropic dielectric gratings,” Journal of the Optical Society of America, vol. 73, no. 7, pp. 901–908, 1983. View at Scopus
  54. S. Visnovsky and K. Yasumoto, “Multilayer anisotropic bi-periodic diffraction gratings,” Czechoslovak Journal of Physics, vol. 51, no. 3, pp. 229–247, 2001. View at Publisher · View at Google Scholar · View at Scopus
  55. M. H. Cho, Y. Lu, J. Y. Rhee, and Y. P. Lee, “Rigorous approach on diffracted magneto-optical effects from polar and longitudinal gyrotropic gratings,” Optics Express, vol. 16, no. 21, pp. 16825–16839, 2008. View at Publisher · View at Google Scholar · View at Scopus
  56. M. H. Cho, H. Zheng, Y. Lu, Y. Lee, and W. Cai, “Improved rigorous coupled-wave analysis for polar magnetic gratings,” Computer Physics Communications, vol. 182, no. 2, pp. 360–365, 2011. View at Publisher · View at Google Scholar · View at Scopus