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Applied Optics

Applied Optics


  • Vol. 43, Iss. 27 — Sep. 20, 2004
  • pp: 5137–5142

Optimization of diffraction grating profiles in fabrication by electron-beam lithography

Masato Okano, Hisao Kikuta, Yoshihiko Hirai, Kazuya Yamamoto, and Tsutom Yotsuya  »View Author Affiliations

Applied Optics, Vol. 43, Issue 27, pp. 5137-5142 (2004)

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We propose a new design method for periodic diffraction gratings to be fabricated with direct-writing electron-beam lithography. When the grating has a small period, the proximity effect of electron scattering restricts the grating profile after developing. Our design method optimizes the electron-dose profile and grating profile simultaneously to obtain the desired diffraction efficiency under the restriction of the proximity effect. The optimization is made with rigorous electromagnetic grating analysis and the resist development simulator. When we designed the diffraction grating with a period of 1.0 µm to obtain the highest efficiency of the first-order diffracted light of a 633-nm wavelength, the calculated grating profile was really different from the profile optimized only with rigorous electromagnetic grating analysis. Moreover, the diffraction grating of the electron-beam resist was fabricated according to the simulation result. The estimated diffraction efficiency was 82%, and the measured efficiency was 70%.

© 2004 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings

Original Manuscript: March 4, 2004
Revised Manuscript: April 28, 2004
Manuscript Accepted: April 28, 2004
Published: September 20, 2004

Masato Okano, Hisao Kikuta, Yoshihiko Hirai, Kazuya Yamamoto, and Tsutom Yotsuya, "Optimization of diffraction grating profiles in fabrication by electron-beam lithography," Appl. Opt. 43, 5137-5142 (2004)

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  1. E.-B. Kley, “Continuous profile writing by electron and optical lithography,” Microelectron. Eng. 34, 261–298 (1997). [CrossRef]
  2. A. R. Neureuther, D. F. Kyser, C. H. Ting, “Electron-beam resist edge profile simulation,” IEEE Trans. Electron. Dev. ED-26, 686–693 (1979). [CrossRef]
  3. P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992). [CrossRef]
  4. F. Nikolajeff, J. Bengtsson, M. Larsson, M. Ekberg, S. Hard, “Measuring and modeling the proximity effect in direct-write electron-beam lithography kinoforms,” Appl. Opt. 34, 897–903 (1995). [CrossRef] [PubMed]
  5. W. Daschner, M. Larsson, S. H. Lee, “Fabrication of monolithic diffractive optical elements by the use of e-beam direct write on an analog resist and a single chemically assisted ion-beam-etching step,” Appl. Opt. 34, 2534–2539 (1995). [CrossRef]
  6. M. Okano, K. Yamamoto, T. Yotsuya, Y. Hirai, H. Kikuta, “Validity and limitation of a proximity-compensation method for fabricating diffractive optical elements using the direct-writing electron-beam lithography,” Jpn. J. Opt. 29, 566–5722000 (in Japanese).
  7. Y. Hirai, H. Kikuta, M. Okano, T. Yotsuya, K. Yamamoto, “Automatic dose optimization system for resist cross-sectional profile in an electron beam lithography,” Jpn. J. Appl. Phys. 39, 6831–6835 (2000). [CrossRef]
  8. D. F. Kyser, K. Murata, “Quantitive electron microprobe analysis of thin films on substrate,” IBM J. Res. Dev. 18, 352–363 (1974). [CrossRef]
  9. F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresists,” IEEE Trans. Electron. Dev. ED-22, 456–464 (1975). [CrossRef]
  10. M. Okano, H. Kikuta, Y. Hirai, K. Yamamoto, T. Yotsuya, “Proximity correction for fabricating a chirped diffraction grating by direct-writing electron-beam lithography,” Jpn. J. Appl. Phys. 42, 5602–5606 (2003). [CrossRef]
  11. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
  12. P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 101–121. [CrossRef]
  13. T. Shiono, T. Hamamoto, K. Takahara, “High-efficiency blazed diffractive optical elements for the violet wavelength fabricated by electron-beam lithography,” Appl. Opt. 13, 2390–2393 (2002). [CrossRef]
  14. E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 31, 5910–5912 (1992). [CrossRef] [PubMed]
  15. Y. Sheng, D. Feng, S. Larochelle, “Analysis and synthesis of circular diffractive lens with local linear grating model and rigorous coupled-wave theory,” J. Opt. Soc. Am. A 14, 1562–1568 (1997). [CrossRef]
  16. I. Kallioniemi, T. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000). [CrossRef]

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