Abstract

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]

2003

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]

2002

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]

2000

I. Kallioniemi, T. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[CrossRef]

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).

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]

1997

1995

1992

1981

1979

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]

1975

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]

1974

D. F. Kyser, K. Murata, “Quantitive electron microprobe analysis of thin films on substrate,” IBM J. Res. Dev. 18, 352–363 (1974).
[CrossRef]

Ammer, T.

I. Kallioniemi, T. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[CrossRef]

Bengtsson, J.

Daschner, W.

Dill, F. H.

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]

Ekberg, M.

Feng, D.

Gaylord, T. K.

Hamamoto, T.

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]

Hard, S.

Hirai, Y.

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]

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).

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]

Kallioniemi, I.

I. Kallioniemi, T. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[CrossRef]

Kikuta, H.

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]

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).

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]

Kley, E.-B.

E.-B. Kley, “Continuous profile writing by electron and optical lithography,” Microelectron. Eng. 34, 261–298 (1997).
[CrossRef]

Kyser, D. F.

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]

D. F. Kyser, K. Murata, “Quantitive electron microprobe analysis of thin films on substrate,” IBM J. Res. Dev. 18, 352–363 (1974).
[CrossRef]

Larochelle, S.

Larsson, M.

Lee, S. H.

Maker, P. D.

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992).
[CrossRef]

Moharam, M. G.

Muller, R. E.

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992).
[CrossRef]

Murata, K.

D. F. Kyser, K. Murata, “Quantitive electron microprobe analysis of thin films on substrate,” IBM J. Res. Dev. 18, 352–363 (1974).
[CrossRef]

Neureuther, A. R.

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]

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]

Nikolajeff, F.

Noponen, E.

Okano, M.

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]

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).

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]

Rossi, M.

I. Kallioniemi, T. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[CrossRef]

Sheng, Y.

Shiono, T.

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]

Takahara, K.

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]

Ting, C. H.

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]

Turunen, J.

Tuttle, J. A.

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]

Vasara, A.

Vincent, P.

P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 101–121.
[CrossRef]

Walker, E. J.

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]

Yamamoto, K.

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]

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).

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]

Yotsuya, T.

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]

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).

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]

Appl. Opt.

IBM J. Res. Dev.

D. F. Kyser, K. Murata, “Quantitive electron microprobe analysis of thin films on substrate,” IBM J. Res. Dev. 18, 352–363 (1974).
[CrossRef]

IEEE Trans. Electron. Dev.

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]

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]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992).
[CrossRef]

Jpn. J. Appl. Phys.

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]

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]

Jpn. J. Opt.

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).

Microelectron. Eng.

E.-B. Kley, “Continuous profile writing by electron and optical lithography,” Microelectron. Eng. 34, 261–298 (1997).
[CrossRef]

Opt. Commun.

I. Kallioniemi, T. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[CrossRef]

Other

P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 101–121.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Optimization process of the series method. The grating profile is designed in the optical optimization process. The electron-dose profile is determined in the proximity correction process.

Fig. 2
Fig. 2

Optimization process of the unified method. Rigorous grating analysis and the electron-beam lithography simulator are unified. The optimized grating profile and electron-dose profile are outputted simultaneously.

Fig. 3
Fig. 3

Grating profiles designed with the different methods: (a) the unified method, (b) the optical optimization process, (c) the series method, and (d) a sawtooth blazed grating. All the grating periods are 1.4 µm.

Fig. 4
Fig. 4

Grating profiles calculated with the unified method for various grating periods. The grating periods are (a) 1.0 µm, (b) 1.4 µm, (c) 2.6 µm, and (d) 6.5 µm.

Fig. 5
Fig. 5

Fabricated grating profiles. (a) The dose profile calculated with the unified method for the 1.0-µm-period grating. (b) The grating profile measured with AFM and the profile designed with the unified method. (c) The scanning electron micrograph of the fabricated grating. (d), (e), and (f) are results for the 1.4-µm-period grating.

Fig. 6
Fig. 6

Overview of the diffraction efficiency as a function of grating periods for different grating profiles. “Optical optimization” is the diffraction efficiency calculated in the optical optimization process, and “Blazed” is the calculated diffraction efficiency of the sawtooth blazed grating. Circles show the efficiencies designed with the unified method for grating periods of 1.0 and 1.4 µm, squares are the measure efficiencies of the fabricated gratings, and triangles are the efficiencies calculated with the series method.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

φ=i WiηAi-ηi2,
R=R0R1+EE0γ,

Metrics