Abstract

Within the direct inclusion method the proximity effect is already taken care of when one calculates the kinoform relief, whereas conventionally the proximity effect is compensated for after one has calculated the relief. In particular, when proximity effects are considerable, that is, for small structures, the direct inclusion method is shown to give significantly better results than the conventional two-step method.

Provided that the proximity effect is correctly modeled, it is shown that for an 8 × 8 array illuminator nearly perfect uniformity can be achieved even for a kinoform with very small structures.

© 1994 Optical Society of America

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References

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  1. G. Owen, “Methods for proximity correction in electron lithography,” J. Vac. Sci. Technol. B 8, 1889–1892 (1990).
    [CrossRef]
  2. F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).
  3. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  4. M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 34–42 (1991).

1993 (1)

F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).

1990 (1)

G. Owen, “Methods for proximity correction in electron lithography,” J. Vac. Sci. Technol. B 8, 1889–1892 (1990).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Bengtsson, J.

F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).

Ekberg, M.

F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).

Farn, M. W.

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 34–42 (1991).

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Hård, S.

F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).

Larsson, M.

F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).

Nikolajeff, F.

F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).

Owen, G.

G. Owen, “Methods for proximity correction in electron lithography,” J. Vac. Sci. Technol. B 8, 1889–1892 (1990).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

IEE Conf. Publ. (1)

F. Nikolajeff, M. Ekberg, M. Larsson, J. Bengtsson, S. Hård, “Shape distortion of diffractive optical elements, directly written with electron beam lithography,” IEE Conf. Publ. 379, 60–61 (1993).

J. Vac. Sci. Technol. B (1)

G. Owen, “Methods for proximity correction in electron lithography,” J. Vac. Sci. Technol. B 8, 1889–1892 (1990).
[CrossRef]

Optik (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Other (1)

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 34–42 (1991).

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Figures (3)

Fig. 1
Fig. 1

Direct-inclusion-method cycle. (The letters in circles refer to corresponding sections in the text.)

Fig. 2
Fig. 2

(a) Input relief from the direct-inclusion method for an 8 × 8 spot array. (b) Input relief from the two-step method for an 8 × 8 spot array.

Fig. 3
Fig. 3

Comparison between the two-step and direct-inclusion methods.

Equations (5)

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PSF ( r ) = 1 2 π { 1 α 2 exp [ - ( r α ) 2 ] + 1 β 2 exp [ - ( r β ) 2 ] } ,
FT { ζ B } = FT { ζ A } FT { PSF } ,
FT { ζ C } = G × FT { ζ B } ,
new virtual amplitude = old virtual amplitude × [ desired intensity intensity from ( D ) ] 0.35 .
uniformity = I max spot - I min spot I max spot + I min spot ,

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