Abstract

There are two methods for discretizing the source when the formation of a photolithographic image is modelled in terms of the Abbe model: This can be done using a rectangular grid with various discretization steps, or with radial placement of the points on a rectangular grid with various steps along a radius and along the arc length between the points. It is shown that the use of a radial distribution of the points significantly speeds up the computation process, with the modelling accuracy being mainly determined by the step along the radius.

© 2012 OSA

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  1. T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
    [CrossRef]
  2. D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).
  3. J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).
  4. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1970; Nauka, Moscow, 1973).
  5. H. H. Hopkins, “Image formation with coherent and partially coherent light,” Photograph. Sci. Eng. 21, 114 (1977).

2010 (1)

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

2008 (1)

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

2004 (1)

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

1977 (1)

H. H. Hopkins, “Image formation with coherent and partially coherent light,” Photograph. Sci. Eng. 21, 114 (1977).

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1970; Nauka, Moscow, 1973).

Brotsack, M.

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

Cao, Y.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Egger, R.

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

Engelen, A.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Finders, J.

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

Flagello, D. G.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Garreis, R.

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

Geh, B.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Graupner, P.

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

Gräupner, P.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Hansen, S.

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

Heil, T.

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

Hellweg, D.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Hennerkes, C.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Hopkins, H. H.

H. H. Hopkins, “Image formation with coherent and partially coherent light,” Photograph. Sci. Eng. 21, 114 (1977).

Jürgens, D.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Liu, P.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Maul, M.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Mulder, M.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Natt, O.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Neumann, J. T.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Noordman, O.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Park, S.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Patra, M.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Socha, R.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Stas, R.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Vocht, J. D.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1970; Nauka, Moscow, 1973).

Zimmermann, J.

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

Photograph. Sci. Eng. (1)

H. H. Hopkins, “Image formation with coherent and partially coherent light,” Photograph. Sci. Eng. 21, 114 (1977).

Proc. SPIE (3)

T. Heil, P. Graupner, R. Garreis, R. Egger, M. Brotsack, J. Finders, and S. Hansen, “Predictive modeling of advanced illumination pupils used as imaging enhancement for low-k1 applications,” Proc. SPIE 5377, 344 (2004).
[CrossRef]

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U-1 (2008).

J. Zimmermann, P. Gräupner, J. T. Neumann, D. Hellweg, D. Jürgens, M. Patra, C. Hennerkes, M. Maul, B. Geh, A. Engelen, O. Noordman, M. Mulder, S. Park, and J. D. Vocht, “Generation of arbitrary freeform source shapes using advanced illumination systems in high-NA immersion scanners,” Proc. SPIE 7640, 764005 (2010).

Other (1)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1970; Nauka, Moscow, 1973).

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