Abstract

Optical scatterometry is a method for the on-line measurement of the geometry of a diffraction grating, which is deduced from diffraction-pattern data. We demonstrate the use of a neural network as a promising method for performing an accurate quantitative characterization of the geometry. As an example, we show the deduction of the geometry of a grating with subwavelength grooves with a rms accuracy of 1.9° for the slope of the groove walls, 0.7 nm for the linewidth, and 1.0 nm for the groove depth.

© 1998 Optical Society of America

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  1. J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).
  2. J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
    [CrossRef]
  6. B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 μm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
    [CrossRef]
  7. K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
    [CrossRef]
  8. R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
    [CrossRef]
  9. S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch-depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” J. Opt. Soc. Am. A 11, 2485–2493 (1994).
    [CrossRef]
  10. J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
    [CrossRef]
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    [CrossRef]
  13. R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
    [CrossRef]
  14. A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,” J. Opt. Soc. Am. 70, 1483–1495 (1980).
    [CrossRef]
  15. A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
    [CrossRef]
  16. S. Haykin, Neural Networks—A Comprehensive Foundation (Prentice-Hall, Englewood Cliffs, N.J., 1994).
  17. K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
    [CrossRef]
  18. E. Hartman, J. D. Keeler, J. M. Kowalski, “Layered neural networks with Gaussian hidden units as universal approximators,” Neural Comput. 2, 210–215 (1990).
    [CrossRef]
  19. E. Oja, “Neural networks—advantages and applications,” in Pattern Recognition in Practice IV, E. Gelsema, L. Kanal, eds. (Elsevier, Amsterdam, 1994), pp. 359–365.
  20. C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, New York, 1995).
  21. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef] [PubMed]
  22. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 51–70.
  23. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]

1994 (2)

1993 (3)

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

1992 (1)

1991 (1)

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

1990 (1)

E. Hartman, J. D. Keeler, J. M. Kowalski, “Layered neural networks with Gaussian hidden units as universal approximators,” Neural Comput. 2, 210–215 (1990).
[CrossRef]

1989 (1)

K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

1986 (1)

1981 (1)

1980 (2)

A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,” J. Opt. Soc. Am. 70, 1483–1495 (1980).
[CrossRef]

A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
[CrossRef]

1977 (1)

Atkinson, J. T.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Baird, W. E.

Bauer, J. J.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Baumgart, J. W.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Bischoff, J.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Bishop, C. M.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, New York, 1995).

Bishop, K.

Bishop, K. P.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 51–70.

Botten, L. C.

Breidne, M.

A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
[CrossRef]

Clark, L. A.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Franke, J. E.

Gaspar, S. M.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

Gaylord, T. K.

George, N.

Giapis, K. P.

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Gottscho, R. A.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch-depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” J. Opt. Soc. Am. A 11, 2485–2493 (1994).
[CrossRef]

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Haaland, D. M.

Hartman, E.

E. Hartman, J. D. Keeler, J. M. Kowalski, “Layered neural networks with Gaussian hidden units as universal approximators,” Neural Comput. 2, 210–215 (1990).
[CrossRef]

Haykin, S.

S. Haykin, Neural Networks—A Comprehensive Foundation (Prentice-Hall, Englewood Cliffs, N.J., 1994).

Hickman, K.

Hickman, K. C.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

Hobson, C. A.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Hornik, K.

K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

Hush, D. R.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

Kaspar, S.

Keeler, J. D.

E. Hartman, J. D. Keeler, J. M. Kowalski, “Layered neural networks with Gaussian hidden units as universal approximators,” Neural Comput. 2, 210–215 (1990).
[CrossRef]

Kornblit, A.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch-depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” J. Opt. Soc. Am. A 11, 2485–2493 (1994).
[CrossRef]

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Kowalski, J. M.

E. Hartman, J. D. Keeler, J. M. Kowalski, “Layered neural networks with Gaussian hidden units as universal approximators,” Neural Comput. 2, 210–215 (1990).
[CrossRef]

Krukar, D. M.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

Krukar, R.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Krukar, R. H.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch-depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” J. Opt. Soc. Am. A 11, 2485–2493 (1994).
[CrossRef]

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

Kruskal, J.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Kruskal, J. B.

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Lambert, D.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Maystre, D.

McNeil, J. R.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch-depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” J. Opt. Soc. Am. A 11, 2485–2493 (1994).
[CrossRef]

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

S. S. H. Naqvi, S. Kaspar, K. Hickman, K. Bishop, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 μm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

Milner, L. M.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

Minhas, B. K.

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 μm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

Moharam, M. G.

Murmane, M. R.

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

Naqvi, S. S. H.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch-depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” J. Opt. Soc. Am. A 11, 2485–2493 (1994).
[CrossRef]

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

S. S. H. Naqvi, S. Kaspar, K. Hickman, K. Bishop, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 μm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

Niemczyk, T. M.

Oja, E.

E. Oja, “Neural networks—advantages and applications,” in Pattern Recognition in Practice IV, E. Gelsema, L. Kanal, eds. (Elsevier, Amsterdam, 1994), pp. 359–365.

Pearson, J. D.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Petersen, G. A.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

Prins, S. L.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 μm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

Raymond, C. J.

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

Reitman, E. A.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Roger, A.

A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
[CrossRef]

A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,” J. Opt. Soc. Am. 70, 1483–1495 (1980).
[CrossRef]

Search, D. J.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Sinatore, D.

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Stinchcombe, M.

K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

Truckenbrodt, H.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Wang, S.-G.

White, H.

K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

Wilson, I. J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 51–70.

Appl. Opt. (4)

J. Appl. Phys. (1)

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

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

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Neural Comput. (1)

E. Hartman, J. D. Keeler, J. M. Kowalski, “Layered neural networks with Gaussian hidden units as universal approximators,” Neural Comput. 2, 210–215 (1990).
[CrossRef]

Neural Networks (1)

K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

Opt. Commun. (1)

A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
[CrossRef]

Solid State Technol. (2)

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

Other (9)

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 μm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

S. Haykin, Neural Networks—A Comprehensive Foundation (Prentice-Hall, Englewood Cliffs, N.J., 1994).

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. T. Postek, ed., Proc. SPIE1926, 60–71 (1993).
[CrossRef]

E. Oja, “Neural networks—advantages and applications,” in Pattern Recognition in Practice IV, E. Gelsema, L. Kanal, eds. (Elsevier, Amsterdam, 1994), pp. 359–365.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, New York, 1995).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 51–70.

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Figures (4)

Fig. 1
Fig. 1

Feedforward neural network with S input nodes I(i, n) at the nth iteration step, one hidden layer of M neurons, and L output nodes. In addition, there is an offset node in both the input [I(0)] and the hidden layer (marked with 0) with a fixed value of 1. For output the desired response is denoted by O(k, n), and the calculated response given by the neural network is denoted by y(k, n) = g[ y(k, n)] when the activation function g(⋯) is linear. The weight coefficients are w ji and v kj for the input–hidden-layer interface and the hidden-layer–output interface, respectively. The inset illustrates the operation of a single neuron in the hidden layer. The weighted sum of the inputs u(j, n) is fed into the activation function f(⋯), which provides the output of the neuron.

Fig. 2
Fig. 2

Geometry of one grating period d characterized by a groove width ω, a groove depth h, and a slope of the groove walls α. The element is illuminated with TE-polarized light (wavelength λ) at an angle θ. At normal incidence there are only the reflected and the transmitted zeroth orders with intensities R 0 and T 0, respectively. However, when θ gets large enough there emerges the -1 transmitted order T -1.

Fig. 3
Fig. 3

Example of the intensities of (a) R 0 and (b) T 0 for 400 sample grating geometries that are chosen from the allowed grating-parameter range. The intensities are calculated by use of light of the wavelength λ = 442 nm at an angle of incidence of θ = 60°.

Fig. 4
Fig. 4

Output given by the neural network (filled circles) and the correct values (solid curve) for (a) the slope angle α, (b) the line width ω, and (c) the depth h, when 100 randomly chosen validation grating geometries are used as input. The output values of the parameters are sorted in ascending order to provide a better visual comparison.

Tables (1)

Tables Icon

Table 1 Calculated Grating Diffraction Patterns for Five Different Geometriesa

Equations (13)

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u M ,   n = i = 0 S   w Mi n I i ,   n = i = 1 S   w Mi n I i ,   n + w M 0
f u M ,   n = f i = 1 S   w Mi n I i ,   n + w M 0 .
y k ,   n = j = 0 M   v kj n f u j ,   n = j = 1 M   v kj n + v k 0
g y k ,   n = g j = 1 M   v kj n f u j ,   n + v k 0
E n = 1 2 k = 1 L g y k ,   n - O k ,   n 2 1 2 k = 1 L e k ,   n 2 .
v kj n + 1 = v kj n + Δ v kj n ,
w ji n + 1 = w ji n + Δ w ji n ,
Δ v kj n = m Δ v kj n - 1 + η   g y k ,   n y k ,   n E n g y k ,   n   u j ,   n ,
Δ w ji n = m Δ w ji n - 1 + η f u j ,   n p = 1 L   v pj n × g y p ,   n y p ,   n E n g y p ,   n   I i ,   n ,
f x = 1 1 + exp - x ,
g x = x .
Δ v kj n = m Δ v kj n - 1 + η y k ,   n - O k ,   n u j ,   n ,
Δ w ji n = m Δ w ji n - 1 + η u j ,   n 1 - u j ,   n × p = 1 L   v pj n y p ,   n - O p ,   n I i ,   n .

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