Abstract

The simulation of optical defect detection on wafers by microscopy requires several approximations. For the simulation with Fourier modal methods, the number of modes is limited by memory and time consumption. Furthermore, the illumination pupil has to be divided into discrete incidence angles for plane waves. We present a way to save the computation of most of these incidence angles. It works only for certain configurations of grating period and illumination wavelength but is an accurate and robust approximation in these cases. We present sample calculations for one- and two-dimensional periodic structures with defects.

© 2009 Optical Society of America

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References

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  1. M. Totzeck, Optik (Stuttgart) 112, 399 (2001).
    [CrossRef]
  2. M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).
  3. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 1068 (1995).
    [CrossRef]
  4. K. Watanabe and K. Higa, in Proceedings of the IEEE Conference on Electromagnetics in Advanced Applications (IEEE, 2007), p. 161.
    [CrossRef]
  5. K. Hattori, J. Nakayama, and Y. Tamura, IEICE Trans. Electron. E91-C, 56 (2008).
    [CrossRef]
  6. I. Scherbatko, in Proceedings of the IEEE ICTON (IEEE, 2007), p. 149.
  7. L. Li, J. Opt. Soc. Am. A 24, 1085 (2007).
    [CrossRef]

2008 (1)

K. Hattori, J. Nakayama, and Y. Tamura, IEICE Trans. Electron. E91-C, 56 (2008).
[CrossRef]

2007 (3)

I. Scherbatko, in Proceedings of the IEEE ICTON (IEEE, 2007), p. 149.

L. Li, J. Opt. Soc. Am. A 24, 1085 (2007).
[CrossRef]

K. Watanabe and K. Higa, in Proceedings of the IEEE Conference on Electromagnetics in Advanced Applications (IEEE, 2007), p. 161.
[CrossRef]

2003 (1)

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

2001 (1)

M. Totzeck, Optik (Stuttgart) 112, 399 (2001).
[CrossRef]

1995 (1)

Gaylord, T. K.

Grann, E. B.

Hattori, K.

K. Hattori, J. Nakayama, and Y. Tamura, IEICE Trans. Electron. E91-C, 56 (2008).
[CrossRef]

Higa, K.

K. Watanabe and K. Higa, in Proceedings of the IEEE Conference on Electromagnetics in Advanced Applications (IEEE, 2007), p. 161.
[CrossRef]

Li, L.

Moharam, M. G.

Nakayama, J.

K. Hattori, J. Nakayama, and Y. Tamura, IEICE Trans. Electron. E91-C, 56 (2008).
[CrossRef]

Nevière, M.

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

Pommet, D. A.

Popov, E.

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

Scherbatko, I.

I. Scherbatko, in Proceedings of the IEEE ICTON (IEEE, 2007), p. 149.

Tamura, Y.

K. Hattori, J. Nakayama, and Y. Tamura, IEICE Trans. Electron. E91-C, 56 (2008).
[CrossRef]

Totzeck, M.

M. Totzeck, Optik (Stuttgart) 112, 399 (2001).
[CrossRef]

Watanabe, K.

K. Watanabe and K. Higa, in Proceedings of the IEEE Conference on Electromagnetics in Advanced Applications (IEEE, 2007), p. 161.
[CrossRef]

IEICE Trans. Electron. (1)

K. Hattori, J. Nakayama, and Y. Tamura, IEICE Trans. Electron. E91-C, 56 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Optik (Stuttgart) (1)

M. Totzeck, Optik (Stuttgart) 112, 399 (2001).
[CrossRef]

Other (3)

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

K. Watanabe and K. Higa, in Proceedings of the IEEE Conference on Electromagnetics in Advanced Applications (IEEE, 2007), p. 161.
[CrossRef]

I. Scherbatko, in Proceedings of the IEEE ICTON (IEEE, 2007), p. 149.

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Figures (4)

Fig. 1
Fig. 1

Cross section of the far-field image of the 1D example. Note the “defect signal” region from 0 to 800 nm and the pattern noise region from 800 to 1200 nm.

Fig. 2
Fig. 2

Convergence plot of the signal-to-noise ratio calculated out of the far-field image with respect to the pupil discretization. Note the value at 0.15, which is already close to the end value.

Fig. 3
Fig. 3

Euclidian distance of far-field image cross sections. The minimal, i.e., optimal distance at the Littrow angle sampling of 0.15 can be seen.

Fig. 4
Fig. 4

Comparison of the cross sections of the 2D example. “Full” is with all Littrow angles; “Littrow” is with just the normal incidence.

Equations (1)

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α m = α 0 + m 2 π d ,

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