Abstract

In mask-alignment systems a reference signal is needed to align the mask with the silicon wafers. The optical reference signal is the autocorrelation of two two-dimensional (2D) codes with binary transmittance. For a long time, one-dimensional codes have been used in grating-measurement systems to obtain a reference signal. The design of this type of code has needed a great computational effort, which limits the size of the code to about 100 elements. Recently, we have applied genetic algorithms to design codes with arbitrary length. We propose the application of these algorithms to design 2D codes to generate 2D optical signals used in mask-alignment systems.

© 2006 Optical Society of America

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References

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  1. M. C. King and D. H. Berry, Appl. Opt. 11, 2455 (1972).
    [Crossref] [PubMed]
  2. Y. Xiangyang and Y. Chunyong, J. Phys. E 19, 34 (1986).
    [Crossref]
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  4. J. Sáez-Landete, J. Alonso, and E. Bernabeu, Opt. Express 13, 195 (2004).
    [Crossref]
  5. Y. Chen, W. Huang, and X. Dang, Rev. Sci. Instrum. 74, 3549 (2003).
    [Crossref]
  6. J. Sáez-Landete, J. Alonso, and E. Bernabeu, Opt. Express 13, 4230 (2005).
    [Crossref] [PubMed]
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    [Crossref]
  8. D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning (Addison-Wesley, 1988).
  9. S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

2005 (2)

S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

J. Sáez-Landete, J. Alonso, and E. Bernabeu, Opt. Express 13, 4230 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

Y. Chen, W. Huang, and X. Dang, Rev. Sci. Instrum. 74, 3549 (2003).
[Crossref]

1988 (1)

Y. Li, Optik (Stuttgart) 79, 67 (1988).

1986 (1)

Y. Xiangyang and Y. Chunyong, J. Phys. E 19, 34 (1986).
[Crossref]

1972 (1)

Alonso, J.

Bernabeu, E.

Berry, D. H.

Bousoño-Calzón, C.

S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

Camps-Vals, G.

S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

Chen, Y.

Y. Chen, W. Huang, and X. Dang, Rev. Sci. Instrum. 74, 3549 (2003).
[Crossref]

Chunyong, Y.

Y. Xiangyang and Y. Chunyong, J. Phys. E 19, 34 (1986).
[Crossref]

Dang, X.

Y. Chen, W. Huang, and X. Dang, Rev. Sci. Instrum. 74, 3549 (2003).
[Crossref]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning (Addison-Wesley, 1988).

Huang, W.

Y. Chen, W. Huang, and X. Dang, Rev. Sci. Instrum. 74, 3549 (2003).
[Crossref]

Jones, D. R.

D. R. Jones, in Encyclopedia of Optimization, C.A.Floudas and P.M.Pardalos, eds. (Kluwer, 2001), p. 431.
[Crossref]

King, M. C.

Li, Y.

Y. Li, Optik (Stuttgart) 79, 67 (1988).

Pérez-Cruz, F.

S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

Sáez-Landete, J.

Salcedo-Sanz, S.

S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

Sepúlveda-Sanchís, J.

S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

Xiangyang, Y.

Y. Xiangyang and Y. Chunyong, J. Phys. E 19, 34 (1986).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Syst. Man Cybern. (1)

S. Salcedo-Sanz, G. Camps-Vals, F. Pérez-Cruz, J. Sepúlveda-Sanchís, and C. Bousoño-Calzón, IEEE Trans. Syst. Man Cybern. Part C 34, 749 (2005).

J. Phys. E (1)

Y. Xiangyang and Y. Chunyong, J. Phys. E 19, 34 (1986).
[Crossref]

Opt. Express (2)

Optik (Stuttgart) (1)

Y. Li, Optik (Stuttgart) 79, 67 (1988).

Rev. Sci. Instrum. (1)

Y. Chen, W. Huang, and X. Dang, Rev. Sci. Instrum. 74, 3549 (2003).
[Crossref]

Other (2)

D. R. Jones, in Encyclopedia of Optimization, C.A.Floudas and P.M.Pardalos, eds. (Kluwer, 2001), p. 431.
[Crossref]

D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning (Addison-Wesley, 1988).

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Figures (3)

Fig. 1
Fig. 1

2D alignment system based on 2D ZRCs.

Fig. 2
Fig. 2

Height of the second maximum of the autocorrelation with respect to the number of transparent pixels. The codes have 16 × 16 pixels, and the number of transparent pixels varies from 1 to 255.

Fig. 3
Fig. 3

Autocorrelation signal obtained with a ZRC of 100 × 100 elements and 300 transparent pixels ( n l ) . The second maximum is 14.

Equations (5)

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c = [ c i j ] = [ c 11 c 1 n c n 1 c n n ] , c i j { 0 , 1 } ,
S k l = i = 1 n k j = 1 n l c i j c i + k , j + l ,
S 00 = i = 1 n j = 1 n c i j 2 = i = 1 n j = 1 n c i j = n 1 .
σ σ 1 = ( 2 n 2 + n 1 ) ( 2 n 2 + n 1 ) 2 + 4 ( 1 + 1 n ) n 1 ( n 1 1 ) 2 ( 1 + 1 n ) .
min c binary f ( c ) , f ( c ) = max k 2 + l 2 0 { S k l } , S k l = i = 1 n k j = 1 n l c i j c i + k , j + l ,

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