Abstract

We present a method to determine constructive and destructive interference areas on the object plane in partially coherent imaging. This method is based on the interference pattern on the image plane. A function Γ that shows constructive and destructive interference areas with respect to the origin on the object plane is derived as the product of mutual intensity on the object plane and the Fourier transform of the pupil function. The convolution integral of Γ and object transmittance gives the constructive and destructive interference areas. Experimental results show that small clear openings placed at constructive interference areas enhance light intensity at desired positions. By applying this method to optical microlithography imaging, one can achieve resolution enhancement of fine features with a relatively small amount of computation.

© 2009 Optical Society of America

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  1. H. H. Hopkins, “On the diffraction theory of optical image,” Proc. R. Soc. London Ser. A 217, 408-432 (1953).
    [Crossref]
  2. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 10.
  3. F. M. Schellenberg, “Resolution enhancement technology: the past, the present, and extensions of the future,” Proc SPIE 5377, 1-20 (2004).
  4. A. K. Wong, Resolution Enhancement Techniques in Optical Lithography, Vol. TT47 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2001), Chap. 4.
    [Crossref]
  5. J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 1985), Chap. 7.
  6. G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
    [Crossref]
  7. J. Garofalo, C. J. Biddick, R. L. Kostelak, and S. Vaidya, “Mask assisted off axis illumination technique for random logic,” J. Vac. Sci. Technol. B 11, 2651-2658 (1993).
    [Crossref]
  8. Y. C. Pati and T. Kailath, “Phase-shifting masks for microlithography: automated design and mask requirements,” J. Opt. Soc. Am. A 11, 2438-2452 (1994).
    [Crossref]
  9. H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, E. Wolf, ed.(North-Holland, 1964), Vol. 3, Chap. 3.
    [Crossref]
  10. R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
    [Crossref]
  11. N. B. Cobb, “Fast optical and process proximity correction algorithms for integrated circuit manufacturing,” Ph.D. dissertation (Electrical Engineering and Computer Science, University of California, Berkeley, 1998).
  12. R. Socha, “Propagation effects of partially coherent light in optical lithography and inspection,” Ph.D. dissertation (Electronics Research Laboratory, University of California, Berkeley, 1997).
  13. J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 1985), pp. 109-111.
  14. K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
    [Crossref]
  15. M. Mansuripur, Classical Optics and Its Applications (Cambridge U. Press, 2002), pp. 89-100.
  16. K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
    [Crossref]
  17. R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
    [Crossref]

2007 (1)

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

2005 (2)

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

2004 (2)

F. M. Schellenberg, “Resolution enhancement technology: the past, the present, and extensions of the future,” Proc SPIE 5377, 1-20 (2004).

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

1998 (1)

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

1994 (1)

1993 (1)

J. Garofalo, C. J. Biddick, R. L. Kostelak, and S. Vaidya, “Mask assisted off axis illumination technique for random logic,” J. Vac. Sci. Technol. B 11, 2651-2658 (1993).
[Crossref]

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical image,” Proc. R. Soc. London Ser. A 217, 408-432 (1953).
[Crossref]

Biddick, C. J.

J. Garofalo, C. J. Biddick, R. L. Kostelak, and S. Vaidya, “Mask assisted off axis illumination technique for random logic,” J. Vac. Sci. Technol. B 11, 2651-2658 (1993).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 10.

Caldwell, R. F.

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

Cantu', P.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Capetti, G.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Capodieci, L.

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

Chen, J. F.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

Cobb, N. B.

N. B. Cobb, “Fast optical and process proximity correction algorithms for integrated circuit manufacturing,” Ph.D. dissertation (Electrical Engineering and Computer Science, University of California, Berkeley, 1998).

Conley, W.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

Corcoran, N.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

Evangelista, E.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Gamo, H.

H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, E. Wolf, ed.(North-Holland, 1964), Vol. 3, Chap. 3.
[Crossref]

Garofalo, J.

J. Garofalo, C. J. Biddick, R. L. Kostelak, and S. Vaidya, “Mask assisted off axis illumination technique for random logic,” J. Vac. Sci. Technol. B 11, 2651-2658 (1993).
[Crossref]

Goodman, J. W.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 1985), Chap. 7.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 1985), pp. 109-111.

Hakko, M.

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

Hasegawa, Y.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Hollerbach, U.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

Holwill, J.

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

Honda, T.

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical image,” Proc. R. Soc. London Ser. A 217, 408-432 (1953).
[Crossref]

Hsu, S. D.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

Iwasa, J.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Kailath, T.

Kawashima, M.

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

Kostelak, R. L.

J. Garofalo, C. J. Biddick, R. L. Kostelak, and S. Vaidya, “Mask assisted off axis illumination technique for random logic,” J. Vac. Sci. Technol. B 11, 2651-2658 (1993).
[Crossref]

Kuno, T.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Kye, J.

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

Laidig, T. L.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

Levinson, H.

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

Loi, S.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Lupo, M.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Mansuripur, M.

M. Mansuripur, Classical Optics and Its Applications (Cambridge U. Press, 2002), pp. 89-100.

McIntyre, G. R.

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

Neureuther, A.

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

Ono, T.

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

Pati, Y. C.

Pepe, A.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Petersen, J. S.

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

Saitoh, K.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Schellenberg, F. M.

F. M. Schellenberg, “Resolution enhancement technology: the past, the present, and extensions of the future,” Proc SPIE 5377, 1-20 (2004).

Sekine, Y.

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

Shi, X.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

Socha, R.

R. Socha, “Propagation effects of partially coherent light in optical lithography and inspection,” Ph.D. dissertation (Electronics Research Laboratory, University of California, Berkeley, 1997).

Socha, R. J.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

Suzuki, A.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Toublan, O.

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Vaidya, S.

J. Garofalo, C. J. Biddick, R. L. Kostelak, and S. Vaidya, “Mask assisted off axis illumination technique for random logic,” J. Vac. Sci. Technol. B 11, 2651-2658 (1993).
[Crossref]

Van Den Broeke, D. J.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

Wampler, K. E.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 10.

Wong, A. K.

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography, Vol. TT47 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2001), Chap. 4.
[Crossref]

Yamazoe, K.

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Zou, Y.

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

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

J. Vac. Sci. Technol. B (2)

G. R. McIntyre, J. Holwill, A. Neureuther, L. Capodieci, Y. Zou, H. Levinson, and J. Kye, “Screening layouts for high-numerical aperture and polarization effects using pattern matching,” J. Vac. Sci. Technol. B 23, 2646-2652 (2005).
[Crossref]

J. Garofalo, C. J. Biddick, R. L. Kostelak, and S. Vaidya, “Mask assisted off axis illumination technique for random logic,” J. Vac. Sci. Technol. B 11, 2651-2658 (1993).
[Crossref]

Jpn. J. Appl. Phys. (1)

K. Yamazoe, P. Cantu', G. Capetti, E. Evangelista, Y. Hasegawa, J. Iwasa, O. Toublan, S. Loi, M. Lupo, A. Pepe, T. Kuno, A. Suzuki, and K. Saitoh, “Full-chip implementation of IDEAL Smile on 90 nm-node devices by ArF lithography,” Jpn. J. Appl. Phys. 44, 5526-5534 (2005).
[Crossref]

Proc SPIE (1)

F. M. Schellenberg, “Resolution enhancement technology: the past, the present, and extensions of the future,” Proc SPIE 5377, 1-20 (2004).

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “On the diffraction theory of optical image,” Proc. R. Soc. London Ser. A 217, 408-432 (1953).
[Crossref]

Proc. SPIE (3)

R. J. Socha, J. S. Petersen, J. F. Chen, T. L.Laidig, K. E.Wampler, and R. F. Caldwell, “Design of 200-nm, 170-nm, and 140-nm DUV contact sweeper high-transmission attenuating phase-shift mask through simulation I,” Proc. SPIE 3546617-641 (1998).
[Crossref]

K. Yamazoe, Y. Sekine, M. Kawashima, M. Hakko, T. Ono, and T. Honda, “Resolution enhancement by aerial image approximation with 2D-TCC,” Proc. SPIE 6730, 67302H (2007).
[Crossref]

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” Proc. SPIE 5377, 222-240 (2004).
[Crossref]

Other (8)

N. B. Cobb, “Fast optical and process proximity correction algorithms for integrated circuit manufacturing,” Ph.D. dissertation (Electrical Engineering and Computer Science, University of California, Berkeley, 1998).

R. Socha, “Propagation effects of partially coherent light in optical lithography and inspection,” Ph.D. dissertation (Electronics Research Laboratory, University of California, Berkeley, 1997).

J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 1985), pp. 109-111.

M. Mansuripur, Classical Optics and Its Applications (Cambridge U. Press, 2002), pp. 89-100.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 10.

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography, Vol. TT47 of SPIE Tutorial Texts in Optical Engineering (SPIE Press, 2001), Chap. 4.
[Crossref]

J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 1985), Chap. 7.

H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, E. Wolf, ed.(North-Holland, 1964), Vol. 3, Chap. 3.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1

Schematic view of the optical microlithography system. The object is illuminated with the Koehler illumination system. We define light intensity distribution S at the aperture stop of the Koehler system. The object plane and the image plane are in conjugate relationship with each other. The direction from the object plane to the image plane is the positive defocus direction.

Fig. 2
Fig. 2

Schematic view to derive the interference pattern with respect to ( x , y ) . Point ( x , y ) shows the target pattern position on the image plane. Since ( x , y ) and ( x , y ) are in conjugate relationship, F ( x x , y y ) is constant and is represented by a light wave. The integral of a ( x 1 , y 1 ) F ( x x 1 , y y 1 ) over ( x 1 , y 1 ) shows all the light waves that reach point ( x , y ) . Mutual intensity Γ o ( x x 1 , y y 1 ) shows the relationship between ( x , y ) and ( x 1 , y 1 ) .

Fig. 3
Fig. 3

Object and intensity distribution at the aperture stop of the Koehler system: (a) the clear 100 nm square aperture square is at the opaque background as a pinhole. (b) The white sections represent the light-emitting area. Each pixel is mutually incoherent.

Fig. 4
Fig. 4

Constructive and destructive interference areas on the best focused image plane computed from both the object described in Fig. 3a and the illumination illustrated in Fig. 3b. The maximum intensity is normalized to unity. The positive area shows constructive interference; the negative area shows destructive interference. This figure has negative value although most of the area is positive.

Fig. 5
Fig. 5

Change of the light intensity through defocus. The object in (a) has eight clear assist features (75 nm x 75 nm), toned gray, at the constructive interference area in Fig 4. The object in (b) has no assist features. The reference light intensity is calculated by the object in (a) at best focus. At best focus, the light intensity of the object in (b) is 28% weaker than that of the object in (a). The object in (a) undergoes a light intensity decrease of 18% through 150 nm defocus; the object in (b) undergoes a 24% light intensity decrease.

Fig. 6
Fig. 6

Exposure results at best focus. (a) Performed by the pinhole without the assist features shown in Fig. 5b. The required dose was 1330 J / m 2 and the hole diameter was 103.6 nm at that dose. (b) Performed by the pinhole with the assist features shown in Fig. 5a. The required dose was 1030 J / m 2 and the hole diameter was 103.4 nm at that dose.

Fig. 7
Fig. 7

(a) Portion of the contact layer of the flash memory design. All the contacts are 100 nm in size. (b) Constructive and destructive interference areas computed from both the object illustrated in (a) and the illumination illustrated in Fig. 3b. The maximum intensity is normalized to unity. (c) The reticle design with assist features, toned gray, at the positive peak position in (b). The assist feature size is 80 nm x 80 nm.

Fig. 8
Fig. 8

Exposure results at best focus. (a) Exposed without the assist feature. The exposure dose, which was adjusted for isolated contact to be approximately 100 nm , was 1290 J / m 2 . (b) Exposed with the assist feature. The exposure dose, which was adjusted for isolated contact to be approximately 100 nm , was 790 J / m 2 .

Fig. 9
Fig. 9

Exposure result under a 100 nm defocused condition. (a) Exposed without the assist feature. The exposure dose was 1290 J / m 2 , i.e., the same as that in Fig. 8a. The measured hole diameter is significantly smaller compared with that in Fig. 8a. (b) Exposed with the assist feature. The exposure dose was 790 J / m 2 , i.e., the same as that in Fig. 8b. The measured hole diameter barely changed compared with that in Fig. 8b.

Equations (6)

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Γ o ( x x 1 , y - y 1 ) = FT [ S ( f , g ) exp { i 2 π ( x 1 f + y 1 g ) } ] ,
Γ i ( x , y ) = Γ o ( x x 1 , y y 1 ) a ( x 1 , y 1 ) F ( x x 1 , y y 1 ) a * ( x , y ) F * ( x x , y y ) d x 1 d y 1 d x d y ,
Γ i ( x , y ) = C * Γ o ( x x 1 , y y 1 ) a ( x 1 , y 1 ) F ( x x 1 , y y 1 ) a * ( x , y ) d x 1 d y 1 d x d y .
Γ i ( x , y ) = C * Γ o ( x x 1 , y y 1 ) F ( x x 1 , y y 1 ) a ( x 1 , y 1 ) d x 1 d y 1 ,
Γ ( x , y ) = C * FT [ S ( f , g ) ] FT [ P ( f , g ) ] = C * Γ o ( x , y ) F ( x , y ) .
Γ i ( x , y ) = Γ ( x x 1 , y y 1 ) a ( x 1 , y 1 ) d x 1 d y 1 = Γ ( x , y ) a ( x , y ) ,

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