Abstract

Optical lithography has enabled the printing of progressively smaller circuit patterns over the years. However, as the feature size shrinks, the lithographic process variation becomes more pronounced. Source-mask optimization (SMO) is a current technology allowing a co-design of the source and the mask for higher resolution imaging. In this paper, we develop a pixelated SMO using inverse imaging, and incorporate the statistical variations explicitly in an optimization framework. Simulation results demonstrate its efficacy in process robustness enhancement.

© 2011 OSA

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  32. R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
    [PubMed]

2011 (2)

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
[CrossRef] [PubMed]

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 99, 1–10 (2011).

2010 (3)

J.-C. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express 18(22), 23331–23342 (2010).
[CrossRef] [PubMed]

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 045601 (2010).
[CrossRef]

M. Rothschild, “A roadmap for optical lithography,” Opt. Photon. News 21(6), 26–31 (2010).
[CrossRef]

2009 (3)

2008 (1)

S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express 16(19), 14,46–14760 (2008).
[CrossRef]

2007 (4)

X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15(23), 15066–15079 (2007).
[CrossRef] [PubMed]

A. Poonawala and P. Milanfar, “Mask design for optical microlithography — an inverse imaging problem,” IEEE Trans. Image Process. 16(3), 774–788 (2007).
[CrossRef] [PubMed]

T. Fühner, A. Erdmann, and S. Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlith. Microfab. Microsys. 6(3), 031006 (2007).

M. K. Ng, H. Shen, E. Y. Lam, and L. Zhang, “A total variation regularization based super-resolution reconstruction algorithm for digital video,” EURASIP Journal on Advances in Signal Processing 2007, Article ID 74,585 (2007).
[CrossRef]

2004 (1)

Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys. 3(4), 509–522 (2004).
[CrossRef]

2003 (1)

D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl. 19(6), 165–187 (2003).
[CrossRef]

2002 (2)

R. Socha, M. Eurlings, F. Nowak, and J. Finders, “Illumination optimization of periodic patterns for maximum process window,” Microelectron. Eng. 61–62, 57–64 (2002).
[CrossRef]

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
[CrossRef]

1998 (1)

M. Burkhardt, A. Yen, C. Progler, and G. Wells, “Illuminator design for the printing of regular contact patterns,” Microelectron. Eng. 41–42, 91–96 (1998).
[CrossRef]

Abrams, D.

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” in Photomask and Next-Generation Lithography Mask Technology XIV, vol. 6607 of Proc. SPIE, p. 660739 (2007).

Arce, G. R.

Bagheri, S.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Baik, K.-H.

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

Bukofsky, S.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
[CrossRef]

Burkhardt, M.

M. Burkhardt, A. Yen, C. Progler, and G. Wells, “Illuminator design for the printing of regular contact patterns,” Microelectron. Eng. 41–42, 91–96 (1998).
[CrossRef]

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Burr, G.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Carpaij, R.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Cecil, T.

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

Chan, S. H.

S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express 16(19), 14,46–14760 (2008).
[CrossRef]

Chan, T.

D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl. 19(6), 165–187 (2003).
[CrossRef]

Chen, D.

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

Chen, J. F.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

Conley, W. E.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

Corcoran, N. P.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

Corliss, D.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Dam, T.

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

Domnenko, V.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

Engelen, A.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Erdmann, A.

T. Fühner, A. Erdmann, and S. Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlith. Microfab. Microsys. 6(3), 031006 (2007).

Eurlings, M.

R. Socha, M. Eurlings, F. Nowak, and J. Finders, “Illumination optimization of periodic patterns for maximum process window,” Microelectron. Eng. 61–62, 57–64 (2002).
[CrossRef]

Fakhry, M.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Faure, T.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Finders, J.

R. Socha, M. Eurlings, F. Nowak, and J. Finders, “Illumination optimization of periodic patterns for maximum process window,” Microelectron. Eng. 61–62, 57–64 (2002).
[CrossRef]

Flagello, D.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Fonseca, C.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
[CrossRef]

Fühner, T.

T. Fühner, A. Erdmann, and S. Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlith. Microfab. Microsys. 6(3), 031006 (2007).

Gallagher, E.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Gleason, B.

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Granik, Y.

Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys. 3(4), 509–522 (2004).
[CrossRef]

Groenendijk, R.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Hageman, J.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Halle, S.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Hartung, F.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

He, L.

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

Hennerkes, C.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Hibbs, M.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
[CrossRef]

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Hoffnagle, J.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Hollerbach, U.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

Hsu, S. D.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

Hu, P.

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

Jia, N.

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
[CrossRef] [PubMed]

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 045601 (2010).
[CrossRef]

N. Jia, A. K. Wong, and E. Y. Lam, “Robust mask design with defocus variation using inverse synthesis,” in Lithography Asia, vol. 7140 of Proc. SPIE, p. 71401W (2008).

N. Jia and E. Y. Lam, “Performance analysis of pixelated source-mask optimization for optical microlithography,” in IEEE International Conference on Electron Devices and Solid-State Circuits (2010).

Kazinczi, R.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Kim, Y.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Klimpel, T.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

Kneer, B.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Küchler, B.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

Lai, K.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
[CrossRef]

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Laidig, T. L.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

Lam, E. Y.

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
[CrossRef] [PubMed]

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 045601 (2010).
[CrossRef]

Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17(26), 23690–23701 (2009).
[CrossRef]

E. Y. Lam and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express 17(15), 12259–12268 (2009).
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S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express 16(19), 14,46–14760 (2008).
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M. K. Ng, H. Shen, E. Y. Lam, and L. Zhang, “A total variation regularization based super-resolution reconstruction algorithm for digital video,” EURASIP Journal on Advances in Signal Processing 2007, Article ID 74,585 (2007).
[CrossRef]

N. Jia and E. Y. Lam, “Performance analysis of pixelated source-mask optimization for optical microlithography,” in IEEE International Conference on Electron Devices and Solid-State Circuits (2010).

N. Jia, A. K. Wong, and E. Y. Lam, “Robust mask design with defocus variation using inverse synthesis,” in Lithography Asia, vol. 7140 of Proc. SPIE, p. 71401W (2008).

Liu, Y.

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” in Photomask and Next-Generation Lithography Mask Technology XIV, vol. 6607 of Proc. SPIE, p. 660739 (2007).

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Mack, C.

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2007).
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K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

McIntyre, G.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Melville, D.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Milanfar, P.

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T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

Ng, M. K.

M. K. Ng, H. Shen, E. Y. Lam, and L. Zhang, “A total variation regularization based super-resolution reconstruction algorithm for digital video,” EURASIP Journal on Advances in Signal Processing 2007, Article ID 74,585 (2007).
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J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

Nowak, F.

R. Socha, M. Eurlings, F. Nowak, and J. Finders, “Illumination optimization of periodic patterns for maximum process window,” Microelectron. Eng. 61–62, 57–64 (2002).
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Pang, L.

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” in Photomask and Next-Generation Lithography Mask Technology XIV, vol. 6607 of Proc. SPIE, p. 660739 (2007).

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

Peng, D.

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

Peng, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 99, 1–10 (2011).

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A. Poonawala and P. Milanfar, “Mask design for optical microlithography — an inverse imaging problem,” IEEE Trans. Image Process. 16(3), 774–788 (2007).
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T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

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K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Rosenbluth, A. E.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
[CrossRef]

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

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K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

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Shen, Y.

Shi, X.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
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A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
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Socha, R.

R. Socha, M. Eurlings, F. Nowak, and J. Finders, “Illumination optimization of periodic patterns for maximum process window,” Microelectron. Eng. 61–62, 57–64 (2002).
[CrossRef]

Socha, R. J.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
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T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

Stock, H.-J.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

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T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

Tian, K.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Tirapu-Azpiroz, J.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Tolani, V.

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

Van Den Broeke, D. J.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

Wagner, A.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

Wampler, K. E.

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
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E. Y. Lam and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express 17(15), 12259–12268 (2009).
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S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express 16(19), 14,46–14760 (2008).
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A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
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A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).
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A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005).
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N. Jia, A. K. Wong, and E. Y. Lam, “Robust mask design with defocus variation using inverse synthesis,” in Lithography Asia, vol. 7140 of Proc. SPIE, p. 71401W (2008).

Wong, N.

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Wright, S. J.

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

Xiao, G.

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

Yen, A.

M. Burkhardt, A. Yen, C. Progler, and G. Wells, “Illuminator design for the printing of regular contact patterns,” Microelectron. Eng. 41–42, 91–96 (1998).
[CrossRef]

Yu, J.-C.

J.-C. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express 18(22), 23331–23342 (2010).
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J.-C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” in Optical Microlithography XXIV, vol. 7973 of Proc. SPIE, p. 797320 (2011).

Yu, P.

J.-C. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express 18(22), 23331–23342 (2010).
[CrossRef] [PubMed]

J.-C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” in Optical Microlithography XXIV, vol. 7973 of Proc. SPIE, p. 797320 (2011).

Yu, Z.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 99, 1–10 (2011).

Zhang, J.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 99, 1–10 (2011).

Zhang, L.

M. K. Ng, H. Shen, E. Y. Lam, and L. Zhang, “A total variation regularization based super-resolution reconstruction algorithm for digital video,” EURASIP Journal on Advances in Signal Processing 2007, Article ID 74,585 (2007).
[CrossRef]

Zimmermann, J.

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

EURASIP Journal on Advances in Signal Processing (1)

M. K. Ng, H. Shen, E. Y. Lam, and L. Zhang, “A total variation regularization based super-resolution reconstruction algorithm for digital video,” EURASIP Journal on Advances in Signal Processing 2007, Article ID 74,585 (2007).
[CrossRef]

IEEE Trans. Image Process. (2)

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 99, 1–10 (2011).

A. Poonawala and P. Milanfar, “Mask design for optical microlithography — an inverse imaging problem,” IEEE Trans. Image Process. 16(3), 774–788 (2007).
[CrossRef] [PubMed]

Inverse Probl. (1)

D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl. 19(6), 165–187 (2003).
[CrossRef]

J. Microlith. Microfab. Microsys. (3)

Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys. 3(4), 509–522 (2004).
[CrossRef]

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. 1(1), 13–30 (2002).
[CrossRef]

T. Fühner, A. Erdmann, and S. Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlith. Microfab. Microsys. 6(3), 031006 (2007).

J. Opt. (1)

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 045601 (2010).
[CrossRef]

Microelectron. Eng. (2)

M. Burkhardt, A. Yen, C. Progler, and G. Wells, “Illuminator design for the printing of regular contact patterns,” Microelectron. Eng. 41–42, 91–96 (1998).
[CrossRef]

R. Socha, M. Eurlings, F. Nowak, and J. Finders, “Illumination optimization of periodic patterns for maximum process window,” Microelectron. Eng. 61–62, 57–64 (2002).
[CrossRef]

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Opt. Photon. News (1)

M. Rothschild, “A roadmap for optical lithography,” Opt. Photon. News 21(6), 26–31 (2010).
[CrossRef]

Other (14)

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).
[CrossRef]

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” in Photomask and Next-Generation Lithography Mask Technology XIV, vol. 6607 of Proc. SPIE, p. 660739 (2007).

J.-C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” in Optical Microlithography XXIV, vol. 7973 of Proc. SPIE, p. 797320 (2011).

K. Lai, S. Bagheri, K. Tian, J. Tirapu-Azpiroz, S. Halle, G. McIntyre, D. Corliss, A. E. Rosenbluth, D. Melville, A. Wagner, M. Burkhardt, J. Hoffnagle, Y. Kim, G. Burr, M. Fakhry, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in Optical Microlithography XXII, vol. 7274 of Proc. SPIE, p. 72740A (2009).

L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K.-H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” in Lithography Asia 2009, vol. 7520 of Proc. SPIE, p. 75200X (2009).

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, vol. 7823 of Proc. SPIE, p. 78233X (2010).

A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005).
[CrossRef]

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2007).
[CrossRef]

N. Jia, A. K. Wong, and E. Y. Lam, “Robust mask design with defocus variation using inverse synthesis,” in Lithography Asia, vol. 7140 of Proc. SPIE, p. 71401W (2008).

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

N. Jia and E. Y. Lam, “Performance analysis of pixelated source-mask optimization for optical microlithography,” in IEEE International Conference on Electron Devices and Solid-State Circuits (2010).

L. Pang, G. Xiao, V. Tolani, P. Hu, T. Cecil, T. Dam, K.-H. Baik, and B. Gleason, “Considering MEEF in inverse lithography technology (ILT) and source mask optimization (SMO),” in Photomask Technology, H. Kawahira and L. S. Zurbrick, eds., vol. 7122 of Proc. SPIE, p. 71221W (2008).

R. J. Socha, D. J. Van Den Broeke, S. D. Hsu, J. F. Chen, T. L. Laidig, N. P. Corcoran, U. Hollerbach, K. E. Wampler, X. Shi, and W. E. Conley, “Contact hole reticle optimization by using interference mapping lithography (IML),” in Photomask and Next–Generation Lithography Mask Technology XI, H. Tanabe, ed., vol. 5446 of Proc. SPIE, pp. 516–534 (2004).
[PubMed]

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Figures (9)

Fig. 1
Fig. 1

Illustration of an optical projection lithography system [1, 3].

Fig. 2
Fig. 2

Relationship among intensity distributions, threshold, and the binarized image.

Fig. 3
Fig. 3

Demonstration of TV regularization. The red and green curves represent aerial image intensity and target design, respectively. The dotted line marks the threshold t.

Fig. 4
Fig. 4

The weight function W(x,y) for TV regularization and its effect. The blue curve in (a) plots the weight function, and the red curve in (b) plots the aerial image intensity by using this weighted TV regularization. The green curve denotes the target design in both figures.

Fig. 5
Fig. 5

Objective of aerial image intensity regularization. The shaded area denotes the vicinity of the target edge.

Fig. 6
Fig. 6

Optimization procedure of SMO.

Fig. 7
Fig. 7

Test patterns and critical locations for process window calculation. Color lines mark critical locations of the two test patterns.

Fig. 8
Fig. 8

Simulation results of test pattern #1.

Fig. 9
Fig. 9

Simulation results of test pattern #2.

Equations (40)

Equations on this page are rendered with MathJax. Learn more.

I a ( x , y ) = J ^ ( f , g ) H ^ ( f + f , g + g ) H ^ ( f + f , g + g ) M ^ ( f , g ) M ^ ( f , g ) × e i 2 π [ ( f f ) x + ( g g ) y ] d f d g d f d g d f d g ,
I a ( x , y ) = J ^ ( f , g ) | H ^ ( f + f , g + g ) M ^ ( f , g ) e i 2 π ( f x + g y ) d f d g | 2 d f d g f , g J ^ ( f , g ) | M ( x , y ) * H ( x , y ; f , g ) | 2 ,
I ( x , y ) = sig { I a ( x , y ) } = 1 1 + e α ( I a ( x , y ) t ) ,
I ( x , y ) = sig { f , g J ^ ( f , g ) | M ( x , y ) * H ( x , y ; f , g ) | 2 } .
minimize 𝒟 { I ( x , y ) , I ¯ ( x , y ) } subject to M ( x , y ) { 0 , 1 } J ^ ( f , g ) 0 .
𝒟 { I ( x , y ) , I ¯ ( x , y ) } = 𝒯 { I ( x , y ) , I ¯ ( x , y ) } + γ 1 TV { I a ( x , y ) } + γ 2 aerial { I a ( x , y ) , I ¯ ( x , y ) } + γ 3 contrast { I a ( x , y ) , I ¯ ( x , y ) } .
( 1 norm ) 𝒯 { I ( x , y ) , I ¯ ( x , y ) } = x , y | I ( x , y ) I ¯ ( x , y ) |
( 2 norm ) 𝒯 { I ( x , y ) , I ¯ ( x , y ) } = x , y | I ( x , y ) I ¯ ( x , y ) | 2 .
|| I a ( x , y ) || TV = | I a ( x , y ) | ,
x I a ( x , y ) = I a ( x + 1 , y ) I a ( x 1 , y ) 2 and y I a ( x , y ) = I a ( x , y + 1 ) I a ( x , y 1 ) 2 ,
I a ( x , y ) [ x I a ( x , y ) ] 2 + [ y I a ( x , y ) ] 2 .
E ( x , y ) = [ I ¯ ( x , y ) S ( x , y ) ] [ I ¯ ( x , y ) S ( x , y ) ] .
W ( x , y ) = [ 1 E ( x , y ) ] * G ( x , y ) ,
TV { I a ( x , y ) } = x , y W ( x , y ) | I a ( x , y ) | .
aerial { I a ( x , y ) , I ¯ ( x , y ) } = x , y [ 1 W ( x , y ) ] [ I a ( x , y ) 2 t I ¯ ( x , y ) ] 2 .
contrast { I a ( x , y ) , I ¯ ( x , y ) } = x , y [ 1 W ( x , y ) ] { | x [ I a ( x , y ) I ¯ ( x , y ) ] | + | y [ I a ( x , y ) I ¯ ( x , y ) ] | } .
H ^ ˜ ( f , g ; β ) = H ^ ( f , g ) e i π β NA 2 λ ( f 2 + g 2 ) ,
minimize E { 𝒟 { I ( x , y ) , I ¯ ( x , y ) } } subject to M ( x , y ) { 0 , 1 } J ^ ( f , g ) 0 ,
E { 𝒟 { I ( x , y ) , I ¯ ( x , y ) } } m , n p ( t m ) p ( β n ) { 𝒟 { I ( x , y ; t m , β n ) , I ¯ ( x , y ) } } .
M E ( 0 ) = m , n p ( t m ) p ( β n ) M 𝒟 m , n ( 0 ) .
M ( k + 1 ) = M ( k ) + ε q M ( k ) ,
M E ( k + 1 ) = m , n p ( t m ) p ( β n ) M 𝒟 m , n ( k + 1 ) .
θ M ( k + 1 ) = x , y [ M E ( k + 1 ) ( M E ( k + 1 ) M E ( k ) ) ] x , y [ q M ( k ) ( M E ( k + 1 ) M E ( k ) ) ] ,
q M ( k + 1 ) = M E ( k + 1 ) + θ M ( k + 1 ) q M ( k ) .
J ^ ( f , g ) = J ^ ( f , g ) f , g J ^ ( f , g ) .
q J ^ ( 0 ) = J ^ E ( 0 ) = m , n p ( t m ) p ( β n ) J ^ 𝒟 m , n ( 0 ) .
J ^ ( k + 1 ) = J ^ ( k ) + φ q J ^ ( k ) ,
J ^ E ( k + 1 ) = m , n p ( t m ) p ( β n ) J ^ 𝒟 m , n ( k + 1 ) .
θ J ^ ( k + 1 ) = f , g [ J ^ E ( k + 1 ) ( J ^ E ( k + 1 ) J ^ E ( k ) ) ] f , g [ q J ^ ( k ) ( J ^ E ( k + 1 ) J ^ E ( k ) ) ] .
q J ^ ( k + 1 ) = J ^ E ( k + 1 ) + θ J ^ ( k + 1 ) q J ^ ( k ) .
M 𝒟 = 𝒯 M + γ 1 TV M + γ 2 aerial M + γ 3 contrast M
J ^ 𝒟 = 𝒯 J ^ + γ 1 TV J ^ + γ 2 aerial J ^ + γ 3 contrast J ^ .
𝒯 M = x , y ( I I ¯ ) 2 M = f , g J ^ ( f , g ) Re { [ 2 α ( I I ¯ ) I ( 1 I ) ( M * H ˜ ( f , g ) ) ] * H ˜ ( f , g ) } .
TV M = x , y W ( D I a ) 2 + ( I a D ) 2 M = f , g J ^ ( f , g ) Re { [ ( D T ( W [ ( D I a ) 2 + ( I a D ) 2 ] 1 2 ( D I a ) ) + ( W [ ( D I a ) 2 + ( I a D ) 2 ] 1 2 ( I a D ) ) D T ) ( M * H ˜ ( f , g ) ) ] * H ˜ ( f , g ) } .
aerial M = x , y ( 1 W ) ( I a 2 t I ¯ ) 2 M = f , g J ^ ( f , g ) Re { [ 2 ( 1 W ) ( I a 2 t I ¯ ) ( M * H ˜ ( f , g ) ) ] * H ˜ ( f , g ) } .
contrast M = x , y ( 1 W ) [ | D ( I a I ¯ ) | + | ( I a I ¯ ) D | ] M = f , g J ^ ( f , g ) Re { [ ( D T ( ( 1 W ) D ( I a I ¯ ) [ D ( I a I ¯ ) ] 2 ) + ( ( 1 W ) ( I a I ¯ ) D [ ( I a I ¯ ) D ] 2 ) D T ) ( M * H ˜ ( f , g ) ) ] * H ˜ ( f , g ) } .
𝒯 J ^ ( f , g ) = x , y [ I ( x , y ) = I ¯ ( x , y ) ] 2 J ^ ( f , g ) = x , y 2 α ( I I ¯ ) I ( 1 I ) | M * H ˜ ( f , g ) | 2 I a f , g J ^ ( f , g ) .
TV J ^ ( f , g ) = x , y W ( D I a ) 2 + ( I a D ) 2 J ^ ( f , g ) = x , y W . [ ( D I a ) 2 + ( I a D ) 2 ] 1 2 [ ( D I a ) D [ | M * H ˜ ( f , g ) | 2 I a ] f , g J ^ ( f , g ) + ( I a D ) [ | M * H ˜ ( f . g ) | 2 I a ] D f , g J ^ ( f , g ) ] .
aerial J ^ ( f , g ) = x , y ( 1 W ) ( I a 2 t I ¯ ) 2 J ^ ( f , g ) = x , y 2 ( 1 W ) ( I a 2 t I ¯ ) | M * H ˜ ( f , g ) | 2 I a f , g J ^ ( f , g ) .
contrast J ^ ( f , g ) = x , y ( 1 W ) [ | D ( I a I ¯ ) | + | ( I a I ¯ ) D | ] J ^ ( f , g ) = x , y ( 1 W ) [ D ( I a I ¯ ) [ D ( I a I ¯ ) ] 2 D [ | M * H ˜ ( f , g ) | 2 I a ] f , g J ^ ( f , g ) + ( I a I ¯ ) D [ ( I a I ¯ ) D ] 2 [ | M * H ˜ ( f , g ) | 2 I a ] D f , g J ^ ( f , g ) ] .

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