Abstract

Extreme ultraviolet (EUV) lithography emerges as a promising technique to fabricate next-generation integrated circuits. In order to improve the lithography imaging fidelity, source optimization (SO) technique is widely used to compensate for the imaging distortion. This paper develops an efficient learning-based SO approach for EUV lithography under the compressive sensing (CS) framework. The dimensionality of EUV-SO problem is significantly reduced by sparsely sampling the layout pattern. Then, the EUV-SO is formulated as an l1-norm inverse reconstruction problem based on the sparse prior of source patterns. The cost function is established based on a rigorous imaging model to take into account the characteristic effects in EUV lithography systems. In addition, a learning-based method is proposed to jointly optimize the source dictionary and projection matrix according to the sparsity and incoherence conditions in CS theory. The optimal source dictionary and projection matrix can be learned from a set of training samples collected from typical layout features in advance. Then, the optimized dictionary and projection matrix can be repetitively used in the following SO algorithms. Based on a set of simulations, the proposed SO method is proved to achieve good performance in both imaging fidelity and computational efficiency.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

X. Ma, Z. Wang, X. Chen, Y. Li, and G. R. Arce, “Gradient-based source mask optimization for extreme ultraviolet lithography,” IEEE Trans. Comput. Imaging 5(1), 120–135 (2019).
[Crossref]

2018 (2)

S. Moore, “EUV lithography finally ready for fabs,” IEEE Spectr. 55(1), 46–48 (2018).
[Crossref]

A. Chen, Y. M. Foong, J. Y. Maeng, N. Jain, and S. McDermott, “Exploration of resist effect in source mask optimization,” Proc. SPIE 10587, 105870J (2018).
[Crossref]

2017 (6)

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

J. Jiang, Q. Mei, Y. Li, and Y. Liu, “Illumination system with freeform fly’s eye to generate pixelated pupil prescribed by source-mask optimization in extreme ultraviolet lithography,” Opt. Eng. 56(6), 065101 (2017).
[Crossref]

X. Ma, D. Shi, Z. Wang, Y. Li, and G. R. Arce, “Lithographic source optimization based on adaptive projection compressive sensing,” Opt. Express 25(6), 7131–7149 (2017).
[Crossref] [PubMed]

B. Li, L. Zhang, T. Kirubarajan, and S. Rajan, “Projection matrix design using prior information in compressive sensing,” Signal Processing 135, 36–47 (2017).
[Crossref]

M. Crouse, L. Liebmann, V. Plachecki, M. Salama, Y. Chen, N. Saulnier, D. Dunn, I. Matthew, S. Hsu, K. Gronlund, and F. Goodwin, “Design intent optimization at the beyond 7nm node: the intersection of DTCO and EUVL stochastic mitigation techniques,” Proc. SPIE 10148, 101480H (2017).
[Crossref]

W. Gillijns, L. E. Tan, Y. Drissi, V. Blanco, D. Trivkovic, R. H. Kim, E. Gallagher, and G. McIntyre, “Reticle enhancement techniques toward iN7 metal2,” Proc. SPIE 10143, 1014314 (2017).
[Crossref]

2015 (7)

X. Ma, J. Wang, X. Chen, Y. Li, and G. R. Arce, “Gradient-based inverse extreme ultraviolet lithography,” Appl. Opt. 54(24), 7284–7300 (2015).
[Crossref] [PubMed]

H. Bai, G. Li, S. Li, Q. Li, Q. Jiang, and L. Chang, “Alternating optimization of sensing matrix and sparsifying dictionary for compressed sensing,” IEEE Trans. Signal Process. 63(6), 1581–1594 (2015).
[Crossref]

Z. Zhang, Y. Xu, J. Yang, X. Li, and D. Zhang, “A survey of sparse representation: algorithms and applications,” IEEE Access 3, 490–530 (2015).
[Crossref]

Q. Mei and Y. Li, “Design of three-mirror illumination system with free-form fly’s eye for extreme ultraviolet lithography,” Appl. Opt. 54(8), 2091–2097 (2015).
[Crossref] [PubMed]

H. Kuo and W. Wu, “Forming freeform source shapes by utilizing particle swarm optimization to enhance resolution in extreme UV nanolithography,” IEEE Trans. NanoTechnol. 14(2), 322–329 (2015).
[Crossref]

L. Wang, S. Li, X. Wang, G. Yan, and C. Yang, “Source optimization using particle swarm optimization algorithm in photolithography,” Proc. SPIE 9426, 94261L (2015).
[Crossref]

S. Hsu, R. Howell, J. Jia, H.-Y. Liu, K. Gronlund, S. Hansen, and J. Zimmermann, “EUV resolution enhancement techniques (RETs) for k1 0.4 and below,” Proc. SPIE 9422, 94221I (2015).
[Crossref]

2014 (4)

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
[Crossref]

Z. Song, X. Ma, J. Gao, J. Wang, Y. Li, and G. R. Arce, “Inverse lithography source optimization via compressive sensing,” Opt. Express 22(12), 14180–14198 (2014).
[Crossref] [PubMed]

J. Mulkens, P. Hinnen, M. Kubis, A. Padiy, and J. Benschop, “Holistic optimization architecture enabling sub-14-nm projection lithography,” J. Micro/Nanolith. MEMS MOEMS 13(1), 011006 (2014).
[Crossref]

V. Philipsen, E. Hendrickx, E. Verduijn, S. Raghunathan, O. Wood, V. Soltwisch, F. Scholze, N. Davydova, and P. Mangat, “Imaging impact of multilayer tuning in EUV masks, experimental validation,” Proc. SPIE 9235, 92350J (2014).
[Crossref]

2013 (1)

P. Liu, X. Xie, W. Liu, and K. Gronlund, “Fast 3D thick mask model for full-chip EUVL simulations,” Proc. SPIE 8679, 86790W (2013).
[Crossref]

2012 (2)

J. T. Neumann, P. Gräupner, W. Kaiser, R. Garreis, and B. Geh, “Interactions of 3D mask effects and NA in EUV lithography,” Proc. SPIE 8522, 852211 (2012).
[Crossref]

J. C. Yu, P. Yu, and H. Y. Chao, “Fast source optimization involving quadratic line-contour objectives for the resist image,” Opt. Express 20(7), 8161–8174 (2012).
[Crossref] [PubMed]

2011 (2)

C. Wu, C. Liao, C. Shih, C. Chang, S. Hsu, H. Liu, and Z. Li, “Freeform source optimization for improving Litho-performance of warm spots,” Proc. SPIE 8166, 81663C (2011).
[Crossref]

H. Song, L. Zavyalova, I. Su, J. Shiely, and T. Schmoeller, “Shadowing effect modeling and compensation for EUV lithography,” Proc. SPIE 7969, 79691O (2011).
[Crossref]

2010 (3)

J. Xu, Y. Pi, and A. Cao, “Optimized projection matrix for compressive sensing,” EURASIP J. Adv. Signal Process. 2010(1), 560349 (2010).
[Crossref]

D. Peng, P. Hu, V. Tolani, T. Dam, J. Tyminski, and S. Slonaker, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

L. Wei, “Multi-class blue noise sampling,” ACM T. Graphic. 29(4), 157–166 (2010).
[Crossref]

2009 (3)

J. F. Cai, S. Osher, and Z. Shen, “Linearized bregman iterations for compressed sensing,” Math. Comput. 78(267), 1515–1536 (2009).
[Crossref]

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

2008 (1)

D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008).
[Crossref]

2007 (2)

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]

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[Crossref]

2006 (1)

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

2005 (1)

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Simul. 4(2), 460–489 (2005).
[Crossref]

2004 (1)

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat. 32(2), 407–499 (2004).
[Crossref]

2003 (1)

D. L. Lau, R. Ulichney, and G. R. Arce, “Blue and green noise halftoning models,” IEEE Signal Process. Mag. 20(4), 28–38 (2003).
[Crossref]

1991 (1)

S. Okazaki, “Resolution limits of optical lithography,” J. Vac. Sci. Technol. B 9(6), 2829–2833 (1991).
[Crossref]

1988 (1)

R. Ulichney, “Dithering with blue noise,” Proc. IEEE 76(1), 56–79 (1988).
[Crossref]

Aharon, M.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Arce, G. R.

Bagheri, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Bai, H.

H. Bai, G. Li, S. Li, Q. Li, Q. Jiang, and L. Chang, “Alternating optimization of sensing matrix and sparsifying dictionary for compressed sensing,” IEEE Trans. Signal Process. 63(6), 1581–1594 (2015).
[Crossref]

Bao, C.

C. Bao, H. Ji, Y. Quan, and Z. Shen, “l0 norm based dictionary learning by proximal methods with global convergence,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2014), pp. 3858–3865.
[Crossref]

Benschop, J.

J. Mulkens, P. Hinnen, M. Kubis, A. Padiy, and J. Benschop, “Holistic optimization architecture enabling sub-14-nm projection lithography,” J. Micro/Nanolith. MEMS MOEMS 13(1), 011006 (2014).
[Crossref]

Bilski, B.

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

Blanco, V.

W. Gillijns, L. E. Tan, Y. Drissi, V. Blanco, D. Trivkovic, R. H. Kim, E. Gallagher, and G. McIntyre, “Reticle enhancement techniques toward iN7 metal2,” Proc. SPIE 10143, 1014314 (2017).
[Crossref]

Bosker, J.-W.

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

Boyd, S.

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[Crossref]

Broman, P.

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

Bruckstein, A.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Burger, M.

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Simul. 4(2), 460–489 (2005).
[Crossref]

Burkhardt, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Burr, G.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Cai, J. F.

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V. Philipsen, E. Hendrickx, E. Verduijn, S. Raghunathan, O. Wood, V. Soltwisch, F. Scholze, N. Davydova, and P. Mangat, “Imaging impact of multilayer tuning in EUV masks, experimental validation,” Proc. SPIE 9235, 92350J (2014).
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Hennerkes, C.

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
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Hollink, T.

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
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Howell, R.

S. Hsu, R. Howell, J. Jia, H.-Y. Liu, K. Gronlund, S. Hansen, and J. Zimmermann, “EUV resolution enhancement techniques (RETs) for k1 0.4 and below,” Proc. SPIE 9422, 94221I (2015).
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Hsu, S.

M. Crouse, L. Liebmann, V. Plachecki, M. Salama, Y. Chen, N. Saulnier, D. Dunn, I. Matthew, S. Hsu, K. Gronlund, and F. Goodwin, “Design intent optimization at the beyond 7nm node: the intersection of DTCO and EUVL stochastic mitigation techniques,” Proc. SPIE 10148, 101480H (2017).
[Crossref]

S. Hsu, R. Howell, J. Jia, H.-Y. Liu, K. Gronlund, S. Hansen, and J. Zimmermann, “EUV resolution enhancement techniques (RETs) for k1 0.4 and below,” Proc. SPIE 9422, 94221I (2015).
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X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
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C. Wu, C. Liao, C. Shih, C. Chang, S. Hsu, H. Liu, and Z. Li, “Freeform source optimization for improving Litho-performance of warm spots,” Proc. SPIE 8166, 81663C (2011).
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Hu, P.

D. Peng, P. Hu, V. Tolani, T. Dam, J. Tyminski, and S. Slonaker, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
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Jain, N.

A. Chen, Y. M. Foong, J. Y. Maeng, N. Jain, and S. McDermott, “Exploration of resist effect in source mask optimization,” Proc. SPIE 10587, 105870J (2018).
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Jasper, H.

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

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J. T. Neumann, P. Gräupner, W. Kaiser, R. Garreis, and B. Geh, “Interactions of 3D mask effects and NA in EUV lithography,” Proc. SPIE 8522, 852211 (2012).
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Maeng, J. Y.

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[Crossref]

Tirapu-Azpiroz, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Tolani, V.

D. Peng, P. Hu, V. Tolani, T. Dam, J. Tyminski, and S. Slonaker, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

Trivkovic, D.

W. Gillijns, L. E. Tan, Y. Drissi, V. Blanco, D. Trivkovic, R. H. Kim, E. Gallagher, and G. McIntyre, “Reticle enhancement techniques toward iN7 metal2,” Proc. SPIE 10143, 1014314 (2017).
[Crossref]

Troost, K.

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
[Crossref]

Tsaig, Y.

D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008).
[Crossref]

Tyminski, J.

D. Peng, P. Hu, V. Tolani, T. Dam, J. Tyminski, and S. Slonaker, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

Ulichney, R.

D. L. Lau, R. Ulichney, and G. R. Arce, “Blue and green noise halftoning models,” IEEE Signal Process. Mag. 20(4), 28–38 (2003).
[Crossref]

R. Ulichney, “Dithering with blue noise,” Proc. IEEE 76(1), 56–79 (1988).
[Crossref]

van Adrichem, P.

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
[Crossref]

van de Kerkhof, M.

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

van Es, R.

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

van Ingen Schenau, K.

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
[Crossref]

Verduijn, E.

V. Philipsen, E. Hendrickx, E. Verduijn, S. Raghunathan, O. Wood, V. Soltwisch, F. Scholze, N. Davydova, and P. Mangat, “Imaging impact of multilayer tuning in EUV masks, experimental validation,” Proc. SPIE 9235, 92350J (2014).
[Crossref]

Wagner, A.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Wang, J.

Wang, L.

L. Wang, S. Li, X. Wang, G. Yan, and C. Yang, “Source optimization using particle swarm optimization algorithm in photolithography,” Proc. SPIE 9426, 94261L (2015).
[Crossref]

Wang, X.

L. Wang, S. Li, X. Wang, G. Yan, and C. Yang, “Source optimization using particle swarm optimization algorithm in photolithography,” Proc. SPIE 9426, 94261L (2015).
[Crossref]

Wang, Z.

X. Ma, Z. Wang, X. Chen, Y. Li, and G. R. Arce, “Gradient-based source mask optimization for extreme ultraviolet lithography,” IEEE Trans. Comput. Imaging 5(1), 120–135 (2019).
[Crossref]

X. Ma, D. Shi, Z. Wang, Y. Li, and G. R. Arce, “Lithographic source optimization based on adaptive projection compressive sensing,” Opt. Express 25(6), 7131–7149 (2017).
[Crossref] [PubMed]

Wei, L.

L. Wei, “Multi-class blue noise sampling,” ACM T. Graphic. 29(4), 157–166 (2010).
[Crossref]

Wood, O.

V. Philipsen, E. Hendrickx, E. Verduijn, S. Raghunathan, O. Wood, V. Soltwisch, F. Scholze, N. Davydova, and P. Mangat, “Imaging impact of multilayer tuning in EUV masks, experimental validation,” Proc. SPIE 9235, 92350J (2014).
[Crossref]

Wu, C.

C. Wu, C. Liao, C. Shih, C. Chang, S. Hsu, H. Liu, and Z. Li, “Freeform source optimization for improving Litho-performance of warm spots,” Proc. SPIE 8166, 81663C (2011).
[Crossref]

Wu, W.

H. Kuo and W. Wu, “Forming freeform source shapes by utilizing particle swarm optimization to enhance resolution in extreme UV nanolithography,” IEEE Trans. NanoTechnol. 14(2), 322–329 (2015).
[Crossref]

Xie, X.

P. Liu, X. Xie, W. Liu, and K. Gronlund, “Fast 3D thick mask model for full-chip EUVL simulations,” Proc. SPIE 8679, 86790W (2013).
[Crossref]

Xu, J.

J. Xu, Y. Pi, and A. Cao, “Optimized projection matrix for compressive sensing,” EURASIP J. Adv. Signal Process. 2010(1), 560349 (2010).
[Crossref]

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Simul. 4(2), 460–489 (2005).
[Crossref]

Xu, Y.

Z. Zhang, Y. Xu, J. Yang, X. Li, and D. Zhang, “A survey of sparse representation: algorithms and applications,” IEEE Access 3, 490–530 (2015).
[Crossref]

Yan, G.

L. Wang, S. Li, X. Wang, G. Yan, and C. Yang, “Source optimization using particle swarm optimization algorithm in photolithography,” Proc. SPIE 9426, 94261L (2015).
[Crossref]

Yang, C.

L. Wang, S. Li, X. Wang, G. Yan, and C. Yang, “Source optimization using particle swarm optimization algorithm in photolithography,” Proc. SPIE 9426, 94261L (2015).
[Crossref]

Yang, J.

Z. Zhang, Y. Xu, J. Yang, X. Li, and D. Zhang, “A survey of sparse representation: algorithms and applications,” IEEE Access 3, 490–530 (2015).
[Crossref]

Yang, K.

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
[Crossref]

Yin, W.

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Simul. 4(2), 460–489 (2005).
[Crossref]

Yu, J. C.

Yu, P.

Zavyalova, L.

H. Song, L. Zavyalova, I. Su, J. Shiely, and T. Schmoeller, “Shadowing effect modeling and compensation for EUV lithography,” Proc. SPIE 7969, 79691O (2011).
[Crossref]

Zdravkov, A.

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

Zhang, D.

Z. Zhang, Y. Xu, J. Yang, X. Li, and D. Zhang, “A survey of sparse representation: algorithms and applications,” IEEE Access 3, 490–530 (2015).
[Crossref]

Zhang, L.

B. Li, L. Zhang, T. Kirubarajan, and S. Rajan, “Projection matrix design using prior information in compressive sensing,” Signal Processing 135, 36–47 (2017).
[Crossref]

Zhang, Z.

Z. Zhang, Y. Xu, J. Yang, X. Li, and D. Zhang, “A survey of sparse representation: algorithms and applications,” IEEE Access 3, 490–530 (2015).
[Crossref]

Zimmermann, J.

S. Hsu, R. Howell, J. Jia, H.-Y. Liu, K. Gronlund, S. Hansen, and J. Zimmermann, “EUV resolution enhancement techniques (RETs) for k1 0.4 and below,” Proc. SPIE 9422, 94221I (2015).
[Crossref]

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
[Crossref]

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

ACM T. Graphic. (1)

L. Wei, “Multi-class blue noise sampling,” ACM T. Graphic. 29(4), 157–166 (2010).
[Crossref]

Ann. Stat. (1)

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat. 32(2), 407–499 (2004).
[Crossref]

Appl. Opt. (2)

EURASIP J. Adv. Signal Process. (1)

J. Xu, Y. Pi, and A. Cao, “Optimized projection matrix for compressive sensing,” EURASIP J. Adv. Signal Process. 2010(1), 560349 (2010).
[Crossref]

IEEE Access (1)

Z. Zhang, Y. Xu, J. Yang, X. Li, and D. Zhang, “A survey of sparse representation: algorithms and applications,” IEEE Access 3, 490–530 (2015).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[Crossref]

IEEE Signal Process. Mag. (1)

D. L. Lau, R. Ulichney, and G. R. Arce, “Blue and green noise halftoning models,” IEEE Signal Process. Mag. 20(4), 28–38 (2003).
[Crossref]

IEEE Spectr. (1)

S. Moore, “EUV lithography finally ready for fabs,” IEEE Spectr. 55(1), 46–48 (2018).
[Crossref]

IEEE Trans. Comput. Imaging (1)

X. Ma, Z. Wang, X. Chen, Y. Li, and G. R. Arce, “Gradient-based source mask optimization for extreme ultraviolet lithography,” IEEE Trans. Comput. Imaging 5(1), 120–135 (2019).
[Crossref]

IEEE Trans. Image Process. (2)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[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]

IEEE Trans. Inf. Theory (1)

D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008).
[Crossref]

IEEE Trans. NanoTechnol. (1)

H. Kuo and W. Wu, “Forming freeform source shapes by utilizing particle swarm optimization to enhance resolution in extreme UV nanolithography,” IEEE Trans. NanoTechnol. 14(2), 322–329 (2015).
[Crossref]

IEEE Trans. Signal Process. (2)

H. Bai, G. Li, S. Li, Q. Li, Q. Jiang, and L. Chang, “Alternating optimization of sensing matrix and sparsifying dictionary for compressed sensing,” IEEE Trans. Signal Process. 63(6), 1581–1594 (2015).
[Crossref]

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

J. Micro/Nanolith. MEMS MOEMS (1)

J. Mulkens, P. Hinnen, M. Kubis, A. Padiy, and J. Benschop, “Holistic optimization architecture enabling sub-14-nm projection lithography,” J. Micro/Nanolith. MEMS MOEMS 13(1), 011006 (2014).
[Crossref]

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

S. Okazaki, “Resolution limits of optical lithography,” J. Vac. Sci. Technol. B 9(6), 2829–2833 (1991).
[Crossref]

Math. Comput. (1)

J. F. Cai, S. Osher, and Z. Shen, “Linearized bregman iterations for compressed sensing,” Math. Comput. 78(267), 1515–1536 (2009).
[Crossref]

Multiscale Model. Simul. (1)

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Simul. 4(2), 460–489 (2005).
[Crossref]

Opt. Eng. (1)

J. Jiang, Q. Mei, Y. Li, and Y. Liu, “Illumination system with freeform fly’s eye to generate pixelated pupil prescribed by source-mask optimization in extreme ultraviolet lithography,” Opt. Eng. 56(6), 065101 (2017).
[Crossref]

Opt. Express (3)

Proc. IEEE (1)

R. Ulichney, “Dithering with blue noise,” Proc. IEEE 76(1), 56–79 (1988).
[Crossref]

Proc. SPIE (14)

A. Chen, Y. M. Foong, J. Y. Maeng, N. Jain, and S. McDermott, “Exploration of resist effect in source mask optimization,” Proc. SPIE 10587, 105870J (2018).
[Crossref]

M. Crouse, L. Liebmann, V. Plachecki, M. Salama, Y. Chen, N. Saulnier, D. Dunn, I. Matthew, S. Hsu, K. Gronlund, and F. Goodwin, “Design intent optimization at the beyond 7nm node: the intersection of DTCO and EUVL stochastic mitigation techniques,” Proc. SPIE 10148, 101480H (2017).
[Crossref]

W. Gillijns, L. E. Tan, Y. Drissi, V. Blanco, D. Trivkovic, R. H. Kim, E. Gallagher, and G. McIntyre, “Reticle enhancement techniques toward iN7 metal2,” Proc. SPIE 10143, 1014314 (2017).
[Crossref]

C. Wu, C. Liao, C. Shih, C. Chang, S. Hsu, H. Liu, and Z. Li, “Freeform source optimization for improving Litho-performance of warm spots,” Proc. SPIE 8166, 81663C (2011).
[Crossref]

M. van de Kerkhof, H. Jasper, L. Levasier, R. Peeters, R. van Es, J.-W. Bosker, A. Zdravkov, E. Lenderink, F. Evangelista, P. Broman, B. Bilski, and T. Last, “Enabling sub-10nm node lithography: presenting the NXE:3400B EUV scanner,” Proc. SPIE 143, 101430D (2017).

V. Philipsen, E. Hendrickx, E. Verduijn, S. Raghunathan, O. Wood, V. Soltwisch, F. Scholze, N. Davydova, and P. Mangat, “Imaging impact of multilayer tuning in EUV masks, experimental validation,” Proc. SPIE 9235, 92350J (2014).
[Crossref]

J. T. Neumann, P. Gräupner, W. Kaiser, R. Garreis, and B. Geh, “Interactions of 3D mask effects and NA in EUV lithography,” Proc. SPIE 8522, 852211 (2012).
[Crossref]

H. Song, L. Zavyalova, I. Su, J. Shiely, and T. Schmoeller, “Shadowing effect modeling and compensation for EUV lithography,” Proc. SPIE 7969, 79691O (2011).
[Crossref]

P. Liu, X. Xie, W. Liu, and K. Gronlund, “Fast 3D thick mask model for full-chip EUVL simulations,” Proc. SPIE 8679, 86790W (2013).
[Crossref]

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, 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,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

L. Wang, S. Li, X. Wang, G. Yan, and C. Yang, “Source optimization using particle swarm optimization algorithm in photolithography,” Proc. SPIE 9426, 94261L (2015).
[Crossref]

S. Hsu, R. Howell, J. Jia, H.-Y. Liu, K. Gronlund, S. Hansen, and J. Zimmermann, “EUV resolution enhancement techniques (RETs) for k1 0.4 and below,” Proc. SPIE 9422, 94221I (2015).
[Crossref]

X. Liu, R. Howell, S. Hsu, K. Yang, K. Gronlund, F. Driessen, H. Y. Liu, S. Hansen, K. van Ingen Schenau, T. Hollink, P. van Adrichem, K. Troost, J. Zimmermann, O. Schumann, C. Hennerkes, and P. Gräupner, “EUV source-mask optimization for 7nm node and beyond,” Proc. SPIE 9048, 90480Q (2014).
[Crossref]

D. Peng, P. Hu, V. Tolani, T. Dam, J. Tyminski, and S. Slonaker, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

Signal Processing (1)

B. Li, L. Zhang, T. Kirubarajan, and S. Rajan, “Projection matrix design using prior information in compressive sensing,” Signal Processing 135, 36–47 (2017).
[Crossref]

Other (5)

Synopsys, “Sentaurus Lithography,” https://www.synopsys.com/silicon/mask-synthesis/sentaurus-lithography.html .

C. Bao, H. Ji, Y. Quan, and Z. Shen, “l0 norm based dictionary learning by proximal methods with global convergence,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2014), pp. 3858–3865.
[Crossref]

S. A. Campbell, The Science and Engineering of Microelectronic Fabrication (Publishing House of Electronics Industry, 2003).

V. Bakshi, EUV Lithography (SPIE, 2009).

G. Kutyniok, “Compressed sensing: theory and applications,” https://arxiv.org/abs/1203.3815v1 .
[Crossref]

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Figures (15)

Fig. 1
Fig. 1 The sketch of EUV lithography system.
Fig. 2
Fig. 2 Transformation of the imaging model.
Fig. 3
Fig. 3 Flowchart of the proposed JODP algorithm: (a) the main procedure, and (b) the procedure of “Step 2”.
Fig. 4
Fig. 4 Comparison between (a) the standard 2D-DCT basis functions, and (b) the circular DCT basis functions.
Fig. 5
Fig. 5 Twelve training layouts and the corresponding optimized source patterns obtained by the ACS-SO method.
Fig. 6
Fig. 6 Comparison between the initial and optimized dictionaries: four atoms in (a) Ψ 0 and (b) Ψ ^ , as well as (c) the difference between them.
Fig. 7
Fig. 7 Comparison of the initial and optimized projection matrices: (a) the initial Bernoulli random projection matrix Φ 0 , (b) the optimized projection matrix Φ ^ , and (c) the absolute value of difference between them.
Fig. 8
Fig. 8 Three testing layouts and the corresponding optimized source patterns obtained by the ACS-SO method.
Fig. 9
Fig. 9 The absolute values of coefficients to represent the testing source patterns on the initial and optimized dictionaries.
Fig. 10
Fig. 10 The curves of REs versus the number of significant coefficients used to represent the testing source patterns.
Fig. 11
Fig. 11 Histograms of the absolute values of off-diagonal elements in the Gram matrices corresponding to the testing layouts.
Fig. 12
Fig. 12 Simulation results obtained by the proposed LCS-SO method, ACS-SO method, CG-SO method, and PSO-SO method based on Testing Layout #1.
Fig. 13
Fig. 13 Simulation results obtained by the proposed LCS-SO method, ACS-SO method, CG-SO method, and PSO-SO method based on Testing Layout #2.
Fig. 14
Fig. 14 Simulation results obtained by the proposed LCS-SO method, ACS-SO method, CG-SO method, and PSO-SO method based on Testing Layout #3.
Fig. 15
Fig. 15 Convergence curves of PEs for the proposed and traditional SO methods based on the testing layouts.

Tables (2)

Tables Icon

Table 1 Algorithm 1. Alternating proximal method for source dictionary learning

Tables Icon

Table 1 The PEs and runtimes of the proposed LCS-SO and other state-of-the-art SO methods.

Equations (17)

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

I = 1 J s u m x s y s [ J ( x s , y s ) I x s y s ( M ) ] ,
I = I CC J ,
Φ Z S = Φ I S = Φ I CC S J .
Θ ^ = a r g m i n Θ Θ 1 s . t . Φ Z S = Φ I S = Φ I CC S J = Φ I CC S Ψ Θ ,
Ψ ^ = a r g m i n Ψ ( 1 2 J T Ψ C 2 2 + γ C 0 ) , s . t .   Ψ χ , C C ,
Q ( Ψ , C ) = 1 2 J T Ψ C 2 2 ,
T C k = C k 1 1 λ k C Q | C = C k 1 , Ψ = Ψ k ,
s p k = ψ p k 1 μ p k ψ p Q | C = C k , Ψ = Ψ ˜ p k ,
D = Φ I CC S Ψ ,
G = Gram ( D ˜ ) = D ˜ T D ˜ ,
Ψ ^ , Φ ^ = a r g m i n Ψ , Φ G I E 2 2 .
Ψ ^ , Φ ^ = a r g m i n Ψ , Φ p = 1 P G p I E 2 2 .
Ψ ^ , Φ ^ = a r g m i n Ψ , Φ ( 1 2 J T Ψ C 2 2 + γ C 0 + ν p = 1 P G p I E 2 2 ) ,
Q ˜ ( Ψ , C , Φ ) = 1 2 J T Ψ C 2 2 + ν p = 1 P G p I E 2 2 .
Φ k + 1 = Φ k s Φ Q ˜ | Φ = Φ k ,
RE = ||approximate source - original source|| 2 ||original source|| 2 .
P = Γ t r ( I ) ,

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