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Pixelated source mask optimization for process robustness in optical lithographyNingning Jia and Edmund Y. Lam »View Author Affiliations
Ningning Jia
and Edmund Y. Lam^{*}
^{}Imaging Systems Laboratory, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong ^{*}Corresponding author: elam@eee.hku.hk |
Optics Express, Vol. 19, Issue 20, pp. 19384-19398 (2011)
http://dx.doi.org/10.1364/OE.19.019384
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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
OCIS Codes
(110.3960) Imaging systems : Microlithography
(110.5220) Imaging systems : Photolithography
(110.1758) Imaging systems : Computational imaging
ToC Category:
Imaging Systems
History
Original Manuscript: June 8, 2011
Revised Manuscript: August 26, 2011
Manuscript Accepted: August 30, 2011
Published: September 22, 2011
Citation
Ningning Jia and Edmund Y. Lam, "Pixelated source mask optimization for process robustness in optical lithography," Opt. Express 19, 19384-19398 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19384
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- 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).
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- D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl.19(6), 165–187 (2003). [CrossRef]
- 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).
- 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]
- 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]
- 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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- 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).
- 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).
- 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).
- T. Fühner, A. Erdmann, and S. Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlith. Microfab. Microsys.6(3), 031006 (2007).
- 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]
- 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).
- 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).
- 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]
- 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).
- 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).
- 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, 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).
- R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).
- Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys.3(4), 509–522 (2004). [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).
- 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).
- 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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- 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]
- 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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- S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express16(19), 14,46–14760 (2008). [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]
- A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005). [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).
- A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001). [CrossRef]
- R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).
- J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).
- 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).
- 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]
- J.-C. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express18(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).
- J.-C. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express18(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).
- 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).
- 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).
- 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 Processing2007, Article ID 74,585 (2007). [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).
EURASIP Journal on Advances in Signal Processing
- 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 Processing2007, Article ID 74,585 (2007). [CrossRef]
IEEE Trans. Image Process.
- 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]
- 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).
Inverse Probl.
- 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.
- 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.
- 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.
- 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]
Opt. Express
- X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express15(23), 15066–15079 (2007). [CrossRef] [PubMed]
- X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express17(7), 5783–5793 (2009). [CrossRef] [PubMed]
- E. Y. Lam and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express17(15), 12259–12268 (2009). [CrossRef] [PubMed]
- Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express17(26), 23690–23701 (2009). [CrossRef]
- J.-C. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express18(22), 23331–23342 (2010). [CrossRef] [PubMed]
- Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express19(6), 5511–5521 (2011). [CrossRef] [PubMed]
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Opt. Photon. News
- M. Rothschild, “A roadmap for optical lithography,” Opt. Photon. News21(6), 26–31 (2010). [CrossRef]
Other
- A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005). [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, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001). [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]
2011, Peng, IEEE Trans. Image Process.
- 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).
- 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. News21(6), 26–31 (2010). [CrossRef]
- S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express16(19), 14,46–14760 (2008). [CrossRef]
- T. Fühner, A. Erdmann, and S. Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlith. Microfab. Microsys.6(3), 031006 (2007).
- 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]
- 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 Processing2007, Article ID 74,585 (2007). [CrossRef]
- Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys.3(4), 509–522 (2004). [CrossRef]
- D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl.19(6), 165–187 (2003). [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]
- 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]
- 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]
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