Abstract

Source mask optimization (SMO) is a useful technique for printing the integrated circuit (IC) on a wafer with increasingly smaller feature size. However, complex SMO algorithms generally lead to undesirably long runtime resulting from an optimization of largely identical regions over the whole mask pattern. In this work, a weighted SMO scheme incorporating both an awareness of the hotspots and robustness against process variations is proposed. We show how optimal solutions are reached with fewer iterations by applying various degrees of correction in the corresponding regions. The proposed method includes identifying the hotspots and combining a weight matrix to the cost function for adjustment and control. Simulation results are compared with the mask optimization (under a fixed source) and conventional SMO to illustrate the performance improvement in terms of pattern fidelity, convergence rate and process window size.

© 2012 OSA

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2012 (2)

J.-C. Yu, P. Yu, and H. Y. Chao, “Fast source optimization involving quadratic line-contour objectives for the resist image,” Opt. Express20, 8161–8174 (2012).
[CrossRef] [PubMed]

S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences5, 625–651 (2012).
[CrossRef]

2011 (3)

2010 (1)

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

2009 (4)

2008 (1)

2007 (2)

X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express15, 15066–15079 (2007).
[CrossRef] [PubMed]

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

2004 (1)

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

1995 (1)

S. Sherif, B. Saleh, and R. De Leone, “Binary images synthesis using mixed linear integar programming,” IEEE Trans. Image Process.4, 1252–1257 (1995).
[CrossRef] [PubMed]

Adam, K.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81663M (2011).

Adamov, A.

T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).

Adrichem, P. V.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

Arce, G. R.

Bagheri, S.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Baik, K.-H.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Barahona, F.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Berger, G.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Bisschop, P. D.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Capodieci, L.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

Carpaij, R.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Chan, S. H.

Chao, H. Y.

Chen, D.

T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).

Chen, L.

S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in Lithography Asia 2009, A. C. Chen, W.-S. Han, B. J. Lin, and A. Yen eds., Proc. SPIE 7520, 75200D (2009).

Choy, S. K.

S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences5, 625–651 (2012).
[CrossRef]

Cobb, N.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Corliss, D.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Coskun, T. H.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Y. Deng, T. H. Coskun, J. Kye, and H. J. Levinson, “Lithography target optimization with source-mask optimization,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83262P (2012).

Dai, H.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Dam, T.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Dam, T. H.

T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).

Dave, A.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

De Leone, R.

S. Sherif, B. Saleh, and R. De Leone, “Binary images synthesis using mixed linear integar programming,” IEEE Trans. Image Process.4, 1252–1257 (1995).
[CrossRef] [PubMed]

Deng, Y.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

H. Hu, Y. Zou, and Y. Deng, “Optimization on illumination source with design of experiments,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE7640, 764027 (2010).

Y. Deng, T. H. Coskun, J. Kye, and H. J. Levinson, “Lithography target optimization with source-mask optimization,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83262P (2012).

Domnenko, V.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Engelen, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Fakhry, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81663M (2011).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Fan, M.

J. Kim and M. Fan, “Hotspot detection on post-OPC layout using full chip simulation based verification tool : a case study with aerial image simulation,” in 23rd Annual BACUS Symposium on Photomask Technology, K. R. Kimmel and W. Staud, eds., Proc. SPIE 5256, 919–925 (2003).

Faure, T.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Flagello, D.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Gallagher, E.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Gleason, B.

T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Granik, Y.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

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

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81663M (2011).

Groenendijk, R.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Gronlund, K.

S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in Lithography Asia 2009, A. C. Chen, W.-S. Han, B. J. Lin, and A. Yen eds., Proc. SPIE 7520, 75200D (2009).

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

Grozev, G.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Hageman, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Halle, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Hartung, F.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Hendrickx, E.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

Hennerkes, C.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Hibbs, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Hoffnagle, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Hsu, C.-M.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Hsu, S.

S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in Lithography Asia 2009, A. C. Chen, W.-S. Han, B. J. Lin, and A. Yen eds., Proc. SPIE 7520, 75200D (2009).

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

Hu, H.

H. Hu, Y. Zou, and Y. Deng, “Optimization on illumination source with design of experiments,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE7640, 764027 (2010).

Hu, P.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Huang, H.-T.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Inoue, T.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Iwase, K.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

Jia, N.

S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences5, 625–651 (2012).
[CrossRef]

N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express19, 19384–19398 (2011).
[CrossRef] [PubMed]

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express19, 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, 045601 (2010).
[CrossRef]

Kamat, V.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Kazinczi, R.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Kempsell, M. L.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

Kim, J.

J. Kim and M. Fan, “Hotspot detection on post-OPC layout using full chip simulation based verification tool : a case study with aerial image simulation,” in 23rd Annual BACUS Symposium on Photomask Technology, K. R. Kimmel and W. Staud, eds., Proc. SPIE 5256, 919–925 (2003).

Kim, Y.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Klimpel, T.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Kneer, B.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Krasnoperova, A.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Küchler, B.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Kye, J.

Y. Deng, T. H. Coskun, J. Kye, and H. J. Levinson, “Lithography target optimization with source-mask optimization,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83262P (2012).

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

Ladanyi, L.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Laenens, B.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

Lai, K.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81663M (2011).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Lam, E. Y.

Lam, M.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Lee, J.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Levinson, H. J.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

Y. Deng, T. H. Coskun, J. Kye, and H. J. Levinson, “Lithography target optimization with source-mask optimization,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83262P (2012).

Li, Z.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in Lithography Asia 2009, A. C. Chen, W.-S. Han, B. J. Lin, and A. Yen eds., Proc. SPIE 7520, 75200D (2009).

Liu, H.-Y.

S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in Lithography Asia 2009, A. C. Chen, W.-S. Han, B. J. Lin, and A. Yen eds., Proc. SPIE 7520, 75200D (2009).

Ma, X.

Ma, Y.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

Manu, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

McIntyre, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Meiring, J.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Melville, D.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Milanfar, P.

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

Mülders, T.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Muta, H.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Ngai, C.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Nocedal, J.

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

Pang, L.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Peng, D.

T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).

Peng, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical oithography,” IEEE Trans. Image Process.20, 2856–2864 (2011).
[CrossRef] [PubMed]

Poonawala, A.

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

Poonawala, A. A.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Reybrouck, M.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Rohmund, F.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Rosenbluth, A.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Rosenbluth, A. E.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Russ, C.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Sakajiri, K.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

Sakamoto, M.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Saleh, B.

S. Sherif, B. Saleh, and R. De Leone, “Binary images synthesis using mixed linear integar programming,” IEEE Trans. Image Process.4, 1252–1257 (1995).
[CrossRef] [PubMed]

Santoro, G.

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

Scarpazza, D.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Shen, Y.

Sherif, S.

S. Sherif, B. Saleh, and R. De Leone, “Binary images synthesis using mixed linear integar programming,” IEEE Trans. Image Process.4, 1252–1257 (1995).
[CrossRef] [PubMed]

Slonaker, S. D.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Smith, B. W.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

Socha, R.

S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in Lithography Asia 2009, A. C. Chen, W.-S. Han, B. J. Lin, and A. Yen eds., Proc. SPIE 7520, 75200D (2009).

Stanton, W. A.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Stock, H.-J.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Strenski, P.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Tabery, C. E.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

Tang, M. L.

S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences5, 625–651 (2012).
[CrossRef]

Taravade, K. N.

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

Tian, K.

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Tirapu-Azpiroz, J.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Tolani, V.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Tong, C. S.

S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences5, 625–651 (2012).
[CrossRef]

Tritchkov, A.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Tyminski, J. K.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Vandenberghe, G.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

Waechter, A.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Wagner, A.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Wang, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical oithography,” IEEE Trans. Image Process.20, 2856–2864 (2011).
[CrossRef] [PubMed]

Wong, A. K.

Wong, N.

Wright, S. J.

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

Yasui, K.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

Yoshimoto, K.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

Yoshitake, S.

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

Yu, J.-C.

J.-C. Yu, P. Yu, and H. Y. Chao, “Fast source optimization involving quadratic line-contour objectives for the resist image,” Opt. Express20, 8161–8174 (2012).
[CrossRef] [PubMed]

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

J.-C. Yu and P. Yu, “Choosing objective functions for inverse lithography patterning,” in Optical Microlithography XXIV, M. V. Dusa, ed., Proc. SPIE7973, 79731N (2011).

Yu, P.

J.-C. Yu, P. Yu, and H. Y. Chao, “Fast source optimization involving quadratic line-contour objectives for the resist image,” Opt. Express20, 8161–8174 (2012).
[CrossRef] [PubMed]

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

J.-C. Yu and P. Yu, “Choosing objective functions for inverse lithography patterning,” in Optical Microlithography XXIV, M. V. Dusa, ed., Proc. SPIE7973, 79731N (2011).

Yu, Z.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical oithography,” IEEE Trans. Image Process.20, 2856–2864 (2011).
[CrossRef] [PubMed]

Zhang, J.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical oithography,” IEEE Trans. Image Process.20, 2856–2864 (2011).
[CrossRef] [PubMed]

Zhou, X.

T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).

Zhuang, L.

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Zimmermann, 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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

Zou, Y.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

H. Hu, Y. Zou, and Y. Deng, “Optimization on illumination source with design of experiments,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE7640, 764027 (2010).

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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

J. Microlith. Microfab. Microsys. (2)

M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009).
[CrossRef]

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

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, 045601 (2010).
[CrossRef]

Opt. Express (8)

SIAM J. Imaging Sciences (1)

S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences5, 625–651 (2012).
[CrossRef]

Other (18)

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

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

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

T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).

D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2X node logic,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).

H. Hu, Y. Zou, and Y. Deng, “Optimization on illumination source with design of experiments,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE7640, 764027 (2010).

T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).

M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81663M (2011).

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

Y. Deng, T. H. Coskun, J. Kye, and H. J. Levinson, “Lithography target optimization with source-mask optimization,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83262P (2012).

T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83260V (2012).

J. Kim and M. Fan, “Hotspot detection on post-OPC layout using full chip simulation based verification tool : a case study with aerial image simulation,” in 23rd Annual BACUS Symposium on Photomask Technology, K. R. Kimmel and W. Staud, eds., Proc. SPIE 5256, 919–925 (2003).

J.-C. Yu and P. Yu, “Choosing objective functions for inverse lithography patterning,” in Optical Microlithography XXIV, M. V. Dusa, ed., Proc. SPIE7973, 79731N (2011).

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. Manu, 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 XXIV, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in Lithography Asia 2009, A. C. Chen, W.-S. Han, B. J. Lin, and A. Yen eds., Proc. SPIE 7520, 75200D (2009).

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

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Figures (6)

Fig. 1
Fig. 1

Typical masks and sources are used to print a sparse pattern consisting of two rectangle shapes at different development stages of lithography.

Fig. 2
Fig. 2

Generation of images at multiple process conditions: (a) is an input pattern, (b) is its printed image at the nominal focus and dose, and (c) is the smallest image created at 70nm and 10% exposure dose increase. The difference between (c) and the input pattern (a) is given in (d).

Fig. 3
Fig. 3

Two test patterns used in experiments: (a) brick contact holes and (b) random contact holes.

Fig. 4
Fig. 4

Simulation results of the first test pattern.

Fig. 5
Fig. 5

Simulation results of the second test pattern.

Fig. 6
Fig. 6

Comparison of average process window of (a) brick contact holes and (b) random contact holes.

Tables (2)

Tables Icon

Table 1 Pseudo-code of SMO

Tables Icon

Table 2 Comparison of performance and convergence rate

Equations (25)

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

I a ( x , y ) = J ( f , g ) M ^ ( f 1 , g 1 ) M ^ ( f 2 , g 2 ) H ^ ( f + f 1 , g + g 1 ) H ^ ( f + f 2 , g + g 2 ) × e i 2 π [ ( f 1 f 2 ) x + ( g 1 g 2 ) y ] d f d g d f 1 d g 1 d f 2 d g 2 = J ( f , g ) | M ( x , y ) * H ˜ ( x , y ) | 2 d f d g ,
H ˜ ( x , y ) = H ( x , y ) e i 2 π ( f x + g y ) ,
J ( f , g ) = J ( f , g ) J ( f , g ) d f d g ,
I a ( x , y ) f , g { J ( f , g ) | M ( x , y ) * H ˜ ( x , y ) | 2 } f , g J ( f , g ) .
I ( x , y ) = sig { I a ( x , y ) } = 1 1 + e α [ I a ( x , y ) t r ] ,
Δ I ( x , y ) = | I 0 ( x , y ) I s ( x , y ) | .
I m ( x , y ) = { 0 , Δ I ( x , y ) = 0 Δ I ( x , y ) * G ( x , y ) , Δ I ( x , y ) 0 .
W ( x , y ) = { 1 , I m ( x , y ) < t w λ 1 I m ( x , y ) , I m ( x , y ) t w .
{ I ( x , y ) , I 0 ( x , y ) } = x , y W ( x , y ) I ( x , y ) I 0 ( x , y ) 2 2 ,
( M ) = f , g J ( f , g ) Re { W [ 2 α ( I I 0 ) I ( 1 I ) ( M * H ˜ ) ] * H ˜ ( x , y ) } ,
( J ) = x , y W 2 α ( I I 0 ) I ( 1 I ) | M * H ˜ 2 | I a f , g J ( f , g ) .
a { I a ( x , y ) , I 0 ( x , y ) } = x , y I a ( x , y ) 2 t r I 0 ( x , y ) 2 2 .
s { J ( f , g ) } = f , g { f [ J ( f , g ) ] 1 + g [ J ( f , g ) ] 1 } ,
f [ J ( f , g ) ] = J ( f + 1 , g ) J ( f , g ) and g [ J ( f , g ) ] = J ( f , g + 1 ) J ( f , g ) .
m { M ( x , y ) } = x , y M ( x , y ) [ 1 M ( x , y ) ] .
a ( M ) + m ( M ) = f , g J ( f , g ) Re { [ 2 ( I a 2 t r I 0 ) ( M * H ˜ ) ] * H ˜ ( x , y ) } + ( 2 M + 1 )
a ( J ) + s ( J ) = x , y 2 ( I a 2 t r I 0 ) | M * H ˜ | 2 I a f , g J ( f , g ) + sgn { f [ J ( f , g ) ] } + sgn { g [ J ( f , g ) ] } ,
𝒞 = { I ( x , y ) , I 0 ( x , y ) } + γ 1 a { I a ( x , y ) , I 0 ( x , y ) } + γ 2 s { J ( f , g ) } + γ 3 m { M ( x , y ) } ,
{ M opt ( x , y ) , J opt ( f , g ) } = arg min { M , J } 𝒞 { I ( x , y ) , I 0 ( x , y ) } .
𝒞 ( M ) = ( M ) + γ 1 a ( M ) + γ 3 m ( M ) .
𝒞 ( J ) = ( J ) + γ 1 a ( J ) + γ 2 s ( J ) .
( M ) = x , y W I I 0 2 2 M = W [ 2 α ( I I 0 ) I ( 1 I ) I a M ] = f , g J ( f , g ) Re { W [ 2 α ( I I 0 ) I ( 1 I ) ( M * H ˜ ) ] * H ˜ ( x , y ) }
( J ) = x , y W I I 0 2 2 J = x , y W 2 α ( I I 0 ) I ( 1 I ) I a J = x , y W 2 α ( I I 0 ) I ( 1 I ) | M * H ˜ | 2 f , g J ( f , g ) f , g J ( f , g ) | M * H ˜ | 2 [ f , g J ( f , g ) ] 2 = x , y W 2 α ( I I 0 ) I ( 1 I ) | M * H ˜ | 2 I a f , g J ( f , g ) .
a ( M ) + m ( M ) = x , y I a 2 t r I 0 2 2 M + x , y M ( 1 M ) M = 2 ( I a 2 t r I 0 ) I a M + ( 2 M + 1 ) = f , g J ( f , g ) Re { [ 2 ( I a 2 t r I 0 ) ( M * H ˜ ) ] * H ˜ ( x , y ) } + ( 2 M + 1 )
a ( J ) + s ( J ) = x , y I a 2 t r I 0 2 2 J + f , g { f [ J ( f , g ) ] 1 + g [ J ( f , g ) ] 1 } J = 2 ( I a 2 t r I 0 ) I a J + f [ J ( f , g ) ] { f [ J ( f , g ) ] } 2 + g [ J ( f , g ) ] { g [ J ( f , g ) ] } 2 = x , y 2 ( I a 2 t r I 0 ) | M * H ˜ | 2 I a f , g J ( f , g ) + sgn { f [ J ( f , g ) ] } + sgn { g [ J ( f , g ) ] } .

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