Abstract

The convergence of lithographic source and mask optimization (SMO) has been plagued by the prohibitive time-step dictated by the stability of the explicit Euler-forward scheme in the gradient-based optimization procedure. As a remedy, we solve the distance level-set regularized reformulation of the SMO by discretizing the stability-relevant terms in an implicit manner and apply operator splitting to separately update source and mask patterns in coordinate dimensions by solving the tridiagonal systems of linear equations using the Thomas method, combining stability and simplicity. Simulation results merit the superiority of the proposed SMO approach with improved convergence by overcoming the stability constraints of the Courant-Friedrichs-Lewy (CFL) condition.

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

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References

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  1. A. K.-K. Wong, Resolution Enhancemenant Techniques in Optical Lithography (SPIE Press, 2001).
  2. A. K.-K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005).
  3. C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE 5454, 315–326 (2004).
    [Crossref]
  4. K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
    [Crossref]
  5. Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
    [Crossref]
  6. A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
    [Crossref]
  7. R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
    [Crossref]
  8. X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783 (2009).
    [Crossref]
  9. X. Ma and G. R. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics, 1st ed. (John Wiley and Sons, 2010).
  10. P. Gao, A. Gu, and A. Zakhor, “Optical Proximity Correction with Principal Component Regression,” Proc. SPIE 6924, 69243N (2008).
    [Crossref]
  11. Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE. Trans. Image. Process 20(10), 2856–2864 (2011).
    [Crossref]
  12. X. Ma, C. Han, Y. Li, L. Dong, and G. R. Arce, “Pixelated source and mask optimization for immersion lithography,” J. Opt. Soc. Am. A 30(1), 112–123 (2013).
    [Crossref]
  13. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19(20), 19384–19398 (2011).
    [Crossref]
  14. W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
    [Crossref]
  15. J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471 (2014).
    [Crossref]
  16. J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented lagrangian methods in optical lithography,” Opt. Express 21(7), 8076–8090 (2013).
    [Crossref]
  17. F. Peng and Y. Shen, “Source and mask co-optimization based on depth learning methods,” in “2018 China Semiconductor Technology International Conference (CSTIC),” (2018), pp. 1–3.
  18. X. Ma, D. Shi, Z. Wang, Y. Li, and G. R. Arce, “Lithographic source optimization based on adaptive projection compressive sensing,” Opt. Express 25(6), 7131–7149 (2017).
    [Crossref]
  19. X. Ma, Z. Wang, Y. Li, G. R. Arce, L. Dong, and J. Garcia-Frias, “Fast optical proximity correction method based on nonlinear compressive sensing,” Opt. Express 26(11), 14479–14498 (2018).
    [Crossref]
  20. X. Ma, Q. Zhao, H. Zhang, Z. Wang, and G. R. Arce, “Model-driven convolution neural network for inverse lithography,” Opt. Express 26(25), 32565–32584 (2018).
    [Crossref]
  21. J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011).
    [Crossref]
  22. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19(20), 19384–19398 (2011).
    [Crossref]
  23. J. Li, Y. Shen, and E. Y. Lam, “Hotspot-aware fast source and mask optimization,” Opt. Express 20(19), 21792–21804 (2012).
    [Crossref]
  24. J. Li and E. Y. Lam, “Joint optimization of source, mask, and pupil in optical lithography,” Proc. SPIE 9052, 90520S (2014).
    [Crossref]
  25. S. Osher and R. P. Fedkiw, “Level set methods: an overview and some recent results,” J. Comput. Phys. 169(2), 463–502 (2001).
    [Crossref]
  26. S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics (Springer, 2003).
  27. L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, and K. H. Baik, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” Proc. SPIE 7520, 75200X (2009).
    [Crossref]
  28. V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
    [Crossref]
  29. Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17(26), 23690–23701 (2009).
    [Crossref]
  30. Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE 7748, 77481U (2010).
    [Crossref]
  31. Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
    [Crossref]
  32. Y. Shen, “Level-set based ILT with a vector imaging model,” in Proceedings of IEEE Conference on Semiconductor Technology International (IEEE2017), pp. 1–3.
  33. Y. Shen, “Level-set based mask synthesis with a vector imaging model,” Opt. Express 25(18), 21775 (2017).
    [Crossref]
  34. Y. Shen, “Lithographic source and mask optimization with narrow-band level-set method,” Opt. Express 26(8), 10065–10078 (2018).
    [Crossref]
  35. S. D. Conte and C. deBoor, Elementary Numerical Analysis (McGraw-Hill Science, 1972).
  36. J. Weickert, Scale-Space Theory in Computer Vision (Springer, 1997).
  37. J. Weickert, B. M. T. H. Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE. Trans. Image. Process 7(3), 398–410 (1998).
    [Crossref]
  38. D. W. Peaceman and J. H. H. Rachford, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
    [Crossref]
  39. D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003).
    [Crossref]
  40. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Science, 1996).
  41. M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).
  42. T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
    [Crossref]
  43. C. Li, C. Xu, C. Gui, and M. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. Trans. Image. Process 19(12), 3243–3254 (2010).
    [Crossref]

2018 (3)

2017 (2)

2014 (2)

J. Li and E. Y. Lam, “Joint optimization of source, mask, and pupil in optical lithography,” Proc. SPIE 9052, 90520S (2014).
[Crossref]

J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471 (2014).
[Crossref]

2013 (3)

J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented lagrangian methods in optical lithography,” Opt. Express 21(7), 8076–8090 (2013).
[Crossref]

X. Ma, C. Han, Y. Li, L. Dong, and G. R. Arce, “Pixelated source and mask optimization for immersion lithography,” J. Opt. Soc. Am. A 30(1), 112–123 (2013).
[Crossref]

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

2012 (1)

2011 (5)

2010 (3)

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

C. Li, C. Xu, C. Gui, and M. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. Trans. Image. Process 19(12), 3243–3254 (2010).
[Crossref]

Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE 7748, 77481U (2010).
[Crossref]

2009 (5)

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

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

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

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783 (2009).
[Crossref]

2008 (1)

P. Gao, A. Gu, and A. Zakhor, “Optical Proximity Correction with Principal Component Regression,” Proc. SPIE 6924, 69243N (2008).
[Crossref]

2005 (1)

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[Crossref]

2004 (1)

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE 5454, 315–326 (2004).
[Crossref]

2003 (1)

D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003).
[Crossref]

2002 (1)

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

2001 (1)

S. Osher and R. P. Fedkiw, “Level set methods: an overview and some recent results,” J. Comput. Phys. 169(2), 463–502 (2001).
[Crossref]

2000 (1)

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[Crossref]

1998 (1)

J. Weickert, B. M. T. H. Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE. Trans. Image. Process 7(3), 398–410 (1998).
[Crossref]

1955 (1)

D. W. Peaceman and J. H. H. Rachford, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
[Crossref]

Arce, G. R.

Aschke, L.

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Bagheri, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Baik, K. H.

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

Barash, D.

D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003).
[Crossref]

Bizjak, T.

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Born, M.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

Bukofsky, S. J.

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

Cecil, T.

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

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

Chen, D.

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

Conley, W.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE 5454, 315–326 (2004).
[Crossref]

Conte, S. D.

S. D. Conte and C. deBoor, Elementary Numerical Analysis (McGraw-Hill Science, 1972).

Dam, T.

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

deBoor, C.

S. D. Conte and C. deBoor, Elementary Numerical Analysis (McGraw-Hill Science, 1972).

Dong, L.

Fakhry, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Fedkiw, R. P.

S. Osher and R. P. Fedkiw, “Level set methods: an overview and some recent results,” J. Comput. Phys. 169(2), 463–502 (2001).
[Crossref]

Fonseca, C. A.

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

Fox, M.

C. Li, C. Xu, C. Gui, and M. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. Trans. Image. Process 19(12), 3243–3254 (2010).
[Crossref]

Gao, P.

P. Gao, A. Gu, and A. Zakhor, “Optical Proximity Correction with Principal Component Regression,” Proc. SPIE 6924, 69243N (2008).
[Crossref]

Garcia-Frias, J.

Gleason, B.

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Science, 1996).

Gu, A.

P. Gao, A. Gu, and A. Zakhor, “Optical Proximity Correction with Principal Component Regression,” Proc. SPIE 6924, 69243N (2008).
[Crossref]

Gui, C.

C. Li, C. Xu, C. Gui, and M. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. Trans. Image. Process 19(12), 3243–3254 (2010).
[Crossref]

H. Romeny, B. M. T.

J. Weickert, B. M. T. H. Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE. Trans. Image. Process 7(3), 398–410 (1998).
[Crossref]

Halle, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Ham, Y.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE 5454, 315–326 (2004).
[Crossref]

Han, C.

He, L.

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

Hibbs, M. S.

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

Hoffnagle, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Hu, P.

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

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

Imgrunt, W.

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Israeli, M.

D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003).
[Crossref]

Jia, N.

Kachalov, D. G.

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Kim, Y.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Kimmel, R.

D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003).
[Crossref]

Lai, K.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

Lam, E. Y.

J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471 (2014).
[Crossref]

J. Li and E. Y. Lam, “Joint optimization of source, mask, and pupil in optical lithography,” Proc. SPIE 9052, 90520S (2014).
[Crossref]

J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented lagrangian methods in optical lithography,” Opt. Express 21(7), 8076–8090 (2013).
[Crossref]

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

J. Li, Y. Shen, and E. Y. Lam, “Hotspot-aware fast source and mask optimization,” Opt. Express 20(19), 21792–21804 (2012).
[Crossref]

N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19(20), 19384–19398 (2011).
[Crossref]

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

N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19(20), 19384–19398 (2011).
[Crossref]

Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE 7748, 77481U (2010).
[Crossref]

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

Lehoty, D.

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[Crossref]

Li, C.

C. Li, C. Xu, C. Gui, and M. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. Trans. Image. Process 19(12), 3243–3254 (2010).
[Crossref]

Li, J.

Li, Y.

Lissotschenko, V. N.

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Liu, S.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented lagrangian methods in optical lithography,” Opt. Express 21(7), 8076–8090 (2013).
[Crossref]

Lv, W.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

Ma, X.

Melville, D.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Miklyaev, Y.

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Neureuther, A. R.

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[Crossref]

Osher, S.

S. Osher and R. P. Fedkiw, “Level set methods: an overview and some recent results,” J. Comput. Phys. 169(2), 463–502 (2001).
[Crossref]

S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics (Springer, 2003).

Pang, L.

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

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

Paragios, N.

S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics (Springer, 2003).

Pavelyev, V. S.

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Peaceman, D. W.

D. W. Peaceman and J. H. H. Rachford, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
[Crossref]

Peng, D.

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

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

Peng, F.

F. Peng and Y. Shen, “Source and mask co-optimization based on depth learning methods,” in “2018 China Semiconductor Technology International Conference (CSTIC),” (2018), pp. 1–3.

Peng, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE. Trans. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

Pistor, T. V.

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[Crossref]

Progler, C.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE 5454, 315–326 (2004).
[Crossref]

Rachford, J. H. H.

D. W. Peaceman and J. H. H. Rachford, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
[Crossref]

Rosenbluth, A. E.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

Schlick, T.

D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003).
[Crossref]

Shen, Y.

Y. Shen, “Lithographic source and mask optimization with narrow-band level-set method,” Opt. Express 26(8), 10065–10078 (2018).
[Crossref]

Y. Shen, “Level-set based mask synthesis with a vector imaging model,” Opt. Express 25(18), 21775 (2017).
[Crossref]

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

J. Li, Y. Shen, and E. Y. Lam, “Hotspot-aware fast source and mask optimization,” Opt. Express 20(19), 21792–21804 (2012).
[Crossref]

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

Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE 7748, 77481U (2010).
[Crossref]

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

Y. Shen, “Level-set based ILT with a vector imaging model,” in Proceedings of IEEE Conference on Semiconductor Technology International (IEEE2017), pp. 1–3.

F. Peng and Y. Shen, “Source and mask co-optimization based on depth learning methods,” in “2018 China Semiconductor Technology International Conference (CSTIC),” (2018), pp. 1–3.

Shi, D.

Shi, X.

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[Crossref]

Singh, R. N.

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

Sinn, R.

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

Socha, B.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE 5454, 315–326 (2004).
[Crossref]

Socha, R.

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[Crossref]

Socha, R. J.

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[Crossref]

Tian, K.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Tirapu-Azpiroz, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Tolani, V.

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

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

Viergever, M. A.

J. Weickert, B. M. T. H. Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE. Trans. Image. Process 7(3), 398–410 (1998).
[Crossref]

Wang, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE. Trans. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

Wang, Z.

Weickert, J.

J. Weickert, B. M. T. H. Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE. Trans. Image. Process 7(3), 398–410 (1998).
[Crossref]

J. Weickert, Scale-Space Theory in Computer Vision (Springer, 1997).

Wolf, E.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

Wong, A. K. K.

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

Wong, A. K.-K.

A. K.-K. Wong, Resolution Enhancemenant Techniques in Optical Lithography (SPIE Press, 2001).

A. K.-K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005).

Wong, N.

Wu, X.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

Xia, Q.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

Xiao, G.

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

Xu, C.

C. Li, C. Xu, C. Gui, and M. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. Trans. Image. Process 19(12), 3243–3254 (2010).
[Crossref]

Yu, J. C.

J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011).
[Crossref]

Yu, P.

J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011).
[Crossref]

Yu, Z.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE. Trans. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

Zakhor, A.

P. Gao, A. Gu, and A. Zakhor, “Optical Proximity Correction with Principal Component Regression,” Proc. SPIE 6924, 69243N (2008).
[Crossref]

Zhang, H.

Zhang, J.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE. Trans. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

Zhao, Q.

IEEE. Trans. Image. Process (3)

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE. Trans. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

J. Weickert, B. M. T. H. Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE. Trans. Image. Process 7(3), 398–410 (1998).
[Crossref]

C. Li, C. Xu, C. Gui, and M. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. Trans. Image. Process 19(12), 3243–3254 (2010).
[Crossref]

J. Comput. Phys. (1)

S. Osher and R. P. Fedkiw, “Level set methods: an overview and some recent results,” J. Comput. Phys. 169(2), 463–502 (2001).
[Crossref]

J. Math. Imaging. Vis. (1)

D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003).
[Crossref]

J. Micro/Nanolithogr., MEMS, MOEMS (1)

A. E. Rosenbluth, S. J. Bukofsky, C. A. Fonseca, M. S. Hibbs, K. Lai, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Micro/Nanolithogr., MEMS, MOEMS 1(1), 13–30 (2002).
[Crossref]

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

J. Soc. Ind. Appl. Math. (1)

D. W. Peaceman and J. H. H. Rachford, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
[Crossref]

J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. (1)

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 31(4), 041605 (2013).
[Crossref]

Opt. Express (13)

J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented lagrangian methods in optical lithography,” Opt. Express 21(7), 8076–8090 (2013).
[Crossref]

J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471 (2014).
[Crossref]

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

Y. Shen, “Level-set based mask synthesis with a vector imaging model,” Opt. Express 25(18), 21775 (2017).
[Crossref]

Y. Shen, “Lithographic source and mask optimization with narrow-band level-set method,” Opt. Express 26(8), 10065–10078 (2018).
[Crossref]

X. Ma, Z. Wang, Y. Li, G. R. Arce, L. Dong, and J. Garcia-Frias, “Fast optical proximity correction method based on nonlinear compressive sensing,” Opt. Express 26(11), 14479–14498 (2018).
[Crossref]

X. Ma, Q. Zhao, H. Zhang, Z. Wang, and G. R. Arce, “Model-driven convolution neural network for inverse lithography,” Opt. Express 26(25), 32565–32584 (2018).
[Crossref]

X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783 (2009).
[Crossref]

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

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

N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19(20), 19384–19398 (2011).
[Crossref]

N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19(20), 19384–19398 (2011).
[Crossref]

J. Li, Y. Shen, and E. Y. Lam, “Hotspot-aware fast source and mask optimization,” Opt. Express 20(19), 21792–21804 (2012).
[Crossref]

Proc. SPIE (11)

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[Crossref]

J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011).
[Crossref]

Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE 7748, 77481U (2010).
[Crossref]

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[Crossref]

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE 5454, 315–326 (2004).
[Crossref]

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, and S. Halle, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[Crossref]

Y. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

P. Gao, A. Gu, and A. Zakhor, “Optical Proximity Correction with Principal Component Regression,” Proc. SPIE 6924, 69243N (2008).
[Crossref]

J. Li and E. Y. Lam, “Joint optimization of source, mask, and pupil in optical lithography,” Proc. SPIE 9052, 90520S (2014).
[Crossref]

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

V. Tolani, P. Hu, D. Peng, T. Cecil, R. Sinn, L. Pang, and B. Gleason, “Source-mask co-optimization (SMO) using level set methods,” Proc. SPIE 7488, 74880Y (2009).
[Crossref]

Other (10)

S. D. Conte and C. deBoor, Elementary Numerical Analysis (McGraw-Hill Science, 1972).

J. Weickert, Scale-Space Theory in Computer Vision (Springer, 1997).

S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics (Springer, 2003).

A. K.-K. Wong, Resolution Enhancemenant Techniques in Optical Lithography (SPIE Press, 2001).

A. K.-K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005).

X. Ma and G. R. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics, 1st ed. (John Wiley and Sons, 2010).

F. Peng and Y. Shen, “Source and mask co-optimization based on depth learning methods,” in “2018 China Semiconductor Technology International Conference (CSTIC),” (2018), pp. 1–3.

Y. Shen, “Level-set based ILT with a vector imaging model,” in Proceedings of IEEE Conference on Semiconductor Technology International (IEEE2017), pp. 1–3.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Science, 1996).

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

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Figures (5)

Fig. 1.
Fig. 1. Simulation of lithographic imaging with a poly dense pattern $\textbf {I}_{01}$. Columns from left to right: illuminating source $\textbf {J}$, illuminated mask pattern $\textbf {M}$ and printed wafer image $\textbf {I}$. Row (a), (b) and (c): simulation results with desired target pattern $\textbf {I}_{01}$ as $\textbf {M}$ illuminated by the original illuminating source $\textbf {J}_0$, synthsized mask illuminated by the synthesized source by conventional level-set SMO method and by the proposed semi-implicit SMO approach with $\tau =1.3$, respectively.
Fig. 2.
Fig. 2. Runtimes for conventional level-set SMO method and the proposed SMO approach with $\tau =1.3$ in Fig. 1 with respect to iteration numbers.
Fig. 3.
Fig. 3. Convergence performance for the simulations in Fig. 1 using the conventional level-set SMO and the proposed approach with stepsizes $\tau =0.55, 0.7, 0.85, 1, 1.15, 1.3$ improving PE from $4139$ to $580$, $574$, $568$, $568$, $574$, $586$ in 40, 35, 30, 25, 20, 15 iterations, respectively.
Fig. 4.
Fig. 4. Simulation of lithographic imaging with $\textbf {I}_{02}$. Columns from left to right: illuminating source $\textbf {J}$, illuminated mask pattern $\textbf {M}$ and printed wafer image $\textbf {I}$. Row (a), (b) and (c): simulation results with desired target pattern $\textbf {I}_{02}$ as $\textbf {M}$ illuminated by the original illuminating source $\textbf {J}_0$, synthsized mask illuminated by the synthesized source by conventional level-set SMO method and by the proposed semi-implicit SMO approach with $\tau =1.3$, respectively.
Fig. 5.
Fig. 5. Convergence performance for simulations in Fig. 4 using the conventional level-set SMO and the proposed approach with stepsizes $\tau =0.55, 0.7, 0.85, 1, 1.15, 1.3$ improving PE from $4631$ to $424$, $465$, $428$, $418$, $436$, $435$, respectively.

Tables (1)

Tables Icon

Table 1. Convergence Stepsize and Runtime (in hours) of Simulations in Fig. 1.

Equations (15)

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

I = T { , M } = s i g ( I a ) = s i g ( 1 J s u m α s β s J ( α s , β s ) p = x , y , z H p ( α s , β s ) B ( α s , β s ) M 2 ) ,
l = { l int for { r : ϕ l ( r ) < 0 } l ext for { r : ϕ l ( r ) > 0 } ,   l = J   or   M ,
E ( ϕ ) = μ R P ( ϕ ) + E e x t ( ϕ ) ,
R p ( ϕ ) = 1 2 Ω R N × N ( | ϕ | 1 ) 2 d r .
E e x t ( ϕ ) = 1 2 Ω R N × N ( T { ϕ J , ϕ M } I 0 ) 2 d r .
J = 1 + cos θ J 2     and     M = 1 + cos θ M 2
ϕ t = μ R p ϕ | ϕ | E e x t ϕ | ϕ | = | ϕ | v l ( r , t ) μ | ϕ | [ ϕ ( ϕ | ϕ | ) ] ,   l = J   or   M ,
v J ( r , t ) = J { ϕ J } T ( T { ϕ J , ϕ M } I 0 ) = 1 2 θ J ( I I 0 ) 2 = a sin θ J α s , β s p = x , y , z E p α s β s 2 I a α s , β s J ( I 0 I ) I ( 1 I ) ,
v M ( r , t ) = J { ϕ M } T ( T { ϕ J , ϕ M } I 0 ) = 1 2 θ M ( I I 0 ) 2 = a sin θ M J s u m α s , β s p = x , y , z J ( α s , β s ) Real [ ( B ) ( ( H p ) { E p α s β s ( I 0 I ) I ( 1 I ) } ) ] ,
ω t = μ | ω | ( ω | ω | )   + | ω | g ( r , t ) ,
ω i k + 1 = ω i k + τ j N ( i ) 2 μ ( | ω | ) i k + ( | ω | ) j k ω j k + 1 ω i k + 1 h 2 + τ | ω | i k g ( i , k ) ,
ω k + 1 = ω k + τ | ω | k g k + τ l { x , y } A l ( ω k ) ω k + 1 ,
a i j l ( ω k ) = { 2 μ ( | ω | ) i k + ( | ω | ) j k [ j N l ( i ) ] m N l ( i ) 2 μ ( | ω | ) i k + ( | ω | ) m k ( j = i ) 0 ( e l s e ) ,
( I τ l { x , y } A l ( ω k ) ) ω k + 1 = ω k + τ | ω | k g k ,
ω k + 1 = 1 2 l { x , y } ( I 2 τ A l ( ω k ) ) 1 ( ω k + τ | ω | k g k ) .

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