Abstract

Source and mask optimization (SMO) remains a key technique to improve the wafer image printability for technology nodes of 22 nm and beyond, enabling the continuation of the immersion lithography. In this paper, we propose a distance level-set regularized reformulation of the SMO maintaining the desired signed distance property, which secures stable curve evolution and accurate computation with a simpler and more efficient numerical implementation. Consequently, computation load caused by convolution operations and memory requirements of the electric-field caching technique (EFCT) is significantly eased by performing computation only in the narrow band; moreover, the convergence of the updating process is further improved by applying larger Euler time steps of the Courant-Friedrichs-Lewy (CFL) condition with reduced optimization dimensionality. Simulation results of the proposed narrow-band level-set based SMO prove to improve the computation efficiency, memory usage and imaging performance of the full domain methods.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. A. K.-K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2001).
    [Crossref]
  2. A. K.-K. Wong, Optical Imaging in Projection Lithography (SPIE Press, 2005).
    [Crossref]
  3. L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” Proc. SPIE,  6607, 660739 (2007).
    [Crossref]
  4. T. S. Gau, R. G. Liu, C. M. Lai, and F. J. Liang, “The customized illumination aperture filter for low k1 photolithography process,” Proc. SPIE,  4000, 271–282 (2000).
    [Crossref]
  5. 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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).
  6. C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent transmission tuning,” Proc. SPIE,  5454, 315–326 (2004).
  7. R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE,  5853, pp. 180–193 (2005).
    [Crossref]
  8. D. Peng, P. Hu, V. Tolani, T. Dam, J. Tyminski, and S. Slonaker, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE,  7640, 76402Y (2010).
    [Crossref]
  9. T. Fühner, A. Erdmann, and Sebastian Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlithogr. Microfabr. Microsyst. 6(3), 031006 (2007).
  10. 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]
  11. 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] [PubMed]
  12. J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE,  7973, 23067–23077 (2011).
  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] [PubMed]
  14. J. Li, Y. Shen, and E. Y. Lam, “Hotspot-aware fast source and mask optimization,” Opt. Express 20(19), 21792–21804 (2012).
    [Crossref] [PubMed]
  15. J. Li and E. Y. Lam, “Joint optimization of source, mask, and pupil in optical lithography,” Proc. SPIE,  9052, 90520S (2014).
    [Crossref]
  16. J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471–9485 (2014).
    [Crossref] [PubMed]
  17. X. Wu, S. Liu, J. Li, and E. Y. Lam, “Efficient source mask optimization with Zernike polynomial functions for source representation,” Opt. Express 22(4), 3924–3937 (2014).
    [Crossref] [PubMed]
  18. Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-Based Source and Mask Optimization in Optical Lithography,” IEEE. T. Image. Process 20(10), 2856–2864 (2011).
    [Crossref]
  19. 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]
  20. 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] [PubMed]
  21. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
    [Crossref]
  22. S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics (Springer, 2003).
  23. S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).
    [Crossref]
  24. 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]
  25. 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]
  26. Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17(26), 23690–23701 (2009).
    [Crossref]
  27. Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE,  7748, 1–8 (2010).
  28. Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
    [Crossref] [PubMed]
  29. Y. Shen, “Level-set based ILT with a vector imaging model,” in Proceedings of IEEE Conference on Semiconductor Technology International (IEEE2017), pp. 1–3.
  30. Y. Shen, “Level-set based mask synthesis with a vector imaging model,” Opt. Express 25(18), 21775 (2017).
    [Crossref] [PubMed]
  31. J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. U. S. A. 93(4), pp. 1591–1595 (1996).
    [Crossref] [PubMed]
  32. J. A. Sethian, Level Set Methods and Fast Marching Methods (Cambridge University, 1999).
  33. D. Adalsteinsson and J. A. Sethian, “A Fast Level Set Method for Propagating Interfaces,” J. Comput. Phys. 118(2), 269–277 (1995).
    [Crossref]
  34. D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
    [Crossref]
  35. M. Sussman and E. Fatemi, “An Efficient Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow,” SIAM J. Sci. Comput. 20(4), 1165–1191 (1999).
    [Crossref]
  36. J. Gomes and O. Faugeras, “Reconciling Distance Functions and Level Sets,” J. Vis. Commun. Image Represent. 11(2), 209–223 (2000).
    [Crossref]
  37. C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: A new variational formulation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE2005), pp. 430–436.
  38. C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. T. Image. Process 19(12), 3243(2010).
    [Crossref]
  39. S. Osher and R. P. Fedkiw, “Level set methods: an overview and some recent results,” J. Comput. Phys. 169(2), 463–502 (2001).
    [Crossref]
  40. T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE,  4000, 228–237 (2000).
    [Crossref]
  41. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Science, 1996).
  42. M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).
    [Crossref]
  43. D. Adalsteinsson and J. A. Sethian, “The fast construction of extension velocities in level set methods,” J. Comput. Phys. 108(1), 2–22 (1999).
    [Crossref]

2017 (1)

2014 (3)

2013 (2)

2012 (1)

2011 (4)

J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE,  7973, 23067–23077 (2011).

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

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-Based Source and Mask Optimization in Optical Lithography,” IEEE. T. Image. Process 20(10), 2856–2864 (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] [PubMed]

2010 (3)

Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE,  7748, 1–8 (2010).

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

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

2009 (5)

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] [PubMed]

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]

2007 (2)

T. Fühner, A. Erdmann, and Sebastian Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlithogr. Microfabr. Microsyst. 6(3), 031006 (2007).

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” Proc. SPIE,  6607, 660739 (2007).
[Crossref]

2005 (1)

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE,  5853, pp. 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).

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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

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 (3)

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

J. Gomes and O. Faugeras, “Reconciling Distance Functions and Level Sets,” J. Vis. Commun. Image Represent. 11(2), 209–223 (2000).
[Crossref]

T. S. Gau, R. G. Liu, C. M. Lai, and F. J. Liang, “The customized illumination aperture filter for low k1 photolithography process,” Proc. SPIE,  4000, 271–282 (2000).
[Crossref]

1999 (3)

D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
[Crossref]

M. Sussman and E. Fatemi, “An Efficient Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow,” SIAM J. Sci. Comput. 20(4), 1165–1191 (1999).
[Crossref]

D. Adalsteinsson and J. A. Sethian, “The fast construction of extension velocities in level set methods,” J. Comput. Phys. 108(1), 2–22 (1999).
[Crossref]

1996 (1)

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. U. S. A. 93(4), pp. 1591–1595 (1996).
[Crossref] [PubMed]

1995 (1)

D. Adalsteinsson and J. A. Sethian, “A Fast Level Set Method for Propagating Interfaces,” J. Comput. Phys. 118(2), 269–277 (1995).
[Crossref]

1992 (1)

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

Abrams, D.

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” Proc. SPIE,  6607, 660739 (2007).
[Crossref]

Adalsteinsson, D.

D. Adalsteinsson and J. A. Sethian, “The fast construction of extension velocities in level set methods,” J. Comput. Phys. 108(1), 2–22 (1999).
[Crossref]

D. Adalsteinsson and J. A. Sethian, “A Fast Level Set Method for Propagating Interfaces,” J. Comput. Phys. 118(2), 269–277 (1995).
[Crossref]

Arce, G. R.

Bagheri, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, 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]

Born, M.

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

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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

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).

Dam, T.

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

L. 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]

Dong, L.

Erdmann, A.

T. Fühner, A. Erdmann, and Sebastian Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlithogr. Microfabr. Microsyst. 6(3), 031006 (2007).

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]

Fatemi, E.

M. Sussman and E. Fatemi, “An Efficient Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow,” SIAM J. Sci. Comput. 20(4), 1165–1191 (1999).
[Crossref]

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

Faugeras, O.

J. Gomes and O. Faugeras, “Reconciling Distance Functions and Level Sets,” J. Vis. Commun. Image Represent. 11(2), 209–223 (2000).
[Crossref]

Fedkiw, R.

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).
[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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

Fox, M. D.

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

C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: A new variational formulation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE2005), pp. 430–436.

Fühner, T.

T. Fühner, A. Erdmann, and Sebastian Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlithogr. Microfabr. Microsyst. 6(3), 031006 (2007).

Gau, T. S.

T. S. Gau, R. G. Liu, C. M. Lai, and F. J. Liang, “The customized illumination aperture filter for low k1 photolithography process,” Proc. SPIE,  4000, 271–282 (2000).
[Crossref]

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]

Gomes, J.

J. Gomes and O. Faugeras, “Reconciling Distance Functions and Level Sets,” J. Vis. Commun. Image Represent. 11(2), 209–223 (2000).
[Crossref]

Goodman, J. W.

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

Gui, C.

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

C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: A new variational formulation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE2005), pp. 430–436.

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).

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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

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.

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

L. 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]

Jia, N.

Kang, M.

D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
[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]

Lai, C. M.

T. S. Gau, R. G. Liu, C. M. Lai, and F. J. Liang, “The customized illumination aperture filter for low k1 photolithography process,” Proc. SPIE,  4000, 271–282 (2000).
[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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

Lam, E. Y.

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

X. Wu, S. Liu, J. Li, and E. Y. Lam, “Efficient source mask optimization with Zernike polynomial functions for source representation,” Opt. Express 22(4), 3924–3937 (2014).
[Crossref] [PubMed]

J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471–9485 (2014).
[Crossref] [PubMed]

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] [PubMed]

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

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

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

Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE,  7748, 1–8 (2010).

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, pp. 180–193 (2005).
[Crossref]

Li, C.

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

C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: A new variational formulation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE2005), pp. 430–436.

Li, J.

Li, Y.

Liang, F. J.

T. S. Gau, R. G. Liu, C. M. Lai, and F. J. Liang, “The customized illumination aperture filter for low k1 photolithography process,” Proc. SPIE,  4000, 271–282 (2000).
[Crossref]

Liu, R. G.

T. S. Gau, R. G. Liu, C. M. Lai, and F. J. Liang, “The customized illumination aperture filter for low k1 photolithography process,” Proc. SPIE,  4000, 271–282 (2000).
[Crossref]

Liu, S.

Liu, Y.

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” Proc. SPIE,  6607, 660739 (2007).
[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]

Merriman, B.

D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
[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]

D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
[Crossref]

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).
[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]

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” Proc. SPIE,  6607, 660739 (2007).
[Crossref]

Paragios, N.

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

Peng, D.

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

L. 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]

D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
[Crossref]

Peng, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-Based Source and Mask Optimization in Optical Lithography,” IEEE. T. 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).

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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

Rudin, L.

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

Seifert, Sebastian

T. Fühner, A. Erdmann, and Sebastian Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlithogr. Microfabr. Microsyst. 6(3), 031006 (2007).

Sethian, J. A.

D. Adalsteinsson and J. A. Sethian, “The fast construction of extension velocities in level set methods,” J. Comput. Phys. 108(1), 2–22 (1999).
[Crossref]

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. U. S. A. 93(4), pp. 1591–1595 (1996).
[Crossref] [PubMed]

D. Adalsteinsson and J. A. Sethian, “A Fast Level Set Method for Propagating Interfaces,” J. Comput. Phys. 118(2), 269–277 (1995).
[Crossref]

J. A. Sethian, Level Set Methods and Fast Marching Methods (Cambridge University, 1999).

Shen, Y.

Shi, X.

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE,  5853, pp. 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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

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]

Slonaker, S.

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

Socha, B.

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

Socha, R.

R. Socha, X. Shi, and D. Lehoty, “Simultaneous source mask optimization (SMO),” Proc. SPIE,  5853, pp. 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]

Sussman, M.

M. Sussman and E. Fatemi, “An Efficient Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow,” SIAM J. Sci. Comput. 20(4), 1165–1191 (1999).
[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.

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

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]

Tyminski, J.

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

Wang, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-Based Source and Mask Optimization in Optical Lithography,” IEEE. T. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

Wolf, E.

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

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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

Wong, A. K.-K.

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

A. K.-K. Wong, Optical Imaging in Projection Lithography (SPIE Press, 2005).
[Crossref]

Wong, N.

Wu, X.

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. D. Fox, “Distance Regularized Level Set Evolution and Its Application to Image Segmentation,” IEEE. T. Image. Process 19(12), 3243(2010).
[Crossref]

C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: A new variational formulation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE2005), pp. 430–436.

Yu, J. C.

J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE,  7973, 23067–23077 (2011).

Yu, P.

J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE,  7973, 23067–23077 (2011).

Yu, Z.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-Based Source and Mask Optimization in Optical Lithography,” IEEE. T. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

Zhang, J.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-Based Source and Mask Optimization in Optical Lithography,” IEEE. T. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

Zhao, H.

D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
[Crossref]

IEEE. T. Image. Process (2)

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-Based Source and Mask Optimization in Optical Lithography,” IEEE. T. Image. Process 20(10), 2856–2864 (2011).
[Crossref]

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

J. Comput. Phys. (4)

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

D. Adalsteinsson and J. A. Sethian, “The fast construction of extension velocities in level set methods,” J. Comput. Phys. 108(1), 2–22 (1999).
[Crossref]

D. Adalsteinsson and J. A. Sethian, “A Fast Level Set Method for Propagating Interfaces,” J. Comput. Phys. 118(2), 269–277 (1995).
[Crossref]

D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys. 155(2), 410–438 (1999).
[Crossref]

J. Microlithogr. Microfabr. Microsyst. (2)

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. Microlithogr. Microfabr. Microsyst. 1(1), 13–30 (2002).

T. Fühner, A. Erdmann, and Sebastian Seifert, “Direct optimization approach for lithographic process conditions,” J. Microlithogr. Microfabr. Microsyst. 6(3), 031006 (2007).

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

J. Vis. Commun. Image Represent. (1)

J. Gomes and O. Faugeras, “Reconciling Distance Functions and Level Sets,” J. Vis. Commun. Image Represent. 11(2), 209–223 (2000).
[Crossref]

Opt. Express (9)

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

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

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] [PubMed]

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

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

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

J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471–9485 (2014).
[Crossref] [PubMed]

X. Wu, S. Liu, J. Li, and E. Y. Lam, “Efficient source mask optimization with Zernike polynomial functions for source representation,” Opt. Express 22(4), 3924–3937 (2014).
[Crossref] [PubMed]

Physica D (1)

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

Proc. Natl. Acad. Sci. U. S. A. (1)

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. U. S. A. 93(4), pp. 1591–1595 (1996).
[Crossref] [PubMed]

Proc. SPIE (12)

Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE,  7748, 1–8 (2010).

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]

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

J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE,  7973, 23067–23077 (2011).

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]

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

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

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

L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45nm and 32nm,” Proc. SPIE,  6607, 660739 (2007).
[Crossref]

T. S. Gau, R. G. Liu, C. M. Lai, and F. J. Liang, “The customized illumination aperture filter for low k1 photolithography process,” Proc. SPIE,  4000, 271–282 (2000).
[Crossref]

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

SIAM J. Sci. Comput. (1)

M. Sussman and E. Fatemi, “An Efficient Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow,” SIAM J. Sci. Comput. 20(4), 1165–1191 (1999).
[Crossref]

Other (9)

C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: A new variational formulation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE2005), pp. 430–436.

J. A. Sethian, Level Set Methods and Fast Marching Methods (Cambridge University, 1999).

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

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

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).
[Crossref]

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

A. K.-K. Wong, Optical Imaging in Projection Lithography (SPIE Press, 2005).
[Crossref]

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

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

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Figures (10)

Fig. 1
Fig. 1 Projection optics in a vector imaging model.
Fig. 2
Fig. 2 (a) The dipole source J0. (b) The desired mask pattern I0. (c) The aerial image Ia of I0 illuminated by J0. (d) The resist image I of I0 illuminated by J0, with PE 2742.
Fig. 3
Fig. 3 Simulation of lithographic imaging with source and mask patterns using the steepest descent (SD) method and the level-set based method. (a) and (e), (b) and (f), (c) and (g), (d) with PE 584 and (h) with PE 517 represent synthesized source patterns, synthesized mask patterns, the corresponding aerial images and resist images, using the SD method and the level-set based method, respectively.
Fig. 4
Fig. 4 Simulation of lithographic imaging using the proposed narrow-band level-set method with different r. Columns Ĵ, , Ia and I represent synthesized source patterns, synthesized mask patterns, the corresponding aerial images and resist images, with r = 1, 2, 3 and 4, respectively. The resist images (d), (h), (l) and (p) with input mask patterns (b), (f), (j) and (n) illuminated by (a), (e), (i) and (m), bear PEs of 643, 506, 487 and 563, respectively.
Fig. 5
Fig. 5 Pattern error versus simulation time for the desired pattern in Fig. 2(b).
Fig. 6
Fig. 6 Runtime for the simulations in Fig. 3 and Fig. 4.
Fig. 7
Fig. 7 (a) Computation load in terms of number of convolutions in every iteration. (b) Optimization complexity in terms of number of source points updated in every iteration.
Fig. 8
Fig. 8 Euler time step δtψ for updating Ĵ in every iteration.
Fig. 9
Fig. 9 (a) The annular source J1. (b) The desired mask pattern I0. (c) The aerial image Ia of I0 illuminated by J1. (d) The resist image I of I0 illuminated by J1, with PE 2361. (e) and (f) The synthesized source and mask patterns using the proposed narrow-band level-set method with r = 3. (g) and (h) The aerial image and the resist image with PE 486 with (f) as input illuminated by (e), respectively.
Fig. 10
Fig. 10 (a) The annular source J1. (b) The desired mask pattern I1. (c) The aerial image Ia of I1 illuminated by J1. (d) The resist image I of I1 illuminated by J1, with PE 3091. (e) and (f) The synthesized source and mask patterns using the proposed narrow-band level-set method with r = 3. (g) and (h) The aerial image and the resist image with PE 346 with (f) as input illuminated by (e), respectively.

Tables (3)

Tables Icon

Algorithm 1 SMO with narrow-band level-set methods

Tables Icon

Table 1 Runtime (minutes) in Fig. 3 and Fig. 4.

Tables Icon

Table 2 Average number of convolution operations and average number of updated source points.

Equations (17)

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

I a = 1 α s , β s J 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 ,
I = 𝒯 { M } = sig ( I a ) .
( J ^ , M ^ ) = argmin J N s × N s argmin M N × N d { I 0 , 𝒯 { J , M } } ,
J = { j int for { r : ψ ( r ) < 0 } j ext for { r : ψ ( r ) > 0 } , and M = { m int for { r : ϕ ( r ) < 0 } m ext for { r : ϕ ( r ) > 0 } ,
d M ( r ) = min ( | r M ( r ) | ) ,
ϕ ( r ) = { d M ( r ) r M 0 r M ( r ) d M ( r ) r M + ,
F ( J , M ) = 1 2 𝒯 { J , M } I 0 2 ,
ψ t = | ψ | v ψ ( r , t ) , and ϕ t = | ϕ | v ϕ ( r , t ) ,
v ψ ( r , t ) = 𝒥 { J } T ( 𝒯 { J } I 0 ) = 1 2 J ( I I 0 ) 2 = 2 a 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 ϕ ( r , t ) = 𝒥 { M } T ( 𝒯 { M } I 0 ) = 1 2 M ( I I 0 ) 2 = 2 a α s , β s J 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 ) } ) ] ,
v ϕ = 2 a α s , β s J α s , β s p = x , y , z J ( α s , β s ) Real [ ( B ) * 1 { [ ( ( H p ) * ° ] [ E p ( I 0 I ) I ( 1 I ) ] ) } ] .
p ς = ( d p ( | ς | ) ς ) ,
p ( ς ) = 1 2 Ω ( | ς | 1 ) 2 ,
ς t = | ς | v ς μ ς | ς | [ Δ ς ( ς | ς | ) ] = | ς | g ς ( r , t ) ,
B r = ( m , n ) Z 𝒩 ( m , n ) r ,
δ t ς max { | g x | δ x + | g y | δ y } = ,
J = 1 + cos θ J 2 and M = 1 + cos θ M 2

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