OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 5511–5521

Robust level-set-based inverse lithography

Yijiang Shen, Ningning Jia, Ngai Wong, and Edmund Y. Lam  »View Author Affiliations

Optics Express, Vol. 19, Issue 6, pp. 5511-5521 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (717 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Level-set based inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem, interpreted with a time-dependent model, and then solved as a partial differential equation with finite difference schemes. This paper focuses on developing level-set based ILT for partially coherent systems, and upon that an expectation-orient optimization framework weighting the cost function by random process condition variables. These include defocus and aberration to enhance robustness of layout patterns against process variations. Results demonstrating the benefits of defocus-aberration-aware level-set based ILT are presented.

© 2011 Optical Society of America

OCIS Codes
(110.3960) Imaging systems : Microlithography
(110.5220) Imaging systems : Photolithography
(110.1758) Imaging systems : Computational imaging

ToC Category:
Imaging Systems

Original Manuscript: January 10, 2011
Revised Manuscript: February 17, 2011
Manuscript Accepted: February 18, 2011
Published: March 9, 2011

Yijiang Shen, Ningning Jia, Ngai Wong, and Edmund Y. Lam, "Robust level-set-based inverse lithography," Opt. Express 19, 5511-5521 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. K.-K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, Bellingham, WA, 2001).
  2. F. Schellenberg, “Resolution enhancement technology: the past, the present, and extensions for the future,” Proc. SPIE 5377, 1–20 (2004).
  3. O. W. Otto, J. G. Garofalo, K. K. Low, C.-M. Yuan, R. C. Henderson, C. Pierrat, R. L. Kostelak, S. Vaidya, and P. K. Vasudev, “Automated optical proximity correction: a rules-based approach,” Proc. SPIE 2197, 278–293 (1994).
  4. S. Shioiri, and H. Tanabe, “Fast optical proximity correction: analytical method,” Proc. SPIE 2440, 261–269 (1995).
  5. 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).
  6. Y. Liu, and A. Zakhor, “Optimal binary image design for optical lithography,” Proc. SPIE 1264, 401–412 (1990).
  7. Y. Liu, and A. Zakhor, “Binary and phase-shifting image design for optical lithography,” Proc. SPIE 1463, 382–399 (1991).
  8. S. Sherif, B. Saleh, and R. De Leone, “Binary image synthesis using mixed linear integer programming,” IEEE Trans. Image Process. 4(9), 1252–1257 (1995). [PubMed]
  9. Y. C. Pati, and T. Kailath, “Phase-shifting masks for microlithography: automated design and mask requirements,” J. Opt. Soc. Am. A 11(9), 2438–2452 (1994).
  10. S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express 16(19), 14746–14760 (2008). [PubMed]
  11. S. H. Chan, and E. Y. Lam, “Inverse image problem of designing phase shifting masks in optical lithography,” in Proceedings of IEEE International Conference on Image Processing, pp. 1832–1835 (2008).
  12. A. Poonawala, and P. Milanfar, “Prewarping techniques in imaging: applications in nanotechnology and biotechnology,” Proc. SPIE 5674, 114–127 (2005).
  13. A. Poonawala, and P. Milanfar, “Mask design for optical microlithography: an inverse imaging problem,” IEEE Trans. Image Process. 16(3), 774–788 (2007). [PubMed]
  14. S. H. Chan, A. K. Wong, and E. Y. Lam, “Inverse synthesis of phase-shifting mask for optical lithography,” in OSA Topical Meeting in Signal Recovery and Synthesis, p. SMD3 (2007).
  15. V. Singh, B. Hu, K. Toh, S. Bollepalli, S. Wagner, and Y. Borodovsky, “Making a trillion pixels dance,” Proc. SPIE 6924, 69240S (2008).
  16. A. Poonawala, Y. Borodovsky, and P. Milanfar, “ILT for double exposure lithography with conventional and novel materials,” Proc. SPIE 6520, 65202Q (2007).
  17. N. Jia, A. K. Wong, and E. Y. Lam, “Regularization of inverse photomask synthesis to enhance manufacturability,” Proc. SPIE 7520, 752032 (2009).
  18. N. Jia, A. K. Wong, and E. Y. Lam, “Robust photomask design with defocus variation using inverse synthesis,” Proc. SPIE 7140, 71401W (2008).
  19. S. Osher, and R. P. Fedkiw, “Level set methods: an overview and some recent results,” J. Comput. Phys. 169(2), 463–502 (2001).
  20. J. A. Sethian, and D. Adalsteinsson, “An overview of level set methods for etching, deposition, and lithography development,” IEEE Trans. Semicond. Manuf. 10, 167–184 (1997).
  21. S. Osher, and N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics (Springer Verlag New York, NJ, USA, 2003).
  22. F. Santosa, ““A level-set approach for inverse problems involving obstacles,” ESAIM Contr¨ole Optim,” Calc. Var. 1, 17–33 (1996).
  23. S. Osher, and F. Santosa, “Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum,” J. Comput. Phys. 171(1), 272–288 (2001).
  24. A. Marquina, and S. Osher, “Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal,” SIAM J. Sci. Comput. 22, 387–405 (2000).
  25. L. Pang, G. Dai, T. Cecil, T. Dam, Y. Cui, P. Hu, D. Chen, K. Baik, and D. Peng, “Validation of inverse lithography technology (ILT) and its adaptive SRAF at advanced technology nodes,” Proc. SPIE 6924, 69240T (2008).
  26. Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17(26), 23690–23701 (2009).
  27. E. Y. Lam, and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express 17(15), 12259–12268 (2009). [PubMed]
  28. E. Y. Lam, and A. K. Wong, ““Nebulous hotspot and algorithm variability in computation lithography,” J. Micro/ Nanolithogr,” MEMS MOEMS 9(3), 033002 (2010).
  29. N. Jia, and E. Y. Lam, “Machine learning for inverse lithography: Using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 045601 (2010).
  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).
  31. M. Born, and E. Wolf, Principles of Optics (Pergamon Press Oxford, 1980).
  32. J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 2000).
  33. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. Lond. 217A(1130), 408–432 (1953).
  34. A. K.-K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, Bellingham, WA, 2005).
  35. B. E. A. Saleh, and M. Rabbani, “Simulation of partially coherent imagery in the space and frequency domains and by modal expansion,” Appl. Opt. 21(15), 2770–2777 (1982). [PubMed]
  36. X. Ma, and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783–5793 (2009). [PubMed]
  37. B. Nijboer, “The diffraction theory of aberrations,” Ph.D. thesis, Groningen University (1942).
  38. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66(3), 207–211 (1976).
  39. P. Dirksen, J. Braat, A. Janssen, and A. Leeuwestein, “Aberration retrieval for high-NA optical systems using the Extended Nijboer-Zernike theory,” Proc. SPIE 5754, 263 (2005).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited