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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 1 — Jan. 1, 2013
  • pp: 112–123

Pixelated source and mask optimization for immersion lithography

Xu Ma, Chunying Han, Yanqiu Li, Lisong Dong, and Gonzalo R. Arce  »View Author Affiliations

JOSA A, Vol. 30, Issue 1, pp. 112-123 (2013)

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Immersion lithography systems with hyper-numerical aperture (hyper-NA) (NA>1) have become indispensable in nanolithography for technology nodes of 45 nm and beyond. Source and mask optimization (SMO) has emerged as a key technique used to further improve the imaging performance of immersion lithography. Recently, a set of pixelated gradient-based SMO approaches were proposed under the scalar imaging models, which are inaccurate for hyper-NA settings. This paper focuses on developing pixelated gradient-based SMO algorithms based on a vector imaging model that is accurate for current immersion lithography. To achieve this goal, an integrative and analytic vector imaging model is first used to formulate the simultaneous SMO (SISMO) and sequential SMO (SESMO) frameworks. A gradient-based algorithm is then exploited to jointly optimize the source and mask. Subsequently, this paper studies and compares the performance of individual source optimization (SO), individual mask optimization (MO), SISMO, and SESMO. Finally, a hybrid SMO (HSMO) approach is proposed to take full advantage of SO, SISMO, and MO, consequently achieving superior performance.

© 2012 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(110.4980) Imaging systems : Partial coherence in imaging
(110.5220) Imaging systems : Photolithography
(110.2945) Imaging systems : Illumination design

ToC Category:
Image Processing

Original Manuscript: August 27, 2012
Revised Manuscript: December 2, 2012
Manuscript Accepted: December 4, 2012
Published: December 19, 2012

Xu Ma, Chunying Han, Yanqiu Li, Lisong Dong, and Gonzalo R. Arce, "Pixelated source and mask optimization for immersion lithography," J. Opt. Soc. Am. A 30, 112-123 (2013)

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  1. A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).
  2. X. Ma and G. R. Arce, Computational Lithography, 1st ed.(Wiley, 2010).
  3. S. Sherif, B. Saleh, and R. Leone, “Binary image synthesis using mixed integer programming,” IEEE Trans. Image Process. 4, 1252–1257 (1995). [CrossRef]
  4. Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semicond. Manuf. 5, 138–152 (1992). [CrossRef]
  5. A. Poonawala and P. Milanfar, “Fast and low-complexity mask design in optical microlithography—an inverse imaging problem,” IEEE Trans. Image Process. 16, 774–788 (2007). [CrossRef]
  6. X. Ma and G. R. Arce, “Binary mask optimization for inverse lithography with partially coherent illumination,” J. Opt. Soc. Am. A 25, 2960–2970 (2008). [CrossRef]
  7. X. Ma and G. R. Arce, “Pixel-based OPC optimization based on conjugate gradients,” Opt. Express 19, 2165–2180 (2011). [CrossRef]
  8. M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836(1982). [CrossRef]
  9. A. Poonawala and P. Milanfar, “OPC and PSM design using inverse lithography: a non-linear optimization approach,” Proc. SPIE 6154, 1159–1172 (2006). [CrossRef]
  10. X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express 16, 20126–20141 (2008). [CrossRef]
  11. X. Ma, G. R. Arce, and Y. Li, “Optimal 3D phase-shifting masks in partially coherent illumination,” Appl. Opt. 50, 5567–5576 (2011). [CrossRef]
  12. S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifing masks in optical projection lithography,” Opt. Express 16, 14746–14760 (2008). [CrossRef]
  13. Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17, 23690–23701 (2009). [CrossRef]
  14. J. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express 18, 23331–23342 (2010). [CrossRef]
  15. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002). [CrossRef]
  16. C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent phase mask transmission tuning,” Proc. SPIE 5454, 315–326 (2005). [CrossRef]
  17. S. Robert, X. Shi, and L. David, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005). [CrossRef]
  18. S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008). [CrossRef]
  19. Y. V. 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, 7640–7674 (2010). [CrossRef]
  20. J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in doe modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 7640–7675 (2010). [CrossRef]
  21. X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17, 5783–5793 (2009). [CrossRef]
  22. Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 20, 2856–2864 (2011). [CrossRef]
  23. J. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011). [CrossRef]
  24. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19, 19384–19398 (2011). [CrossRef]
  25. G. M. Gallatin, “High-numerical-aperture scalar imaging,” Appl. Opt. 40, 4958–4964 (2001). [CrossRef]
  26. D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010). [CrossRef]
  27. T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000). [CrossRef]
  28. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill Science, 1996).
  29. M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005). [CrossRef]
  30. X. Ma, Y. Li, and L. Dong, “Mask optimization approaches in optical lithography based on a vector imaging model,” J. Opt. Soc. Am. A 29, 1300–1312 (2012). [CrossRef]
  31. K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009). [CrossRef]
  32. N. Jia and E. Y. Lam, “Performance analysis of pixelated source-mask optimization for optical microlithography,” in Proceedings of IEEE International Conference of Electron Devices and Solid-State Circuits (EDSSC) (IEEE, 2010).
  33. X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15, 15066–15079 (2007). [CrossRef]
  34. http://www.mentor.com/ .
  35. X. Ma and Y. Li, “Resolution enhancement optimization methods in optical lithography with improved manufacturability,” J. Microlith. Microfab. Microsyst. 10(2), 023009 (2011). [CrossRef]

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