OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 18 — Jun. 20, 2013
  • pp: 4200–4211

Hybrid source mask optimization for robust immersion lithography

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

Applied Optics, Vol. 52, Issue 18, pp. 4200-4211 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (675 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



To keep pace with the shrinkage of critical dimension, source and mask optimization (SMO) has emerged as a promising resolution enhancement technique to push the resolution of 193 nm argon fluoride immersion lithography systems. However, most current pixelated SMO approaches relied on scalar imaging models that are no longer accurate for immersion lithography systems with hyper-NA (NA>1). This paper develops a robust hybrid SMO (HSMO) algorithm based on a vector imaging model capable of effectively improving the robustness of immersion lithography systems to defocus and dose variations. The proposed HSMO algorithm includes two steps. First, the individual source optimization approach is carried out to rapidly reduce the cost function. Subsequently, the simultaneous SMO approach is applied to further improve the process robustness by exploiting the synergy in the joint optimization of source and mask patterns. The conjugate gradient method is used to update the source and mask pixels. In addition, a source regularization approach and source postprocessing are both used to improve the manufacturability of the optimized source patterns. Compared to the mask optimization method, the HSMO algorithm achieves larger process windows, i.e., extends the depth of focus and exposure latitude, thus more effectively improving the process robustness of 45 nm immersion lithography systems.

© 2013 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(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:
Imaging Systems

Original Manuscript: April 12, 2013
Revised Manuscript: May 9, 2013
Manuscript Accepted: May 18, 2013
Published: June 14, 2013

Xu Ma, Chunying Han, Yanqiu Li, Bingliang Wu, Zhiyang Song, Lisong Dong, and Gonzalo R. Arce, "Hybrid source mask optimization for robust immersion lithography," Appl. Opt. 52, 4200-4211 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. A. Campbell, The Science and Engineering of Microelectronic Fabrication, 2nd ed. (Publishing House of Electronics Industry, 2003).
  2. F. Schellenberg, “Resolution enhancement technology: the past, the present, and extensions for the future, optical microlithography,” Proc. SPIE 5377, 1–20 (2004). [CrossRef]
  3. A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).
  4. X. Ma and G. R. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics (Wiley, 2010).
  5. 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. Microlithogr. Microfabr. Microsyst. 1, 13–30 (2002). [CrossRef]
  6. C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent phase mask transmission tuning,” Proc. SPIE 5454, 315–326 (2005). [CrossRef]
  7. S. Robert, X. Shi, and L. David, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005). [CrossRef]
  8. 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]
  9. 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, 764024 (2010). [CrossRef]
  10. 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, 764025 (2010). [CrossRef]
  11. 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]
  12. J. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011). [CrossRef]
  13. Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “High performance source optimization using a gradient-based method in optical lithography,” IEEE 11th International Symposium on Quality Electronic Design (IEEE, 2010), pp. 108–113.
  14. 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]
  15. N. Jia and E. Y. Lam, “Performance analysis of pixelated source-mask optimization for optical microlithography,” IEEE International Conference of Electron Devices and Solid-State Circuits (EDSSC) (IEEE, 2010).
  16. N. Jia and E. Y. Lam, “Robustness enhancement in optical lithography: from pixelated mask optimization to pixelated source-mask optimization,” ECS Trans. 34, 203–208 (2011). [CrossRef]
  17. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19, 19384–19398 (2011). [CrossRef]
  18. G. M. Gallatin, “High-numerical-aperture scalar imaging,” Appl. Opt. 40, 4958–4964 (2001). [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, 112–123 (2013). [CrossRef]
  20. 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]
  21. J. Moon, B. Nam, J. Jeong, D. Kong, B. Nam, and D. G. Yim, “Binary and attenuated PSM mask evaluation for sub 50 nm device development perspective,” Proc. SPIE 6924, 692436 (2008). [CrossRef]
  22. T. Yamazaki, Y. Kojima, M. Yamana, T. Haraguchi, and T. Tanaka, “Fine pattern fabrication property of binary mask and attenuated phase shift mask,” Proc. SPIE 7379, 73791V (2009). [CrossRef]
  23. A. Poonawala and P. Milanfar, “OPC and PSM design using inverse lithography: a non-linear optimization approach,” Proc. SPIE 6154, 1159–1172 (2006). [CrossRef]
  24. X. Ma and G. R. Arce, “Pixel-based OPC optimization based on conjugate gradients,” Opt. Express 19, 2165–2180 (2011). [CrossRef]
  25. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  26. 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]
  27. K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmerman, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, and J. Hageman, “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).
  28. X. Ma, Y. Li, X. Guo, L. Dong, and G. R. Arce, “Vectorial mask optimization methods for robust optical lithography,” J. Micro/Nanolith. MEMS MOEMS 11, 043008 (2012). [CrossRef]
  29. X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15, 15066–15079 (2007). [CrossRef]
  30. 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]
  31. http://www.mentor.com/ .
  32. T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000). [CrossRef]
  33. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill Science, 1996).
  34. M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 031108 (2005). [CrossRef]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited