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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 25, Iss. 12 — Dec. 1, 2008
  • pp: 2960–2970

Binary mask optimization for inverse lithography with partially coherent illumination

Xu Ma and Gonzalo Arce  »View Author Affiliations

JOSA A, Vol. 25, Issue 12, pp. 2960-2970 (2008)

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Recently, a set of generalized gradient-based optical proximity correction optimization methods have been developed to solve for the inverse lithography problem under coherent illumination. Most practical lithography systems, however, operate under partially coherent illumination. This paper focuses on developing gradient-based binary mask optimization methods that account for the inherent nonlinearities of partially coherent systems. Two nonlinear models are used in the optimization. The first relies on a Fourier representation that approximates the partially coherent system as a sum of coherent systems. The second model is based on an average coherent approximation that is computationally faster. To influence the solution patterns toward more desirable manufacturability properties, wavelet regularization is added to the optimization framework.

© 2008 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(100.7410) Image processing : Wavelets
(110.4980) Imaging systems : Partial coherence in imaging
(220.3740) Optical design and fabrication : Lithography

ToC Category:
Optical Design and Fabrication

Original Manuscript: June 30, 2008
Revised Manuscript: September 16, 2008
Manuscript Accepted: September 21, 2008
Published: November 11, 2008

Xu Ma and Gonzalo Arce, "Binary mask optimization for inverse lithography with partially coherent illumination," J. Opt. Soc. Am. A 25, 2960-2970 (2008)

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  1. A. K. Wong, Resolution Enhancement Techniques, Vol. 1 (SPIE Press, 2001). [CrossRef]
  2. S. A. Campbell, The Science and Engineering of Microelectronic Fabrication, 2nd ed. (Publishing House of Electronics Industry, 2003).
  3. F. Schellenberg, “Resolution enhancement technology: The past, the present, and extensions for the future,” Proc. SPIE 5377, 1-20 (2004). [CrossRef]
  4. F. Schellenberg, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2004).
  5. L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, “Tcad development for lithography resolution enhancement,” IBM J. Res. Dev. 45, 651-665 (2001). [CrossRef]
  6. A. Poonawala and P. Milanfar, “Mask design for optical microlithography--An inverse imaging problem,” IEEE Trans. Image Process. 16, 774-788 (2007). [CrossRef] [PubMed]
  7. S. Sherif, B. Saleh, and R. Leone, “Binary image synthesis using mixed integer programming,” IEEE Trans. Image Process. 4, 1252-1257 (1995). [CrossRef] [PubMed]
  8. Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semicond. Manuf. 5, 138-152 (1992). [CrossRef]
  9. Y. C. Pati and T. Kailath, “Phase-shifting masks for microlithography: automated design and mask requirements,” J. Opt. Soc. Am. A 11, 2438-2452 (1994). [CrossRef]
  10. A. Erdmann, R. Farkas, T. Fuhner, B. Tollkuhn, and G. Kokai, “Towards automatic mask and source optimization for optical lithography,” Proc. SPIE 5377, 646-657 (2004). [CrossRef]
  11. L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): What is the impact to the photomask industry?” Proc. SPIE 6283, 62830X-1 (2006). [CrossRef]
  12. Y. Granik, “Illuminator optimization methods in microlithography,” Proc. SPIE 5524, 217-229 (2004). [CrossRef]
  13. Y. Granik, “Fast pixel-based mask optimization for inverse lithography,” J. Microlithogr., Microfabr., Microsyst. 5, 043002 (2006). [CrossRef]
  14. A. Poonawala and P. Milanfar, “Opc and psm design using inverse lithography: A non-linear optimization approach,” Proc. SPIE 6154, 1159-1172 (2006).
  15. X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Proc. SPIE 6520, 65200U (2007). [CrossRef]
  16. X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15, 15066-15079 (2007). [CrossRef] [PubMed]
  17. B. Salik, J. Rosen, and A. Yariv, “Average coherent approximation for partially coherent optical systems,” J. Opt. Soc. Am. A 13, 2086-2090 (1996). [CrossRef]
  18. A. K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005). [CrossRef]
  19. 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, 2770-2777 (1982). [CrossRef] [PubMed]
  20. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  21. R. Wilson, Fourier Series and Optical Transform Techniques in Contemporary Optics (Wiley, 1995).
  22. N. Cobb and A. Zakhor, “Fast sparse aerial image calculation for opc,” Proc. SPIE 2440, 313-327 (1995). [CrossRef]
  23. C. Vogel, Computational Methods for Inverse Problems (SIAM Press, 2002). [CrossRef]

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