OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 23 — Nov. 12, 2007
  • pp: 15066–15079

Generalized inverse lithography methods for phase-shifting mask design

Xu Ma and Gonzalo R. Arce  »View Author Affiliations


Optics Express, Vol. 15, Issue 23, pp. 15066-15079 (2007)
http://dx.doi.org/10.1364/OE.15.015066


View Full Text Article

Enhanced HTML    Acrobat PDF (217 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Optical proximity correction (OPC) and phase shifting masks (PSM) are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In this paper, we develop generalized gradient-based RET optimization methods to solve for the inverse lithography problem, where the search space is not constrained to a finite phase tessellation but where arbitrary search trajectories in the complex space are allowed. Subsequent mask quantization leads to efficient design of PSMs having an arbitrary number of discrete phases. In order to influence the solution patterns to have more desirable manufacturability properties, a wavelet regularization framework is introduced offering more localized flexibility than total-variation regularization methods traditionally employed in inverse problems. The proposed algorithms provide highly effective four-phase PSMs capable of generating mask patterns with arbitrary Manhattan geometries. Furthermore, a double-exposure optimization method for general inverse lithography is developed where each exposure uses an optimized two-phase mask.

© 2007 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(100.3190) Image processing : Inverse problems
(100.7410) Image processing : Wavelets
(220.3740) Optical design and fabrication : Lithography

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: August 15, 2007
Revised Manuscript: September 21, 2007
Manuscript Accepted: October 26, 2007
Published: October 31, 2007

Citation
Xu Ma and Gonzalo R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," Opt. Express 15, 15066-15079 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15066


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. V. G. J. Schneider, J. Murakowski and D. W. Prather, "Combination lithography for photoniccrystal circuits,"J.of Vacuum Science and Technology B 22(1), 146-151 (2004). [CrossRef]
  2. J. M. M. J. M. P. Yao, G. J. Schneider and D.W. Prather, "Micro/nano lithography realized by chemical printing," in Proceedings of SPIE - The International Society for Optical Engineering, vol. 6151I of Emerging Lithographic Technologies X, p. 61511N (2006).
  3. D. W. P. E. D. W. P. Yao, G. J. Schneider and D. J. O’Brien, "Fabrication of three-dimensional photonic crystals with multilayer photolithography," Optics Express 13, 2370-2376 (2005). [CrossRef] [PubMed]
  4. B. L. M. J. M. D. W. P. E. D. W. P. Yao, G. J. Schneider and D. J. O’Brien, "Multilayer three-dimensional photolithography with traditional planar method," Applied Physics Letters 85, 2920-2922 (2004). [CrossRef]
  5. A. K. Wong, Resolution enhancement techniques, vol. 1 (SPIE Press, 2001). [CrossRef]
  6. S. A. Campbell, The science and engineering of microelectronic fabrication, 2nd ed. (Publishing House of Electronics Industry, 2003).
  7. F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future, Optical Microlithography," Proc. SPIE 5377, 1-20 (2004). [CrossRef]
  8. F. Schellenberg, Resolution enhancement techniques in optical lithography (SPIE Press, 2004).
  9. A. W. M. L. W. L. L. Liebmann, S. Mansfield and T. Dunham, "TCAD development for lithography resolution enhancement," IBM Journal of Research and Development pp. 651-665 (2001). [CrossRef]
  10. N. S. V. M. D. Levenson and R. A. Simpson, "Improving resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron Devices ED-29, 1828-1836 (1982). [CrossRef]
  11. B. S. S. Sherif and R. Leone, "Binary image synthesis using mixed integer programming," IEEE Transactions on Image Processing 4(9), 1252-1257 (1995). [CrossRef] [PubMed]
  12. Y. Liu and A. Zakhor, "Binary and phase shifting mask design for optical lithography," IEEE Transactions on Semiconductor Manufacturing 5(2) (1992). [CrossRef]
  13. Y. C. Pati and T. Kailath, "Phase-shifting masks for microlithography: Automated design and mask requirements," Optical Society of America 11 (1994).
  14. T. F. B. T. A. Erdmann, R. Farkas and G. Kokai, "Towards automatic mask and source optimization for optical lithography," Optical Microlithography, Proc. SPIE 5377, 646-657 (2004).
  15. Y. L. L. Pang and D. Abrams, "Inverse lithography technology (ILT): What is the impact to the photomask industry?" Proc. SPIE (2006). [CrossRef]
  16. Y. Granik, "Illuminator optimization methods in microlithography," Optical Microlithography Proc. SPIE 5754, 217-229 (2005).
  17. A. Poonawala and P. Milanfar, "OPC and PSM design using inverse lithography: A non-linear optimization approach," in Proceedings of the SPIE, vol. 6154, pp. 1159-1172 (San Jose, CA, 2006).
  18. C. Vogel, Computational methods for inverse problems (SIAM Press, 2002). [CrossRef]
  19. X. Ma and G. R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," in Proceedings of SPIE, vol. 65200U (2007).
  20. A. Poonawala and P. Milanfar, "Double Exposure Mask Synthesis using Inverse Lithography," submitted toJournal of Microlithography, Microfabrication, and Microsystems.
  21. M. Born and E. Wolfe, Principles of optics (Cambridge University Press, 1999).
  22. N. Cobb and A. Zakhor, "Fast sparse aerial image calculation for OPC," BACUS Symposium on Photomask Technology, Proc. SPIE 2440, 313-327 (1995).

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