OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 7 — Jul. 1, 2012
  • pp: 1300–1312

Mask optimization approaches in optical lithography based on a vector imaging model

Xu Ma, Yanqiu Li, and Lisong Dong  »View Author Affiliations


JOSA A, Vol. 29, Issue 7, pp. 1300-1312 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001300


View Full Text Article

Enhanced HTML    Acrobat PDF (1025 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Recently, a set of gradient-based optical proximity correction (OPC) and phase-shifting mask (PSM) optimization methods has been developed to solve for the inverse lithography problem under scalar imaging models, which are only accurate for numerical apertures (NAs) of less than approximately 0.4. However, as lithography technology enters the 45 nm realm, immersion lithography systems with hyper-NA ( NA > 1 ) are now extensively used in the semiconductor industry. For the hyper-NA lithography systems, the vector nature of the electromagnetic field must be taken into account, leading to the vector imaging models. Thus, the OPC and PSM optimization approaches developed under the scalar imaging models are inadequate to enhance the resolution in immersion lithography systems. This paper focuses on developing pixelated gradient-based OPC and PSM optimization algorithms under a vector imaging model. We first formulate the mask optimization framework, in which the imaging process of the optical lithography system is represented by an integrative and analytic vector imaging model. A gradient-based algorithm is then used to optimize the mask iteratively. Subsequently, a generalized wavelet penalty is proposed to keep a balance between the mask complexity and convergence errors. Finally, a set of methods is exploited to speed up the proposed algorithms.

© 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

ToC Category:
Imaging Systems

History
Original Manuscript: November 30, 2011
Revised Manuscript: March 3, 2012
Manuscript Accepted: March 26, 2012
Published: June 14, 2012

Citation
Xu Ma, Yanqiu Li, and Lisong Dong, "Mask optimization approaches in optical lithography based on a vector imaging model," J. Opt. Soc. Am. A 29, 1300-1312 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-7-1300


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).
  2. X. Ma and G. R. Arce, Computational Lithography, 1st ed., Wiley Series in Pure and Applied Optics (Wiley, 2010).
  3. S. A. Campbell, The Science and Engineering of Microelectronic Fabrication, 2nd ed. (Oxford University, 2003).
  4. F. Schellenberg, “Resolution enhancement technology: the past, the present, and extensions for the future, optical microlithography,” Proc. SPIE 5377, 1–20 (2004). [CrossRef]
  5. F. Schellenberg, Selected Papers on Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2004).
  6. L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, “Tcad development for lithography resolution enhancement,” IBM J. Res. Devel. 45, 651–665 (2001). [CrossRef]
  7. 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]
  8. S. Sherif, B. Saleh, and R. Leone, “Binary image synthesis using mixed integer programming,” IEEE Trans. Image Process. 4, 1252–1257 (1995). [CrossRef]
  9. Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semicond. Manuf. 5, 138–152 (1992). [CrossRef]
  10. 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]
  11. Y. Granik, “Solving inverse problems of optical microlithography,” Proc. SPIE 5754, 506–526 (2004). [CrossRef]
  12. Y. Granik, “Fast pixel-based mask optimization for inverse lithography,” J. Microlith. Microfab. Microsyst. 5, 043002(2006). [CrossRef]
  13. 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]
  14. A. Poonawala and P. Milanfar, “Prewarping techniques in imaging: applications in nanotechnology and biotechnology,” Proc. SPIE 5674, 114–127 (2005). [CrossRef]
  15. A. Poonawala and P. Milanfar, “Mask design for optical microlithography—an inverse imaging problem,” IEEE Trans. Image Process. 16, 774–788 (2007). [CrossRef]
  16. A. Poonawala and P. Milanfar, “OPC and PSM design using inverse lithography: a non-linear optimization approach,” Proc. SPIE 6154, 1159–1172 (2006).
  17. A. Poonawala, Y. Borodovsky, and P. Milanfar, “Double exposure inverse lithography,” Microlithogr. World 16, 7–9 (2007).
  18. A. Poonawala and P. Milanfar, “Double exposure mask synthesis using inverse lithography,” J. Micro/Nanolith. MEMS MOEMS 6, 043001 (2007). [CrossRef]
  19. A. Poonawala and P. Milanfar, “A pixel-based regularization approach to inverse lithography,” Microelectron. Eng. 84, 2837–2852 (2007). [CrossRef]
  20. X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15, 15066–15079 (2007). [CrossRef]
  21. 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]
  22. X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express 16, 20126–20141 (2008). [CrossRef]
  23. X. Ma and G. R. Arce, “Pixel-based OPC optimization based on conjugate gradients,” Opt. Express 19, 2165–2180 (2011). [CrossRef]
  24. X. Ma and Y. Li, “Resolution enhancement optimization methods in optical lithography with improved manufacturability,” J. Micro/Nanolith. MEMS MOEMS 10, 023009 (2011). [CrossRef]
  25. X. Ma and G. R. Arce, “Binary mask optimization for forward lithography based on boundary layer model in coherent systems,” J. Opt. Soc. Am. A 26, 1687–1695 (2009). [CrossRef]
  26. X. Ma, G. R. Arce, and Y. Li, “Optimal 3D phase-shifting masks in partially coherent illumination,” Appl. Opt. 50, 5567–5576 (2011). [CrossRef]
  27. 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]
  28. N. Jia, A. K. Wong, and E. Y. Lam, “Robust mask design with defocus variation using inverse synthesis,” Proc. SPIE 7140, 71401W (2008). [CrossRef]
  29. E. Y. Lam and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express 17, 12259–12268 (2009). [CrossRef]
  30. 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, 14746–14760 (2008). [CrossRef]
  31. N. Jia and E. Y. Lam, “Machine learning for inverse lithography: Using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12, 045601 (2010). [CrossRef]
  32. Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17, 23690–23701 (2009). [CrossRef]
  33. Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express 19, 5511–5521(2011). [CrossRef]
  34. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19, 19384–19398 (2011). [CrossRef]
  35. J. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express 18, 23331–23342 (2010). [CrossRef]
  36. Y. Shen, N. Wong, and E. Y. Lam, “Aberration-aware robust mask design with level-set-based inverse lithography,” Proc. SPIE 7748, 77481U (2010). [CrossRef]
  37. G. M. Gallatin, “High-numerical-aperture scalar imaging,” Appl. Opt. 40, 4958–4964 (2001). [CrossRef]
  38. M. Yeung, “Modeling high numerical aperture optical lithography,” Proc. SPIE 922, 149–167 (1988).
  39. D. G. Flagello, “High numerical aperture imaging in homogeneous thin films,” Ph.D. dissertation (University of Arizona, 1993).
  40. T. V. Pistor, “Electromagnetic simulation and modeling with applications in lithography,” Ph.D. dissertation (University of California, Berkeley, 2001).
  41. K. Adam, Y. Granik, A. Torres, and N. Cobb, “Improved modeling performance with an adapted vectorial formulation of the Hopkins imaging equation,” Proc. SPIE 5040, 78–91 (2003). [CrossRef]
  42. 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]
  43. T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000). [CrossRef]
  44. 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]
  45. Y. Zhou and Y. Li, “Optimization of double bottom antireflective coating for hyper numerical aperture lithography,” Acta Opt. Sin. 28, 472–477 (2008). [CrossRef]
  46. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill Science, 1996).

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