For advanced CMOS processes, inverse lithography promises better patterning fidelity than conventional mask correction techniques due to a more complete exploration of the solution space. However, the success of inverse lithography relies highly on customized cost functions whose design and know-how have rarely been discussed. In this paper, we investigate the impacts of various objective functions and their superposition for inverse lithography patterning using a generic gradient descent approach. We investigate the most commonly used objective functions, which are the resist and aerial images, and also present a derivation for the aerial image contrast. We then discuss the resulting pattern fidelity and final mask characteristics for simple layouts with a single isolated contact and two nested contacts. We show that a cost function composed of a dominant resist-image component and a minor aerial-image or image-contrast component can achieve a good mask correction and contour targets when using inverse lithography patterning.

© 2010 OSA

1. D. S. Abrams and L. Pang, “Fast inverse lithography technology,” Proc. SPIE 6154, 534–542 (2006).
2. C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, “Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation,” Proc. SPIE 6154, 61541M (2006). [CrossRef]
3. L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): What is the impact to the photomask industry?” Proc. SPIE 6283, 62830X (2006). [CrossRef]
4. S. Sherif, B. Saleh, and R. De Leone, “Binary image synthesis using mixed linear integer programming,” IEEE Trans. Image Process. 4(9), 1252–1257 (1995). [CrossRef] [PubMed]
5. K. Nashold and B. Saleh, “Image construction through diffraction-limited high-contrast imaging systems: An iterative approach,” J. Opt. Soc. Am. A 2(5), 635–643 (1985). [CrossRef]
6. B. Saleh and S. Sayegh, “Reductions of errors of microphotographic reproductions by optical corrections of original masks,” Opt. Eng. 20, 781–784 (1981).
7. Y. Granik, “Fast pixel-based mask optimization for inverse lithography,” J. Microlith. Microfab. Microsyst. 5, 043002 (2006). [CrossRef]
8. A. Poonawala and P. Milanfar, “Mask design for optical microlithography--an inverse imaging problem,” IEEE Trans. Image Process. 16(3), 774–788 (2007). [CrossRef] [PubMed]
9. X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15(23), 15066–15079 (2007). [CrossRef] [PubMed]
10. 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(19), 14746–14760 (2008). [CrossRef] [PubMed]
11. J.-C. Yu, P. Yu, and H.-Y. Chao, “Model-based sub-resolution assist features using an inverse lithography method,” Proc. SPIE 7140, 714014 (2008). [CrossRef]
12. X. Ma and G. Arce, “Binary mask optimization for inverse lithography with partially coherent illumination,” J. Opt. Soc. Am. A 25(12), 2960–2970 (2008). [CrossRef]
13. X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express 16(24), 20126–20141 (2008). [CrossRef] [PubMed]
14. X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783–5793 (2009). [CrossRef] [PubMed]
15. M. Born, and E. Wolf, Principles of Optics, 7th(expanded) ed. (Cambridge University Press, 1999).
16. J. W. Goodman, Statistical Optics (John Wiley and Sons, 1985).
17. A. K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005).
18. N. B. Cobb, Fast optical and process proximity correction algorithms for integrated circuit manufacturing (University of California at Berkeley, Berkely, California, 1998).
19. E. Y. Lam and A. K. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express 17(15), 12259–12268 (2009). [CrossRef] [PubMed]
20. J. S. Leon, Linear Algebra with applications, 6th ed. (Prentice-Hall, 2002).
21. 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(15), 2770–2777 (1982). [CrossRef] [PubMed]
22. W. Huang, C. Lin, C. Kuo, C. Huang, J. Lin, J. Chen, R. Liu, Y. Ku, and B. Lin, “Two threshold resist models for optical proximity correction,” Proc. SPIE 5377, 1536–1543 (2001). [CrossRef]
23. M. Minoux, Mathematical programming theory and algorithms (John Wiley and Sons, Chichester, 1986).
24. E. Hecht, Optics, 4thed (Addison Wesley, San Francisco, 2002).

Appl. Opt.

• 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(15), 2770–2777 (1982). [CrossRef] [PubMed]

IEEE Trans. Image Process.

• S. Sherif, B. Saleh, and R. De Leone, “Binary image synthesis using mixed linear integer programming,” IEEE Trans. Image Process. 4(9), 1252–1257 (1995). [CrossRef] [PubMed]
• A. Poonawala and P. Milanfar, “Mask design for optical microlithography--an inverse imaging problem,” IEEE Trans. Image Process. 16(3), 774–788 (2007). [CrossRef] [PubMed]

J. Microlith. Microfab. Microsyst.

• Y. Granik, “Fast pixel-based mask optimization for inverse lithography,” J. Microlith. Microfab. Microsyst. 5, 043002 (2006). [CrossRef]

J. Opt. Soc. Am. A

• K. Nashold and B. Saleh, “Image construction through diffraction-limited high-contrast imaging systems: An iterative approach,” J. Opt. Soc. Am. A 2(5), 635–643 (1985). [CrossRef]
• X. Ma and G. Arce, “Binary mask optimization for inverse lithography with partially coherent illumination,” J. Opt. Soc. Am. A 25(12), 2960–2970 (2008). [CrossRef]

Opt. Eng.

• B. Saleh and S. Sayegh, “Reductions of errors of microphotographic reproductions by optical corrections of original masks,” Opt. Eng. 20, 781–784 (1981).

Opt. Express

• X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15(23), 15066–15079 (2007). [CrossRef] [PubMed]
• 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(19), 14746–14760 (2008). [CrossRef] [PubMed]
• X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express 16(24), 20126–20141 (2008). [CrossRef] [PubMed]
• X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783–5793 (2009). [CrossRef] [PubMed]
• E. Y. Lam and A. K. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express 17(15), 12259–12268 (2009). [CrossRef] [PubMed]

Proc. SPIE

• W. Huang, C. Lin, C. Kuo, C. Huang, J. Lin, J. Chen, R. Liu, Y. Ku, and B. Lin, “Two threshold resist models for optical proximity correction,” Proc. SPIE 5377, 1536–1543 (2001). [CrossRef]
• J.-C. Yu, P. Yu, and H.-Y. Chao, “Model-based sub-resolution assist features using an inverse lithography method,” Proc. SPIE 7140, 714014 (2008). [CrossRef]
• D. S. Abrams and L. Pang, “Fast inverse lithography technology,” Proc. SPIE 6154, 534–542 (2006).
• C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, “Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation,” Proc. SPIE 6154, 61541M (2006). [CrossRef]
• L. Pang, Y. Liu, and D. Abrams, “Inverse lithography technology (ILT): What is the impact to the photomask industry?” Proc. SPIE 6283, 62830X (2006). [CrossRef]

Other

• M. Minoux, Mathematical programming theory and algorithms (John Wiley and Sons, Chichester, 1986).
• E. Hecht, Optics, 4thed (Addison Wesley, San Francisco, 2002).
• M. Born, and E. Wolf, Principles of Optics, 7th(expanded) ed. (Cambridge University Press, 1999).
• J. W. Goodman, Statistical Optics (John Wiley and Sons, 1985).
• A. K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005).
• N. B. Cobb, Fast optical and process proximity correction algorithms for integrated circuit manufacturing (University of California at Berkeley, Berkely, California, 1998).
• J. S. Leon, Linear Algebra with applications, 6th ed. (Prentice-Hall, 2002).

Click here to see a list of articles that cite this paper

Related Journal Articles

• Multichannel sampling schemes for optical imaging systems (AO)
• Increased field of view through optical multiplexing (OE)
• Fast source optimization involving quadratic line-contour objectives for the resist image (OE)
• High-resolution lightfield photography using two masks (OE)
• Design of an image restoration algorithm for the TOMBO imaging system (JOSAA)

Related Conference Papers

• Imaging Systems with Extreme Form Factors
• Time Resolved Optical Imaging with Patterned Light for Pre-Clinical Studies
• Increased Field of View through Optical Multiplexing
• Coded Strobing Photography for High-Speed Periodic Events
• Quantum Inspired Imaging with Compressive Sensing