ABSTRACT
As the technology migrates into the deep submicron manufacturing(DSM) era, the critical dimension of the circuits is getting smaller than the lithographic wavelength. The unavoidable light diffraction phenomena in the sub-wavelength technologies have become one of the major factors in the yield rate. Optical proximity correction (OPC) is one of the methods adopted to compensate for the light diffraction effect as a post layout process.However, the process is time-consuming and the results are still limited by the original layout quality. In this paper, we propose a maze routing method that considers the optical effect in the routing algorithm. By utilizing the symmetrical property of the optical system, the light diffraction is efficiently calculated and stored in tables. The costs that guide the router to minimize the optical interferences are obtained from these look-up tables. The problem is first formulated as a constrained maze routing problem, then it is shown to be a multiple constrained shortest path problem. Based on the Lagrangian relaxation method, an effective algorithm is designed to solve the problem.
- R. K. Ahuja, T. L. Magnanti, and J. B. Orlin. "Network Flows: Theory, Algorithms, and Applications". Prentice Hall, 1993. Google ScholarDigital Library
- N. Cobb and A. Zakhor. "Large Area Phase-Shift Mask Design". SPIE, 2197:348--359, 1994.Google Scholar
- N. Cobb, A. Zakhor, and E. Miloslavsky. "Mathematical and CAD Framework for Proximity Correction". SPIE, 2726:208--222, 1996.Google Scholar
- T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. "Introduction to Algorithms". MIT Press, 2001. Google ScholarDigital Library
- C.-C. Fu, T. Yang, and D. R. Stone. "Enhancement of lithography patterns by using serif features". IEEE Trans. Electron Devices, 38(12):2599--2603, Dec. 1991.Google ScholarCross Ref
- K. Harazaki, Y. Hasegawa, Y. Shichijo, H. Tabuchi, and K. Fujii. "High Accurate Optical Proximity Correction under the Influences of Lens Aberration in 0.15 um Logic Process ". In International Microprocesses and Nanotechnology Conference, pages 14--15, 2000.Google Scholar
- M. D. Levenson, N. Viswanathan, and R. A. Simpson. "Improving Resolution in Photolithography with a Phase-Shifting Mask". IEEE Trans. Electron Devices, 29(12):1828--1836, Dec. 1982.Google ScholarCross Ref
- C. A. Mack. "Understanding focus effects in submicrometer optical lithography: a review". Optical Engineering, 32(10):2350--2362, Oct. 1993.Google ScholarCross Ref
- Y. Pati, Y.-T. Wang, J.-W. Liang, and T. Kailiath. "Phase-Shift Masks: Automated Design and Mask Requirements". SPIE, 2197:314--327, 1994.Google Scholar
- F. Schellenberg. "Design for manufacturing in the semiconductor industry: the litho/ design workshop". 12th Internatioal Conference on VLSI Design, pages 111--119, Jan. 1999. Google ScholarDigital Library
- TSMC. In U.S. Technology Symposium, 2003.Google Scholar
- K. Yamamoto, S. Kobayashi, T. Uno, T. Kotani, S. Tanaka, S. Inoue, S. Watanabe, and H. Higurashi. "Hierarchical optical proximity correction on contact hole layers". In International Microprocesses and Nanotechnology Conference, pages 40--41, 2000.Google ScholarCross Ref
Index Terms
- Optical proximity correction (OPC): friendly maze routing
Recommendations
ELIAD: efficient lithography aware detailed router with compact post-OPC printability prediction
DAC '08: Proceedings of the 45th annual Design Automation ConferenceIn this paper, we present ELIAD, an efficient lithography aware detailed router to optimize silicon image after optical proximity correction (OPC) in a correct-by-construction manner. We first propose a compact post-OPC litho-metric for a detailed ...
Multilevel Full-Chip Gridless Routing With Applications to Optical-Proximity Correction
To handle modern routing with nanometer effects, we need to consider designs with variable wire/via widths and spacings, for which gridless-routing approaches are desirable due to its great flexibility. In this paper, we introduce a gridless-routing ...
Multilevel full-chip gridless routing considering optical proximity correction
ASP-DAC '05: Proceedings of the 2005 Asia and South Pacific Design Automation ConferenceTo handle modern routing with nanometer effects, we need to consider designs of variable wire widths and spacings, for which gridless routers are desirable due to their great flexibility. The gridless routing is much more difficult than the grid-based ...
Comments