Discrete relaxation method for hybrid e-beam and triple patterning lithography layout decomposition

Abstract

Hybrid electron beam lithography (EBL) and triple patterning lithography (TPL) is an advanced technology for IC manufacture. To solve the hybrid EBL and TPL layout decomposition problem (HETLD), we propose a discrete relaxation method in this paper. Existed works hard to evaluate the quality of the obtained results theoretically. Our discrete relaxation is the first approach which can be used to evaluate the solution quality. First, we introduce an extended minimum weight dominating set coloring problem (EMDSC). We show that the EMDSC problem is a discrete relaxation of the HETLD problem, which is solved by an integer linear programming (ILP) approach. Second, we legalize the relaxation solution to a feasible solution of the initial problem by inserting stitches and assigning EBLs. Experimental results show that our method achieves the near-optimal solution.

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Acknowledgements

This work was supported in part by Young Scientists Fund and the National Natural Science Foundation of China (NSFC) under Grants No. 61907024, the Natural Science Foundation of Fujian Province under Grants No. 2020J05161, and the Starting Research Fund from Minnan Normal University (Project No. KJ18009).

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Correspondence to Xingquan Li.

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Li, X., Li, J., Wu, H. et al. Discrete relaxation method for hybrid e-beam and triple patterning lithography layout decomposition. J Ambient Intell Human Comput (2021). https://doi.org/10.1007/s12652-021-02939-x

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Keywords

  • VLSI circuit manufacture
  • Electron beam lithography
  • Triple patterning lithography
  • Layout decomposition
  • Discrete relaxation