Incorporating cut redistribution with mask assignment to enable 1D gridded design

Abstract

1D gridded design is one of the most promising solutions that can enable the scaling to 10nm technology node and beyond. Line-end cuts are needed to fabricate 1D layouts, where two techniques are available to resolve the conflicts between cuts: cut redistribution and cut mask assignment. In this paper, we consider incorporating the two techniques to enable the manufacturing of cut patterns in 1D gridded design. We first present an accurate integer linear programming (ILP) formulation that can solve the co-optimization of cut redistribution and mask assignment optimally. In addition, we propose an efficient graph-theoretic approach based on a novel integrated graph model and a longest-path-based refinement algorithm. Experimental results demonstrate that our graphtheoretic approach is orders of magnitude faster than the ILP-based method and meanwhile can obtain very comparable results. Comparing with the method that solves mask assignment and cut redistribution optimally but separately, our graph-theoretic approach that solves the two tasks simultaneously can achieve 95.0× smaller cost and 84.8× speedup on average.