A cost-driven fracture heuristics to minimize external sliver length

In optical lithography, mask pattern is first fractured into basic trapezoids, and then fabricated by the variable shaped beam mask writing machine. Ideally, mask fracture tools aim at both suppressing the trapezoid count to speed up the write time, and minimizing the external sliver length to improve CD uniformity. However, the increasing transistor density, smaller feature sizes, and the aggressive use of resolution enhancement techniques pose new challenges to write time and CD uniformity. In this paper, we propose a fracture heuristics to improve the sliver performance of current commercially available fracturing tools. In the proposed approach, the mask layout is first decomposed into elemental rectangles by the rays emitted from each concave corner. Then, a rectangle combination technique is applied to search and eliminate the external slivers from the polygon boundaries by moving them to the center. This approach guarantees that the resulting trapezoid count approaches the theoretical lower bound. Compared to a current commercially available fracturing tools, our proposed approach effectively reduces the external sliver length by 8% to 13%.