A cost-driven fracture heuristics to minimize external sliver length

Abstract

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%.

Shot overlap model-based fracturing for edge-based OPC layouts

“…3 Many existing fracturing approaches focus on reducing sliver length. 13,14 In addition, Spence et al have demonstrated that the number of shots is directly correlated with the write-time. 5 While there are algorithms which simultaneously minimize sliver number and length along with number of shots, 1, 2 they ignore the underlying physics behind the mask writing process; rather, they solve a simpler geometric partitioning problem by introducing rules to capture the manufacturing parameters.…”

Design for manufacturability and reliability in extreme-scaling VLSI

“…[92,93] formulate this problem to an ILP, and also propose some speed-up techniques. Ma et al [94] present a heuristic algorithm for rectangle fracturing and sliver reduction. Compared to rectangle fracturing, the L-shape fracturing is an effective way to further reduce the number of shots [95][96][97].…”

L-Shape based Layout Fracturing for E-Beam Lithography

“…Recently, Ma et. al [11] presented a heuristic algorithm to generate rectangular shots and further reduce the sliver. Compared with the rectangular fracturing problem, the L-shape fracturing problem is new and there is only limited work, mostly describing methodology, but no systematic algorithm has been proposed so far.…”

“…The experimental results show that our algorithms are very promising for both shot count reduction and sliver minimization. In addition, DLF can even achieve significant speed-up compared with previous state-of-the-art rectangular fracturing algorithm [11].…”