1. : Grid graph :Draw two rays from each concave point Rays are divided into non-intersected ray-segments Conflict pair: two ray segments from the same point Rule 1: One of ray segments from any concave point must be used Rule 2: At most one ray segment in each conflict pair can be used Rule 3: No internal concave points Fracture = select ray segments obeying the rules Fast Yield-Driven Fracture for Variable Shaped-Beam Mask Writing Andrew B. Kahng 1, Xu Xu 1, and Alex Z. Zelikovsky 2 1. CSE Dept. University of California, San Diego 2. CS Department, Georgia State University The aggressive use of RET techniques with each successive process generation have presented new challenges for current fracture tools, which are at the heart of layout data preparation. One main challenge is to reduce the number of small dimension trapezoids (slivers) to improve mask yield. Some commercial tools are available for handling the sliver minimization problem in fracture. The integer linear programming (ILP) method can significantly reduce sliver number at the expense of long runtime. In this work, we propose a new ray-segment selection heuristic which can find a near-optimal fracture solution in practical time while being flexible enough to take into account all specified requirements. We also extend the heuristics with the introduce of auxiliary ray-segments. Compared with state-of-art sliver-driven fracturing tools, the proposed method reduces the number of slivers in the fractures of two industry testcases by 76.7% and 58.6%, respectively, without inflating the runtime and shot count. Similarly, compared with the previous ILP based fracture, the new method reduces the number of slivers by 56.1% and 2.2% respectively, with more than 60X speedup and negligent shot count overhead. Fracture: Decompose a list of polygons into trapezoids (shots) ABSTRACTFracture in Mask Data Process : Sliver : A shot whose minimum dimension <  Sliver number Mask CD variation Mask yield Sliver Minimization Challenge Gain Based Selection Heuristics For any ray segment i, weight of i W(i)= increased sliver number after using i For any conflict pair (i, j), gain of i G(i)=W(j)-W(i) = sliver number saved by using I Initially, the set S = {All ray segments from concave points} While (S≠Ø) - Choose one ray segment i with the largest gain, delete its conflict pair from the S - If there is a ray segment j connected with i, add j into S - Update the gains of ray segments in S Kahng et al., “Yield- and Cost-Driven Fracturing for Variable Shaped-Beam Mask Writing”, BACUS 2004 Nakao et al. “A new figure fracturing algorithm for variable-shaped EB exposure-data generation”, ECJ 2003 Cobb et al. “High performance Hierarchical fracturing” SPIE 4754 Cobb et al. “Hierarchical GDSII based fracturing and job deck system” SPIE 4562 Experimental Results CONCLUSIONS BIBLIOGRAPHY Compared with two commercial fracture tools: - Reduce sliver number by 76.7% and 58.6% - No runtime overhead Compared with previous ILP method: - Reduce sliver number by 28.9% - 60x speedup Future work: fracture-friendly OPC Yield Driven Fracture Yield Driven Fracture Problem Given: List of rectilinear polygons P Slivering size  Partition: P into non-overlapping trapezoidal shots To minimize: Number of shots and number of slivers Layout Extraction RET Circuit Design Tape Out Job Decomposition Mask Data Preparation Mask Making Writing Inspection Metrology Tonality PEC Fracture Job Finishing Fracture <  2 shots Ray-Segment Selection Formulation concave point rays ray segments No sliver with good fracture Conflict pair concave pointsconvex points 0 1 0 1 0 1 1 In S Chosen Auxiliary Ray Segments Sliver number may be reduced with the introduction of auxiliary ray segments Auxiliary ray segment addition rule: If two rays form a sliver whose length grater than 3 , and no rays partition the sliver in the middle, add one auxiliary ray in the middle. Method Design ADesign B shotssliversCPUshotssliversCPU Tool A107546111017335115720 Tool B104554451017130107970 Tool C975578621719565023 ILP9750417134176842750222 Proposed978618311765626914 0 sliver sliver >3 