A new figure fracturing algorithm for variable-shaped EB exposure-data generation

Nakao, H.; Terai, M.; Moriizumi, Koichi

doi:10.1002/(sici)1520-6440(200008)83:8<87::aid-ecjc10>3.0.co;2-1

Cited by 5 publications

(6 citation statements)

References 1 publication

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“…The requirements of the fracture pattern can be summarized as follows: 7,8 (1) Mask pattern must be fractured into a set of trapezoids without overlap. Overlapping regions on the mask are overexposed and scatter more electrons to the periphery, leading to variation of the desired trapezoid dimension.…”

Section: Fracturing Problem Formulationmentioning

confidence: 99%

“…7 In Fig. 3(a), if the segment is deleted during the rectangle combination, then becomes a singular segment.…”

Section: Case Imentioning

confidence: 99%

“…[4][5][6][7][8][9] Ohtsuki, et al developed an algorithm to decompose the rectilinear polygons into minimum number of rectangles by searching the set of maximum independent degenerate lines. 5 A rectilinear polygon only has horizontal and vertical edges.…”

Section: Introductionmentioning

confidence: 99%

“…4 Nakao, et al introduced a fracturing approach based on "relation graph" to suppress sliver and CD partition, and to minimize the trapezoid count. 7 Kahng, et al suggested a fracturing method relying on integer linear programming (ILP) and a set of heuristics to speed it up. 8 The ILP method takes into account all specified requirements, such as trapezoid count, sliver length, keeping intact slant edges and CDs, and maximum shot size limitation.…”

Section: Introductionmentioning

confidence: 99%

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A cost-driven fracture heuristics to minimize external sliver length

Jiang

Zakhor

2011

SPIE Proceedings

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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%.

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Section: Fracturing Problem Formulationmentioning

confidence: 99%

“…7 In Fig. 3(a), if the segment is deleted during the rectangle combination, then becomes a singular segment.…”

Section: Case Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A cost-driven fracture heuristics to minimize external sliver length

Jiang

Zakhor

2011

SPIE Proceedings

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“…Nakao et al 1 have developed a fairly complicated ad hoc heuristic based on the generalization of the same bipartite graph which takes in account all other constraints except the constraint (b). In fact, they have introduced a different objective -minimize the weighted length of slivers and slices cutting through critical features -while minimizing shot number over all obtained solutions that are (sub)optimal with respect to the new objective.…”

Section: Previous Workmentioning

confidence: 99%

Yield- and cost-driven fracturing for variable shaped-beam mask writing

Kahng

Zelikovsky

2004

SPIE Proceedings

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Mask manufacturing for the approaching 90nm and 65nm nodes increasingly deploys variable shaped beam (VSB) mask writing machines. This has led to high interest in the fracturing methods which are at the heart of layout data preparation for VSB mask writing. In this paper, we set out the main requirements for fracturing and suggest a new solution approach based on integer linear programming (ILP). The main advantage of the new method is that the ILP finds optimal solutions while being flexible enough to take into account all specified requirements. We also suggest several decomposition (polygon partitioning) heuristics which speed up the ILP approach. Experimental comparisons with leading industry tools show significant improvement in quality, as well as acceptable scalability, of the proposed methods. In particular, our fracturing solutions reduce shot count (which reflects write time and mask cost) and dramatically reduce sliver count (which reflects the risk of mask critical-dimension errors). Our results reveal significant headroom that can be exploited by future design-to-mask tools to reduce the manufacturing variability and cost of IC designs.

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Resolution enhancement optimization methods in optical lithography with improved manufacturability

2011

J. Micro/Nanolith. MEMS MOEMS

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A new figure fracturing algorithm for variable-shaped EB exposure-data generation

Cited by 5 publications

References 1 publication

A cost-driven fracture heuristics to minimize external sliver length

A cost-driven fracture heuristics to minimize external sliver length

Yield- and cost-driven fracturing for variable shaped-beam mask writing

Resolution enhancement optimization methods in optical lithography with improved manufacturability

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