A recursive cost-based approach to fracturing

Jiang, Shangliang; Ma, Xu; Zakhor, Avideh

doi:10.1117/12.879583

Cited by 9 publications

(3 citation statements)

References 8 publications

(9 reference statements)

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“…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.…”

Section: Mask Manufacturing Qualitymentioning

confidence: 99%

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

Jiang

Zakhor

2014

SPIE Proceedings

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In this paper, we develop a novel fracturing algorithm with shot overlap that is tailored towards rectilinear masks, such as those generated via edge based OPC software. Our proposed fracturing algorithm generates both the location and dosage of shots given the mask layout and mask making parameters. In the first step we heuristically cover the mask polygon with overlapping shots. Next, we incorporate the forward scattering and resist model in a least squares problem to compute the best dosage for all shots. Finally, we update the locations of the shot edges by computing the edge placement error between our simulated contour and the desired contour. One unique feature of our algorithm is that it can readily trade off between edge placement error and shot count by adjusting two input parameters. Compared to a commercially available non-overlapping shot software package, for a 400µm × 400µm micron SRAM unit with about 1 million polygons, our algorithm results in a 23% reduction in shot count, while increasing the weighted average EPE from 0.7 to 1 nanometers.

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Section: Mask Manufacturing Qualitymentioning

confidence: 99%

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

Jiang

Zakhor

2014

SPIE Proceedings

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“…A faster heuristic based on selection of rays from concave corners is also proposed by the same authors [19]. Jiang and Zakhor propose a recursive algorithm to minimize a weighted sum of shot count and slivers [15].…”

Section: Introductionmentioning

confidence: 99%

Benchmarking of Mask Fracturing Heuristics

Chan

Gupta

Han

et al. 2017

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Aggressive resolution enhancement techniques such as inverse lithography (ILT) often lead to complex, non-rectilinear mask shapes which make mask writing extremely slow and expensive. To reduce shot count of complex mask shapes, mask writers allow overlapping shots, due to which the problem of fracturing mask shapes with minimum shot count is NP-hard. The need to correct for e-beam proximity effect makes mask fracturing even more challenging. Although a number of fracturing heuristics have been proposed, there has been no systematic study to analyze the quality of their solutions. In this work, we propose a new method to generate benchmarks with known optimal solutions that can be used to evaluate the suboptimality of mask fracturing heuristics. We also propose a method to generate tight upper and lower bounds for actual ILT mask shapes by formulating mask fracturing as an integer linear program and solving it using branch and price. Our results show that a state-of-the-art prototype [version of] capability within a commercial EDA tool for e-beam mask shot decomposition can be suboptimal by as much as 3.7× for generated benchmarks, and by as much as 3.6× for actual ILT shapes.

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“…In order to take more detailed specification, such as silver reduction, into account, the integer linear programming (ILP) algorithm is introduced to approach it with constraints [18]. A recursive cost-based algorithm is developed by Jiang et al to decrease the external silver length and trapezoid numbers [19]. Other than the fracturing algorithms, the mask writers also evolved from non-overlapping shots to overlapping ones so that the shot count can be reduced [20].…”

Section: Introductionmentioning

confidence: 99%

Sparse nonlinear inverse imaging for shot count reduction in inverse lithography

Liu

et al. 2015

Opt. Express

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Inverse lithography technique (ILT) is significant to reduce the feature size of ArF optical lithography due to its strong ability to overcome the optical proximity effect. A critical issue for inverse lithography is the complex curvilinear patterns produced, which are very costly to write due to the large number of shots needed with the current variable shape beam (VSB) writers. In this paper, we devise an inverse lithography method to reduce the shot count by incorporating a model-based fracturing (MBF) in the optimization. The MBF is formulated as a sparse nonlinear inverse imaging problem based on representing the mask as a linear combination of shots followed by a threshold function. The problem is approached with a Gauss-Newton algorithm, which is adapted to promote sparsity of the solution, corresponding to the reduction of the shot count. Simulations of inverse lithography are performed on several test cases, and results demonstrate reduced shot count of the resulting mask.

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A recursive cost-based approach to fracturing

Cited by 9 publications

References 8 publications

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

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

Benchmarking of Mask Fracturing Heuristics

Sparse nonlinear inverse imaging for shot count reduction in inverse lithography

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