Optimization of mask shot count using MB-MDP and lithography simulation

Chua, Gek Soon; Wang, Wei Long; Choi, B. C.; Zou, Yi; Tabery, Cyrus; Bork, Ingo; Nguyen, Tam H.; Fujimura, Aki

doi:10.1117/12.897037

“…4,5 Recently, D2S has introduced the concept of model-based mask data preparation by simulating the electron beam (e-beam) mask writing process. [6][7][8][9] Their approach operates on the mask that has been optimized by pixel-based OPC. 24,25 They place overlapping shots in such a way that the simulated mask image approximates the desired target mask.…”

Section: Model Based Fracturingmentioning

confidence: 99%

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

Jiang

¹

,

Zakhor

²

2014

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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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“…Fracturing these polygons using traditional methods with acceptable fidelity can dramatically increase the shot count [24]. To manage the shot count of such complex patterns, Chua et al propose model-based fractur-ing [7]. Two key features of model-based fracturing distinguish it from traditional mask fracturing:…”

Section: Introductionmentioning

confidence: 99%

Benchmarking of mask fracturing heuristics

Chan¹,

Gupta²,

Han³

et al. 2014

2014 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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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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“…Although each shot is rectangular, the e-beam proximity effect blurs its boundary [7]. As a result, the developed mask pattern is different from the union of rectangular shots.…”

Section: Mask Fracturing Problemmentioning

confidence: 99%

“…Fracturing these polygons using traditional methods with acceptable fidelity can dramatically increase the shot count [24]. To manage the shot count of such complex patterns, Chua et al propose model-based fracturing [7]. Two key features of model-based fracturing distinguish it from traditional mask fracturing:…”

Section: Introductionmentioning

confidence: 99%

Benchmarking of Mask Fracturing Heuristics

Chan

¹

,

Gupta

²

,

Han

³

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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Optimization of mask shot count using MB-MDP and lithography simulation

Cited by 10 publications

References 13 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

Benchmarking of Mask Fracturing Heuristics

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