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Non-stitch Triple Patterning- Aware Routing Based on Conflict Graph Pre-coloring Po-Ya Hsu Yao-Wen Chang
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Outline INTRODUCTION THE NON-STITCH TRIPLE PATTERNING-AWARE ROUTING ALGORITHM EXPERIMENTAL RESULTS CONCLUSIONS
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INTRODUCTION Before the next-generation lithography technologies are mature for production, multiple patterning lithography is a dominating solution for nanometer circuit designs [9].
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INTRODUCTION Double patterning lithography is the simplest case of multiple patterning lithography and can reduce the feature size down below 32nm [4] by using two photo masks. Triple patterning lithography uses one more mask to manufacture a layout and becomes a feasible method to improve the feature size down below 14nm [15], even below 10nm [14].
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INTRODUCTION An earlier work shows that most of the hard-to-decompose patterns are generated from the detailed routing stage. Thus it is desirable to address the multiple patterning-aware routing problem that considers the multiple patterning decomposability during routing.
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INTRODUCTION Coloring (mask) conflicts are resolved by stitch insertion which is a layout decomposition solution partitioning a single pattern into multiple photo masks. Stitch insertion may incur stitch overlay errors, which would significantly reduce yield and increase cost.
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INTRODUCTION Leading foundries such as TSMC directly prohibit stitch insertion in their design methodologies. How to minimize color conflict counts without any stitch insertion during routing becomes a timely issue for industry production.
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THE NON-STITCH TRIPLE PATTERNING-AWARE ROUTING ALGORITHM Our non-stitch triple patterning-aware routing algorithm has to solve the two main problems: (1) conflict graph pre-coloring and (2)pre-coloring-based non-stitch routing
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Potential Color Difference Estimation We use a global-routing-based estimator with A*-search routing to find possible routing paths.
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Potential Color Difference Estimation
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Conflict Graph Construction
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Conflict Graph Pre-coloring Algorithm We formulate the pre-coloring problem into the maximum 3-cut problem. Recently, Ling et al. [13] proposed a variable neighborhood stochastic (VNS)meta-heuristic which can obtain high-quality solutions efficiently. In our conflict graph pre-coloring algorithm, we use the VNS meta- heruistic for its efficiency.
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Conflict Graph Pre-coloring Algorithm
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Pre-coloring-based Non-stitch Routing Algorithm To eliminate the self-crossing net problem, our graph model has the property that a net will not change its color during routing and will not generate any self-crossing path. In our graph model, each grid node at the coordinate (x, y, z) contains three graph vertices.
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Pre-coloring-based Non-stitch Routing Algorithm
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Feedback Pre-coloring-based Non-stitch Routing Scheme
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EXPERIMENTAL RESULTS We implemented our triple patterning-aware non-stitch routing algorithm in the C++ programming language and conducted our experiments on a Linux machine with 24 Intel 2.00 GHz CPUs and 72 GB memory.
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EXPERIMENTAL RESULTS
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CONCLUSIONS This paper has presented the first non-stitch triple patterning-aware routing algorithm. Compared with the extension of the state-of-the-art work [16], the experimental results have shown that our algorithm can obtain non- stitch routing results with no color conflicts effectively and efficiently.
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