Concurrent Guiding Template Assignment and Redundant via Insertion for DSA-MP Hybrid Lithography

Ou, Jiaojiao; Yu, Bei; Pan, David Z.

doi:10.1145/2872334.2872352

Cited by 17 publications

(4 citation statements)

References 14 publications

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“…Heuristics and exact approaches for multiple patterning with DSA (and variants) have been investigated in [5,12,26,37,38,43]. Note that in all studies, the number of patterning steps is fixed and the goal is to group vias into feasible guiding patterns so as to minimize the number of conflicts remaining (allowing sometimes for the insertion of redundant vias).…”

Section: Mask After 3-mask Splitmentioning

confidence: 99%

“…In principle, it would be possible to use the exact methods developed in some prior studies in parallel: run the algorithm for a given number of patterning steps and then verify for which number of patterning steps zero coloring conflicts emerge. However, most of these methods either employ heuristics to accelerate finding a coloring solution at a large scale (and hence no longer guaranteeing optimality) [37,43], propose formulations that do not work for any number of patterning steps [5,26], or exploit additional structures and/or placement options [12,26,38]. In our case, given that the objective is to formally find the minimum number of patterning steps required for (large scale) layouts, we do not build on the methods developed in prior research.…”

Section: Mask After 3-mask Splitmentioning

confidence: 99%

“…Variable λ i ∈ {0, 1} indicates whether color i is chosen, and x i g ∈ {0, 1} indicates whether a group g ∈ V is colored with color i. Constraint (37) imposes that each via is assigned to exactly one group and one color. Constraint (38) imposes that groups in conflict (for which there are two vias that are too close) have to receive different colors.…”

Section: Toward a Column-generation Approach For The Naïve Modelmentioning

confidence: 99%

See 2 more Smart Citations

Combining lithography and Directed Self Assembly for the manufacturing of vias: Connections to graph coloring problems, integer programming formulations, and numerical experiments

Ait-Ferhat

Juliard

Stauffer

et al. 2020

European Journal of Operational Research

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In this paper, we investigate the manufacturing of vias in integrated circuits with a new technology combining lithography and Directed Self Assembly (DSA). Optimizing the production time and costs in this new process entails minimizing the number of lithography steps, which constitutes a generalization of graph coloring. We develop integer programming formulations for several variants of interest in the industry, and then study the computational performance of our formulations on true industrial instances. We show that the best integer programming formulation achieves good computational performance, and indicate potential directions to further speed-up computational time and develop exact approaches feasible for production.

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Section: Mask After 3-mask Splitmentioning

confidence: 99%

Section: Mask After 3-mask Splitmentioning

confidence: 99%

Section: Toward a Column-generation Approach For The Naïve Modelmentioning

confidence: 99%

See 1 more Smart Citation

Combining lithography and Directed Self Assembly for the manufacturing of vias: Connections to graph coloring problems, integer programming formulations, and numerical experiments

Ait-Ferhat

Juliard

Stauffer

et al. 2020

European Journal of Operational Research

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show abstract

“…Several works [8], [9], [10], [11] have addressed the problem of simultaneous DSA Grouping and Mask assignment for hybrid DSA-MP technologies. Ou et al [12] solved the same problem while adding redundant vias, while Lin et al [13] added cut redistribution. DSA-aware routing has been addressed in [14] for DSA+Double Patterning (DP) technology.…”

Section: Prior Work In Dsa-mpmentioning

confidence: 99%

Hotspot-aware DSA Grouping and Mask Assignment

Badr,

Gupta

2017

Preprint

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In Directed Self Assembly (DSA), poor printing of guiding templates can cause misassembly resulting in high defect probability. Therefore, hotspots should be avoided in the choice of the DSA groups. Accordingly, Directed Self-Assembly (DSA) technologies which use Multiple Patterning (MP) to print the guiding templates need to be aware of hotspots during the DSA grouping and MP Decomposition. In this paper, we present a hotspot-aware heuristic for DSA grouping and MP decomposition. Results show that that the proposed heuristic eliminates 78% of the hotspots and conflicts that result from using a hotspotunaware grouping and decomposition algorithm. In comparison to the optimal solution using Integer Linear Programming, the proposed heuristic results in 24% more violations.

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Cut Optimization

Shim¹,

Shin²

2018

Physical Design and Mask Synthesis for Directed Self-Assembly Lithography

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Concurrent Guiding Template Assignment and Redundant via Insertion for DSA-MP Hybrid Lithography

Cited by 17 publications

References 14 publications

Combining lithography and Directed Self Assembly for the manufacturing of vias: Connections to graph coloring problems, integer programming formulations, and numerical experiments

Combining lithography and Directed Self Assembly for the manufacturing of vias: Connections to graph coloring problems, integer programming formulations, and numerical experiments

Hotspot-aware DSA Grouping and Mask Assignment

Cut Optimization

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