Layer Assignment Problem for Three-Layer Routing
IEEE Transactions on Computers
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Note: MAX-CUT and MAX-BISECTION are NP-hard on unit disk graphs
Theoretical Computer Science
Layout decomposition for double patterning lithography
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Double patterning technology friendly detailed routing
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Robust layer assignment for via optimization in multi-layer global routing
Proceedings of the 2009 international symposium on Physical design
Double patterning lithography friendly detailed routing with redundant via consideration
Proceedings of the 46th Annual Design Automation Conference
GREMA: graph reduction based efficient mask assignment for double patterning technology
Proceedings of the 2009 International Conference on Computer-Aided Design
A matching based decomposer for double patterning lithography
Proceedings of the 19th international symposium on Physical design
Post-routing layer assignment for double patterning
Proceedings of the 16th Asia and South Pacific Design Automation Conference
An efficient approach to multilayer layer assignment with an application to via minimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Congestion-Constrained Layer Assignment for Via Minimization in Global Routing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Hi-index | 0.00 |
Double patterning lithography is promising for 32nm technology and beyond. In this technique, one-layer layout is decomposed into two masks. Much work has been proposed to solve feature decomposition problem. However, post-routing layer assignment, which determines the layout features on each layer, thus having great impact on double patterning related parameters, has not been explored in the merit of double patterning. In this paper, we formulate post-routing layer assignment for double patterning problem for the first time. Both this problem and traditional single layer double patterning problem are proved to be NP-complete. An effective algorithm is further proposed to solve it. The algorithm consists of three major phases: multi-layer assignment to minimize double patterning risks, single layer double patterning, and via reduction. Since blind post-routing layer assignment may jeopardize timing critical paths obtained in the routing stage, our algorithm also considers total wire length and coupling capacitance on critical paths as timing metrics. Experimental results on Collaborative Benchmarking Laboratory benchmarks demonstrate the effectiveness of our algorithm. In comparison with single layer double patterning, our method achieves 62% and 11% average reduction on unresolvable conflicts and stitches, respectively, with only 0.30% increase of via number in layouts. Furthermore, the via height and parallel wire length on critical paths are decreased by 8% and 14% on average.