New graph bipartizations for double-exposure, bright field alternating phase-shift mask layout
Proceedings of the 2001 Asia and South Pacific Design Automation Conference
Bright-Field AAPSM Conflict Detection and Correction
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
A new algorithm for layout of dark field alternating phase shifting masks
GLSVLSI '05 Proceedings of the 15th ACM Great Lakes symposium on VLSI
Wire sizing and spacing for lithographic printability and timing optimization
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
WISDOM: wire spreading enhanced decomposition of masks in double patterning lithography
Proceedings of the International Conference on Computer-Aided Design
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We describe new, efficient algorithms for layout modification and phase assignment for dark field alternating-type phase shifting masks in the single exposure regime. We make the following contributions. First, we suggest new two-coloring and compaction approach that simultaneously optimizes layout and phase assignment which is based on planar embedding of an associated conflict graph. We also describe additional approaches to cooptimization of layout and phase assignment for alternating PSM. Second, we give optimal and fast algorithms to minimize the number of phase conflicts that must be removed to ensure two colorability of the conflict graph. We reduce this problem to the T-join problem which asks for a minimum weight edge set A such that a node u is incident to an odd number of edges of A if u belongs to a given node subset T of a weighted graph. Third, we suggest several practical algorithms for the T-join problem. In sparse graphs, our algorithms are faster than previously known methods. Computational experience with industrial VLSI layout benchmarks shows the advantages of the new algorithms