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, the problem of minimizing the number of phase conflicts that must be removed to ensure 2-colorability of the conflict graph is transformed to the T-join problem. Second, we give new exact and approximate algorithms for the resulting T-join problem. The exact algorithm is linear in space and substantially faster for sparse graphs than previously known algorithms. The output of the approximate algorithm is much closer to the optimum than the algorithm suggested in [9]. These algorithms are applied within a "'one-shot" phase assignment method suggested in [9] for co-optimization of layout and phase assignment for alternating phaseshifting masks. Preliminary computational experience is pmmising.
Abstract| Chemical-mechanical polishing CMP and other manufacturing steps in very deep submicron VLSI have varying e ects on devic e and inter connect features, dep ending on local char acteristics of the layout. T o enhance manufacturability and performance p r edictability, we seek to make the layout uniform with respect to prescribed densit ycriteria, by inserting ll" geometries into the layout. We propose several new Monte-Carlo based lling methods with fast dynamic data structures and report the tradeo between runtime and accuracy for the suggested methods. Compared to existing linear programming based a p p r oaches, our Monte-Carlo methods seem very promising as they produc enearly-optimal solutions within reasonable runtimes.
Highly mutable RNA viruses such as influenza A virus, human immunodeficiency virus and hepatitis C virus exist in infected hosts as highly heterogeneous populations of closely related genomic variants.
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