As minimum feature size keeps shrinking, and the next generation lithography (e.g, EUV) further delays, double patterning lithography (DPL) has been widely recognized as a feasible lithography solution in 20nm technology node. However, as technology continues to scale to 14/10nm, DPL begins to show its limitations and usually generates too many undesirable stitches. Triple patterning lithography (TPL) is a natural extension of DPL to conquer the difficulties and achieve a stitch-free layout decomposition. In this paper, we study the standard cell based row-structure layout decomposition problem in TPL. Although the general TPL layout decomposition problem is NP-hard, in this paper we will show that for standard cell based TPL layout decomposition problem, it is polynomial time solvable. We propose a polynomial time algorithm to solve the problem optimally and our approach has the capability to find all stitch-free decompositions. Color balancing is also considered to ensure a balanced triple patterning decomposition. To speed up the algorithm, we further propose a hierarchical algorithm for standard cell based layout, which can reduce the run time by 34.5% on average without sacrificing the optimality. We also extend our algorithm to allow stitches for complex circuit designs, and our algorithm guarantees to find optimal solutions with minimum number of stitches.
Digital Microfluidic Biochip (DMFB) is a revolutionary technology for performing lab-on-a-chip experiments. Comparing to traditional direct-addressing design of DMFB, CrossReferencing Biochip is a flexible design which not only helps to reduce pin number on chip but also brings down manufacturing cost. Following the generally accepted DMFB top-down design methodology, namely task scheduling, resource binding, module placement, droplet routing, previous works that focus on cross-referencing biochip routing are all based on the placement result generated for directaddressing biochip. In this paper, we present an ILP-based placement method that first utilizes the property of crossreferencing for the purpose of optimizing routing. Furthermore, one previously ignored electrode interference problem on modules (blocks) is addressed in this paper. Real-life bioassay protocol based benchmarks are used to evaluate the proposed method. Experimental results show that the placement result generated by our placer yields better routing result comparing with those from placer for direct-addressing DMFB.
Triple patterning lithography (TPL) has been recognized as one of the most promising candidates for 14/10nm technology node. Apart from obtaining legal TPL decompositions, various concerns have been raised by the designers, among them consistently assigning the same pattern for the same type of standard cells and balancing the usage of the three masks are two most critical ones. In this paper, a hybrid approach (SAT followed by a sliding-window approach) is proposed targeting at these two problems. To assign the same pattern for the same type of standard cell, we pre-color the boundary polygons of each type of cell by solving a small SAT problem. Following that we propose a sliding-window based approach to compute a locally balanced decomposition. Our algorithm guarantees to find a feasible solution if one exists. Experimental results verify that the problem can be solved very efficiently with the proposed algorithm. Superior locally balanced decompositions are achieved compared with the previous approach in [19].
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