Non-stitch Triple Patterning- Aware Routing Based on Conflict Graph Pre-coloring Po-Ya Hsu Yao-Wen Chang

Outline INTRODUCTION THE NON-STITCH TRIPLE PATTERNING-AWARE ROUTING ALGORITHM EXPERIMENTAL RESULTS CONCLUSIONS

INTRODUCTION Before the next-generation lithography technologies are mature for production, multiple patterning lithography is a dominating solution for nanometer circuit designs [9].

INTRODUCTION Double patterning lithography is the simplest case of multiple patterning lithography and can reduce the feature size down below 32nm [4] by using two photo masks. Triple patterning lithography uses one more mask to manufacture a layout and becomes a feasible method to improve the feature size down below 14nm [15], even below 10nm [14].

INTRODUCTION An earlier work shows that most of the hard-to-decompose patterns are generated from the detailed routing stage. Thus it is desirable to address the multiple patterning-aware routing problem that considers the multiple patterning decomposability during routing.

INTRODUCTION Coloring (mask) conflicts are resolved by stitch insertion which is a layout decomposition solution partitioning a single pattern into multiple photo masks. Stitch insertion may incur stitch overlay errors, which would significantly reduce yield and increase cost.

INTRODUCTION Leading foundries such as TSMC directly prohibit stitch insertion in their design methodologies. How to minimize color conflict counts without any stitch insertion during routing becomes a timely issue for industry production.

THE NON-STITCH TRIPLE PATTERNING-AWARE ROUTING ALGORITHM Our non-stitch triple patterning-aware routing algorithm has to solve the two main problems: (1) conflict graph pre-coloring and (2)pre-coloring-based non-stitch routing

Potential Color Difference Estimation We use a global-routing-based estimator with A*-search routing to find possible routing paths.

Potential Color Difference Estimation

Conflict Graph Construction

Conflict Graph Pre-coloring Algorithm We formulate the pre-coloring problem into the maximum 3-cut problem. Recently, Ling et al. [13] proposed a variable neighborhood stochastic (VNS)meta-heuristic which can obtain high-quality solutions efficiently. In our conflict graph pre-coloring algorithm, we use the VNS meta- heruistic for its efficiency.

Conflict Graph Pre-coloring Algorithm

Pre-coloring-based Non-stitch Routing Algorithm To eliminate the self-crossing net problem, our graph model has the property that a net will not change its color during routing and will not generate any self-crossing path. In our graph model, each grid node at the coordinate (x, y, z) contains three graph vertices.

Pre-coloring-based Non-stitch Routing Algorithm

Feedback Pre-coloring-based Non-stitch Routing Scheme

EXPERIMENTAL RESULTS We implemented our triple patterning-aware non-stitch routing algorithm in the C++ programming language and conducted our experiments on a Linux machine with 24 Intel 2.00 GHz CPUs and 72 GB memory.

EXPERIMENTAL RESULTS

CONCLUSIONS This paper has presented the first non-stitch triple patterning-aware routing algorithm. Compared with the extension of the state-of-the-art work [16], the experimental results have shown that our algorithm can obtain non- stitch routing results with no color conflicts effectively and efficiently.