Optimal Layout Decomposition for Double Patterning Technology

1. Optimal Layout Decomposition for Double PatterningTechnology Xiaoping Tang, MinsikCho IBM T.J. Waston Research Center ICCAD 2011

2. Outline • Introduction • Problem formulation • Decomposition method • Experimental results • Conclusion

3. Introduction • DPT decomposes a single layout into two masks and applies double exposure to print the shapes in the layout. • DPT requires accurate overlay control. • minimize the number of stitches (overlay) • conjectured to be NP-hard-ILP-Heuristics

4. Problem formulation • Given a single layer of layout and a DPT distance threshold, find a decomposed layout which consists of two sets of shapes, such that no shapes within the same set is closer than the distance threshold, the union of the two sets of shapes is equivalent to the original layout, and the number of stitches is minimized.

5. Decomposition method

6. Constraint graph • A graph node is constructed to represent a segment. If two segments from different shapes are closer than the distance threshold, an arc is constructed between the two nodes. • The graph can be divided into “components” • The number of stitches within a component is a constant.

7. Stitch graph • The stitch graph is constructed as follows.

8. The min-cut in the stitch graph gives the decomposition solution to the original layout with the minimum number of stitches.

10. Experimental results

12. Conclusion • The problem of minimizing the number of stitches in DPT decomposition is conjectured to be NP-hard. • We show that the problem is actually in P and present a method to decompose a layout for DPT and minimize the number of stitches optimally. • The method is even faster than the fast heuristics.