Effective decomposition algorithm for self-aligned double patterning lithography

Self-aligned double patterning (SADP) lithography is a novel lithography technology that has the intrinsic capability to reduce the overlay in the double patterning lithography (DPL). Although SADP is the critical technology to solve the lithography difficulties in sub-32nm 2D design, the problems of how to decompose a layout with reasonable overlay and how to perform a decomposability check remain open with no published work. In this paper, by formulating the problem into a SAT formation, we can solve the above two problems optimally. This is the first published paper with a detailed algorithm to perform the SADP decomposition. In a layout, we can efficiently check whether a layout is decomposable. For a decomposable layout, our algorithm guarantees to find a decomposition solution with reasonable overlay reduction requirement. With little changes on the clauses in the SAT formula, we can address the decomposition problem for both the positive tone process and the negative tone process. Experimental results validate our method, and decomposition results for Nangate Open Cell Library and larger test cases are also provided with competitive run times.