ROAD: Routability Analysis and Diagnosis Framework Based on SAT Techniques

Routability diagnosis has increasingly become the bottleneck in detailed routing for sub-10nm technology due to the limited tracks, high density, and complex design rules. The conventional ways to examine the routability of detailed routing are ILP- and SAT-based techniques. However, once we identify the routability, the diagnosis remains an open problem for physical designers. In this paper, we propose a novel framework, called ROAD, which diagnoses explicit reasons for routing failures. The proposed ROAD framework utilizes a diagnosis-friendly SAT formulation to represent design's layout and diagnoses the routability with SAT solving techniques. Based on the diagnosis, ROAD provides human-interpretable explanations for conflicted routing conditions. To show the practical value of our framework, we also generate comprehensive test-sets that enable exhaustive exploration of layouts based on Rent's rule. We demonstrate that ROAD successfully examines conflict causes for diverse pin layouts. Throughout extensive diagnosis, we also present several key findings for design failure. ROAD performs routability diagnosis within 2 minutes on average for 90 grids testsets, while diagnosing the exact causes of routing failures in terms of congestion and conditional design rules.