Placement is a critical stage for VLSI routability optimization. A placement engine without considering the layout congestion might lead to poor solutions with routing failures. This paper introduces a Coulomb force-based global placement framework that addresses global and local routing congestions. We first present a routing path-based cell padding strategy for local congestion mitigation. Then, we construct a routability-aware placement model that utilizes virtual Coulomb forces to eliminate crucial global congestion. Compared with a leading academic placer, RePlAce, and the advanced commercial tool, Innovus, the experimental results on industrial benchmark suites show that our proposed algorithm achieves the best routability within the shortest runtime.

Routability estimation identifies potentially congested areas in advance to achieve high-quality routing solutions. To improve the routing quality, this paper presents a deep learning-based congestion estimation algorithm that applies the estimation to a global router. Unlike existing methods based on traditional compressed 2D features for model training and prediction, our algorithm extracts appropriate 3D features from the placed netlists. Furthermore, an improved RUDY (Rectangular Uniform wire DensitY) method is developed to estimate 3D routing demands. Besides, we develop a congestion estimator by employing a U-net model to generate a congestion heatmap, which is predicted before global routing and serves to guide the initial pattern routing of a global router to reduce unexpected overflows. Experimental results show that the Pearson Correlation Coefficient (PCC) between actual and our predicted congestion is high at about 0.848 on average, significantly higher than the counterpart by 21.14%. The results also show that our guided routing can reduce the respective routing overflows, wirelength, and via count by averagely 6.05%, 0.02%, and 1.18%, with only 24% runtime overheads, compared with the state-of-the-art CUGR global router that can balance routing quality and efficiency very well. In particular, our work provides a new generic machine learning model for not only routing congestion estimation demonstrated in this paper, but also general layout optimization problems.