Routability-driven Analytical Placement with Precise Penalty Models for Large-Scale 3D ICs

Quality of a true 3D placement approach greatly relies on the correctness of the models used in its formulation. However, the models used by previous approaches are not precise enough. Moreover, they do not actually place TSVs which makes their approach unable to get accurate wirelength and construct a correct congestion map. Besides, they rarely discuss routability which is the most important issue considered in 2D placement. To resolve this insufficiency, this paper proposes more accurate models to estimate placement utilization and TSV number by the softmax function which can align cells to exact tiers. Moreover, we propose a fast parallel algorithm to update the locations of TSVs when cells are moved during optimization. Finally, we present a novel penalty model to estimate routing overflow of regions covered by cells and inflate cells in congested regions according to this model. Experimental results show that our methodology can obtain better results than previous works.