TSV-Aware Analytical Placement for 3-D IC Designs Based on a Novel Weighted-Average Wirelength Model

摘要

Through-silicon vias (TSVs) are required for transmitting signals among different dies for the 3-D integrated circuit (IC) technology. The significant silicon areas occupied by TSVs bring critical challenges for 3-D IC placement. Unlike most published 3-D placement works that only minimize the number of TSVs during placement due to the limitations in their techniques, this paper proposes a new 3-D cell placement algorithm that can additionally consider the sizes of TSVs and the physical positions for TSV insertion during placement. The algorithm consists of three stages: 1) 3-D analytical global placement with density optimization and whitespace reservation for TSVs; 2) TSV insertion and TSV-aware legalization; and 3) layer-by-layer detailed placement. In particular, the global placement is based on a novel weighted-average (WA) wirelength model, giving the first published model that can outperform the well-known log-sum-exp wirelength model theoretically and empirically. Also, a scheme is proposed to enhance the numerical stability of the WA wirelength model. Furthermore, 3-D routing can easily be accomplished by traditional 2-D routers since the physical positions of TSVs are determined during placement. Experimental results show the effectiveness of our algorithm. Compared with state-of-the-art 3-D cell placement works, our algorithm can achieve the best routed wirelength, TSV counts, and total silicon area, in shortest running time.