先进制程技术下可布线性驱动的VLSI混合高度单元布局研究

随着先进制程技术持续演进，可布线性和混合高度标准单元库的运用给超大规模集成电路（VLSI）布局问题带来巨大的挑战。本项目研究可布线性驱动的VLSI混合高度单元布局问题。本项目拟采用在图像到图像的回归任务中表现优异的U-net模型，并直接提取三维的引脚密度、布线容量和线网密度特征来进行训练和预测，从而在布局阶段快速获取较为准确的布线拥塞图。接着，本项目通过构造解决布线拥塞的线网罚新模型，设计光滑函数来刻画VDD/VSS对齐约束，从而建立同时考虑VDD/VSS约束和布线拥塞的全局布局新模型，并设计基于广义增广拉格朗日法的算法来求解该模型。最后，本项目将建立考虑布线拥塞和引脚移动量的合法化模型，并设计基于模迭代的合法化算法和基于哈密顿路的单元交换来提高可布线性。本项目的研究将提出可布线性驱动的混合高度单元布局的新模型和新算法，最终形成一套速度快、效果好并可处理单元规模达到千万级的布局工具。

With the continuous development of advanced node technologies, routability and the popularity of mixed-cell-height standard cell libraries have brought great challenges to the very large scale integration (VLSI) placement problems. In this project, we will consider the routability-driven VLSI mixed-cell-height placement problem. We will use the U-net model that has an excellent performance in the image-to-image regression task, and directly extract the three-dimensional features (i.e., pin density, routing capacity, and net density) for training and prediction, so as to obtain a relatively accurate routing congestion map quickly during the placement stage. Then, we will construct a novel net penalty model to characterize routing congestion, design a smooth function to characterize VDD/VSS alignment constraint, and thus establish a new mathematical model for mixed-cell-height global placement considering both VDD/VSS alignment constraint and routing congestion. In order to solve the model efficiently, we will develop a novel global placement algorithm based on the generalized augmented Lagrangian method. Finally, we will build a legalization model considering routing congestion and pin movement, and design a legalization algorithm based on the modulus-based matrix splitting iteration method and a cell swapping based on the shortest Hamiltonian path to improve the routability. The outcomes of this project will be the new mathematical models and novel algorithms for routability-driven VLSI mixed-cell-height placement, and finally form the VLSI placement tool that can effectively and efficiently address the routability-driven mixed-cell-height placement problem with tens of millions of cells.