SHF:Small: Learning-based Fast Analysis and Fixing for Electromigration Damage

由于亚3nm技术中铜基互连的尺寸缩小和电流密度增加，电迁移（EM）具有重要的可靠性问题和先进的超大规模集成电路（VLSI）设计限制因素。因此，未来的芯片预计将比前几代芯片老化得更快。虽然电磁建模和评估技术取得了最新进展，但由于需要基于物理的建模，包括求解大型互连中流体静力应力的偏微分方程，因此对大型电网网络进行快速准确的电磁分析和自动优化仍然具有挑战性。这对于全芯片级EM管理来说变得更加困难。机器学习技术，特别是基于深度神经网络（dnn）的深度学习，如卷积神经网络（cnn）和科学机器学习（SciML）方法，已经成为求解偏微分方程（PDEs）的传统数值分析技术的有前途的解决方案。无监督物理信息/约束神经网络（PINN/PCNN）框架在scil领域显示出强大的能力，如无网格和参数化数值解。然而，现有的PINN/PCNN工作只能解决边界条件简单的小PDE问题。对于设计自动化中常见的具有数百万变量的大型工程问题，PINN/PCNN方法即使收敛，也表现出缓慢的收敛。此外，由于基于灵敏度的优化框架和缺乏足够的片上温度传感器，在设计和运行时，修复电磁诱发的故障或损坏以达到预期的电磁平均故障时间仍然具有挑战性。在这个项目中开发的工具将有助于推进对这一重要问题的理解，并减少互补金属氧化物半导体（CMOS）芯片的寿命可靠性问题。该项目将开发基于PINN/PCNN框架的新型基于学习的EM分析，以及用于纳米级VLSI芯片的高效机器学习加速全芯片EM固定和运行时管理方法。首先，该项目将探索新的基于sciml的解决方案，如增强的PINN/PCNN方法，用于多段互连树的静水应力分析。在这些方法的基础上，将开发考虑焦耳热效应的全芯片多物理场耦合电磁感应红外降（即电压降低）分析和电网寿命估计。其次，该项目将在深度神经网络的帮助下，开发高效的全芯片电磁感知电网优化技术，以及动态运行时电磁感知管理方法，以识别处理器的真正热点。该项目将通过利用训练好的DNN模型的可微分性来研究DNN加速全芯片电网优化，从而允许基于一系列线性规划技术的快速灵敏度计算。最后，我们将设计一种基于dnn的方法来估计热点，并开发一种动态运行时EM寿命管理方法，考虑处理器的实际热点。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Electromigration (EM) has a significant reliability issue and limiting factor for advanced very large scale integration (VLSI) designs due to the shrinking size and increasing current density of copper-based interconnects in sub-3nm technology. As a result, future chips are expected to age faster than previous generations. While recent advances in EM modeling and assessment techniques have been made, fast and accurate EM analysis and automatic optimization for large-scale power grid networks remain challenging due to the need for physics-based modeling that involves solving partial differential equations for hydrostatic stress in large interconnects. This becomes even more difficult for full-chip level EM management. Machine learning techniques, particularly deep learning based on deep neural networks (DNNs), such as convolutional neural networks (CNNs), and scientific machine learning (SciML) approaches, have emerged as promising solutions to traditional numerical analysis techniques for solving partial differential equations (PDEs). The unsupervised physics-informed/constrained neural network (PINN/PCNN) framework in the SciML field shows powerful capabilities such as mesh-free and parametrized numerical solutions. However, existing PINN/PCNN works can only solve small PDE problems with simple boundary conditions. For large engineering problems with millions of variables commonly seen in design automation, PINN/PCNN approaches show slow convergence, if they converge at all. Additionally, fixing EM-induced failure or damage to achieve the expected EM mean time to failure at both design and run times remains challenging due to the sensitivity-based optimization framework and lack of sufficient on-chip temperature sensors. The tools to be developed in this project will be valuable to advancing the understanding of this important problem and curtailing the lifetime reliability issue of complementary metal-oxide semiconductor (CMOS) chips.This project will develop novel learning-based EM analysis based on PINN/PCNN framework and efficient machine learning-accelerated full-chip EM fixing and run-time management methods for VLSI chips in the nanometer regime. First, the project will explore new SciML-based solutions such as enhanced PINN/PCNN methods, for hydrostatic stress analysis for multi-segment interconnect trees. On top of those methods, full-chip multi-physics coupled EM induced IR drop (i.e., reduction in voltage) analysis and lifetime estimation for power grid networks considering Joule heating effects will be developed. Second, the project will develop efficient full-chip EM-aware power grid optimization techniques, aided by DNNs, along with a dynamic run-time EM-aware management method to identify the real hotspots of processors. The project will investigate DNN-accelerated full-chip power grid optimization by exploiting the differentiability of the trained DNN models to allow for rapid sensitivity calculations based on a sequence of linear programming techniques. Finally, we will devise a DNN-based method to estimate hotspots and develop a dynamic run-time EM lifetime management method, considering the actual hotspots of processors.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.