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

在先进的超大规模集成电路(VLSI)设计中，由于铜基互连线尺寸的缩小和电流密度的增加，电迁移(EM)对于先进的超大规模集成电路(VLSI)设计来说是一个重要的可靠性问题和限制因素。因此，未来的芯片预计会比前几代老化得更快。虽然在电磁建模和评估技术方面取得了新的进展，但大规模电网的快速、准确的电磁分析和自动优化仍然具有挑战性，因为需要基于物理的建模，这涉及到求解大型互连中的静水应力偏微分方程组。对于全芯片级的EM管理来说，这变得更加困难。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(CNNS)和科学机器学习(SciML)方法，已经成为解决偏微分方程(PDE)问题的传统数值分析技术的有前途的解决方案。在本论文中，无监督物理信息/约束神经网络(Pinn/PCNN)框架显示出强大的能力，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偏微分方程组问题。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方法表现出缓慢的收敛速度，如果它们真的收敛的话。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，修复EM引起的故障或损坏以在设计和运行时实现预期的EM平均故障时间仍然具有挑战性。本项目开发的工具将有助于加深对这一重要问题的认识，减少互补金属氧化物半导体芯片的寿命可靠性问题。本项目将开发基于PINN/PCNN框架的基于学习的新型EM分析和高效的机器学习加速的VLSI芯片纳米级全芯片EM固定和运行管理方法。首先，该项目将探索新的基于SciML的解决方案，如增强型Pinn/PCNN方法，用于多节段互连树的静水压力分析。在这些方法的基础上，将发展考虑焦耳加热效应的全芯片多物理耦合电磁诱导IR降(即电压降低)分析和电网寿命估计。其次，该项目将在DNN的帮助下开发高效的全芯片EM感知电网优化技术，以及一种动态运行时EM感知管理方法来识别处理器的真正热点。该项目将通过利用训练的DNN模型的可微性来研究DNN加速的全芯片电网优化，以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的方法来评估热点，并开发一种动态运行时EM生命周期管理方法，考虑到处理器的实际热点。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.