Fast Physics-Based Electromigration Analysis for Full-Chip Networks by Efficient Eigenfunction-Based Solution
Fast Physics-Based Electromigration Analysis for Full-Chip Networks by Efficient Eigenfunction-Based Solution
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DOI：
10.1109/tcad.2020.3001264
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发表时间：
2021-03
影响因子：
2.9
通讯作者：
Xiaoyi Wang;Shaobin Ma;Chase Cook;Liang Chen;Jianlei Yang;Wenjian Yu
中科院分区：
文献类型：
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作者：
Xiaoyi Wang;Shaobin Ma;Chase Cook;Liang Chen;Jianlei Yang;Wenjian Yu
电迁移（EM）成为当前及未来10纳米及以下技术节点集成电路面临的最具挑战性的可靠性问题之一。本文提出了一种用于二维多分支互连树EM静水应力分析的新方法，这是大规模片上互连网络（如片上电源网格网络）EM可靠性评估的基础。所提方法基于本征函数技术，能够高效计算在不同电流密度和非均匀分布热效应作用下多分支互连树的静水应力演变。该方法能更高效地求解瞬态EM应力的偏微分方程，因为它无需像有限差分法和有限元法等数值方法那样在空间或时间上进行离散化。通过与解析解和商业工具对比，验证了所提瞬态分析方法的准确性。通过对实际电源/地网络的数值实验展示了该方法的收敛性，结果表明只需少量本征函数项就能获得精确解。由于其解析特性，所提方法还应用于高效的EM分析技术中，例如通过改进的二分算法搜索空洞形核时间。数值结果表明，所提方法比有限差分法快10到100倍，并且对于更大规模的互连树具有更好的扩展性。
Electromigration (EM) becomes one of the most challenging reliability issues for current and future ICs in 10-nm technology and below. In this article, a novel method is proposed for the EM hydrostatic stress analysis on 2-D multibranch interconnect trees, which is the foundation of the EM reliability assessment for large-scale on-chip interconnect networks, such as on-chip power grid networks. The proposed method, which is based on an eigenfunction technique, could efficiently calculate the hydrostatic stress evolution for multibranch interconnect trees stressed with different current densities and nonuniformly distributed thermal effects. The proposed method solves the partial differential equations of transient EM stress more efficiently since it does not require any discretization either spatially or temporally, which is in contrast to numerical methods, such as the finite difference method and finite element method. The accuracy of the proposed transient analysis approach is validated against the analytical solution and commercial tools. The convergence of the proposed method is demonstrated by numerical experiments on practical power/ground networks, showing that only a small number of eigenfunction terms are necessary for the accurate solution. Thanks to its analytical nature, the proposed method is also utilized in efficient EM analysis techniques, such as searching for the void nucleation time by a modified bisection algorithm. The numerical results show that the proposed method is 10X–100X faster than the finite difference method and scales better for larger interconnect trees.