High-density through-substrate vias (TSVs) enable 2.5D/3D heterogeneous integration but introduce significant signal-integrity and thermal-reliability challenges due to electrical coupling, insertion loss, and self-heating. Conventional full-wave finite-element method (FEM) simulations provide high accuracy but become computationally prohibitive for large design-space exploration. This work presents a scalable electro-thermal modeling and optimization framework that combines physics-informed analytical modeling, graph neural network (GNN) surrogates, and full-wave sign-off validation. A multi-conductor analytical model computes broadband S-parameters and effective anisotropic thermal conductivities of TSV arrays, achieving $5\%-10\%$ relative Frobenius error (RFE) across array sizes up to $15x15$. A physics-informed GNN surrogate (TSV-PhGNN), trained on analytical data and fine-tuned with HFSS simulations, generalizes to larger arrays with RFE below $2\%$ and nearly constant variance. The surrogate is integrated into a multi-objective Pareto optimization framework targeting reflection coefficient, insertion loss, worst-case crosstalk (NEXT/FEXT), and effective thermal conductivity. Millions of TSV configurations can be explored within minutes, enabling exhaustive layout and geometric optimization that would be infeasible using FEM alone. Final designs are validated with Ansys HFSS and Mechanical, showing strong agreement. The proposed framework enables rapid electro-thermal co-design of TSV arrays while reducing per-design evaluation time by more than six orders of magnitude.

翻译：高密度衬底通孔（TSV）实现了2.5D/3D异构集成，但由于电耦合、插入损耗和自热效应，带来了显著的信号完整性和热可靠性挑战。传统的全波有限元法（FEM）仿真虽然精度高，但在大规模设计空间探索中计算代价过高。本工作提出一种可扩展的电热建模与优化框架，融合了物理信息解析建模、图神经网络（GNN）代理模型以及全波签收验证。基于多导体解析模型计算TSV阵列的宽带S参数和等效各向异性热导率，在阵列尺寸达15×15范围内实现了5%-10%的相对Frobenius误差（RFE）。基于物理信息的GNN代理模型（TSV-PhGNN）在解析数据上训练并通过HFSS仿真微调后，可推广至更大阵列，RFE低于2%且方差近乎恒定。将该代理模型集成至多目标Pareto优化框架中，目标函数涵盖反射系数、插入损耗、最坏串扰（近端串扰/远端串扰）及等效热导率。数分钟内即可探索数百万种TSV配置，实现采用FEM无法完成的穷举式布局与几何优化。最终设计经Ansys HFSS与Mechanical验证，结果高度一致。本框架在将单个设计评估时间降低六个数量级以上的同时，实现了TSV阵列的快速电热协同设计。