用物理模型+神经网络，600万次设计优化仅需几分钟。
From Physics to Surrogate Intelligence: A Unified Electro-Thermo-Optimization Framework for TSV Networks
- 结合解析模型与图神经网络，快速估算TSV阵列电热特性。
- 对15×15阵列误差低于10%，更大阵列平均误差低于5%。
- 适合芯片封装设计人员做大规模布局优化，省时百万倍。
高密度通过基板通孔（TSVs）支持2.5D/3D异构集成，但因电气耦合、插入损耗和自加热带来显著信号完整性与热可靠性挑战。传统全波有限元法（FEM）仿真精度高，但大规模设计空间探索时计算成本过高。本文提出一种可扩展的电热建模与优化框架，融合物理引导的解析模型、图神经网络（GNN）代理模型及全波签核验证。多导体解析模型在高达15×15阵列下计算宽带S参数与有效各向异性热导率，相对弗罗贝尼乌斯误差（RFE）为5%–10%。基于解析数据训练并经HFSS仿真微调的物理引导GNN代理模型（TSV-PhGNN），在分布内大阵列上平均RFE低于5%。该代理模型集成至多目标帕累托优化框架，同时优化回波损耗、插入损耗、串扰（NEXT/FEXT）与有效热导率。可在数分钟内探索数百万种TSV配置，实现传统FEM无法企及的布局与几何优化。最终设计经Ansys HFSS与Mechanical验证，结果高度一致。该框架使TSV阵列的快速电热协同设计成为可能，单次评估耗时减少超过六数量级。
原文摘要 · Abstract (English)
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 $15\times15$. A physics-informed GNN surrogate (TSV-PhGNN), trained on analytical data and fine-tuned with HFSS simulations, generalizes to larger arrays with mean RFE below $5\%$ in-distribution. 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.
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