From Physics to Surrogate Intelligence: A Unified Electro-Thermo-Optimization Framework for TSV Networks

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.