Rapid parametric electrostatic modeling of TSV port cross-section using physics-informed neural network

Three-dimensional (3D) integration technology has emerged as a novel paradigm for extending Moore's Law, offering high integration density and design flexibility. Through-Silicon Vias (TSVs) are key interconnects in 3D integration. The integrity of chip signals is critically dependent on electromagnetic (EM) characteristics of TSVs.This criticality necessitates accurate and efficient EM modeling. While traditional numerical methods provide high accuracy, they are computationally expensive and rendered inefficient for design parameter optimization by repeated simulations. Conversely, conventional neural network-based EM parametric models offer design efficiency but struggle with inefficient data acquisition and ensuring physical consistency. The Physics-Informed Neural Network (PINN) has emerged as a promising approach, which yields accuracy, physical consistency, and efficient parametric modeling. In this study, a PINN-based electrostatic model was initially developed for a fixed-geometry Ground-Signal (G-S) TSV port cross-section. When benchmarked against COMSOL Multiphysics, this model demonstrated relative L2 norm errors of 0.88% for electric potential and 0.99% for electric field strength. Subsequently, a parametric PINN model was developed for the G-S TSV port cross-section, incorporating TSV radius and spacing as input parameters. An approximately 52-fold speedup in computational time over COMSOL was achieved by this parametric model in parameter sweep tasks, while maintaining electric potential and field strength relative L2 norm errors below 1% and 2% respectively. These results demonstrate that the proposed PINN-based parametric modeling approach provides an efficient and reliable solution for the rapid design and optimization of TSV ports.