Electromagnetic modeling of massively coupled through silicon vias for 3D interconnects

This article presents a full‐wave electromagnetic approach for analyzing the electrical performance of massively coupled through silicon vias (TSV). The TSVs are modeled with SiO 2 insulation coating and are placed in the sandwiched SiO 2 ‐Si‐SiO 2 substrate. The planar guided wave is analyzed to determine the fundamental mode and high order modes in stratified media. Cylindrical wave expansions and Foldy–Lax equations for multiple scattering techniques are adapted to the TSV problems. The effect of SiO 2 coating around the via is modeled by the general expression of T ‐matrix coefficients. Both dispersive silicon loss and copper loss are included in this approach. Numerical simulation of a 4‐by‐4 TSV array is demonstrated to show the signal performance and crosstalk. It shows that the coupling issues among the TSVs will become significant beyond 15 GHz. The results are in excellent agreement with general purpose field solver.