Efficient full-wave modeling of high density TSVs for 3D integration

This paper presents a full-wave electromagnetic approach for modeling the electrical performance of massively-coupled and coated through silicon vias in a sandwiched SiO2-Si-SiO2 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 used to efficiently calculate the couplings among the vias. The effect of SiO2 coating around the via is modeled by general T-matrix coefficients. Both silicon loss and copper loss are included in this approach. Numerical simulations of insertion loss, return loss and crosstalk of 1-by-3 and 4-by-4 through silicon via arrays are presented and compared with general-purpose field-solver.