FDFD Modeling of Signal Paths With TSVs in Silicon Interposer

This paper proposes an efficient method to model signal paths with through-silicon vias (TSVs) in silicon interposer for 3-D systems. The proposed method utilizes 3-D finite-difference frequency-domain (FDFD) method to model the redistribution layer transmission lines to capture the parasitic effects of multiple transmission lines on lossy silicon interposer. TSVs are modeled using an integral equation based solver, which uses cylindrical modal basis functions. A new formulation on incorporating multiport network into 3-D FDFD formulation is presented to include the parasitic effects of TSV arrays into the system matrix. The overall matrix is divided into several subdomains and solved by a divide-and-conquer approach in a parallel manner. The accuracy and efficiency of the proposed method are validated by comparing with 3-D full-wave simulations.