FDFD Nonconformal Domain Decomposition Method for the Electromagnetic Modeling of Interconnections in Silicon Interposer

This paper proposes an efficient method to model interconnections with through-silicon vias (TSVs) in silicon interposer for 3-D systems. The proposed method uses 3-D finite-difference frequency-domain nonconformal domain decomposition method to model the redistribution layer transmission lines on lossy silicon interposer. Using the nonconformal domain decomposition approach, the interposer can be divided into separate subdomains. Individual subdomains can be discretized independently based on its feature size. Field continuity at interfaces between domains is enforced by introducing Lagrange multiplier and vector basis functions at the interfaces. TSVs are modeled using an integral-equation-based solver, which uses cylindrical modal basis functions. The formulation on incorporating multiport network into nonconformal domain decomposition is presented to include the parasitic effects of TSV arrays into the system matrix. By comparing with 3-D full-wave simulations and commercial solvers, this paper validates the accuracy and efficiency of the proposed modeling approach.