A generalized modeling method for signal/power integrity analysis of 3D coupled interconnects in finite cavity based on 1D technology

In this paper, an innovative 1D technology is used to model complex vias structures in 3D IC and package system, which can include the layout of both eccentric single-ended and differential signaling types. The problem under investigation is an essential basic unit which can be applied to build and model complex multilayer structures. We first obtain the impedance matrix for finite cavity, which includes the reflection feartures of the cavity boundaries. Then the scattered field from a single via and T matrix in the presence of walls for a single via are derived. The Foldy-Lax multiple scatteing equations are furthermore listed based on the scattering mechanism. For the incident field, we calculate the exciting and scattering field coefficients on the vias in the arbitrarily shaped antipad based on 1D technology. Then the coupling among vertical interconnects are solved by applying reformulated Foldy-Lax multiple scattering equation. Finally, the scattering matrix of coupling among vias is calculated. Numerical results for the method are in good agreement with a commercial full wave numerical tool up to 50 GHz.