Modeling multiple scattering among vertical interconnects for SIW structures and 3D ICs in arbitrarily shaped waveguide

In this work, we use a mostly analytical approach of Foldy-Lax multiple scattering equation method with a recent major improvement, 1D technology, to efficiently model and solve physical/electromagnetics properties of the structures of SIW based devices and 3D IC in chip-package-board system which include multiple vertical interconnects. We first use MoM with 1D discretization to obtain the surface currents´ distributions on the side walls of arbitrarily shaped finite cavity. Then the coupling among vertical interconnects are solved by applying Foldy-Lax multiple scattering equation. We consider cases when the vias are placed close to each other and also to cavity boundary. The effects of higher order waveguide modes, axially anisotropic modes are considered and leakage through periodic via gaps are carefully studied. The waveguide and cavity modes are decoupled in the Foldy-Lax equations. 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 100 GHz.