Efficient electromagnetic modeling and analysis for off-chip interconnects in SIW structures and 3D ICs

In this work, we use a mostly analytical approach of Foldy-Lax multiple scattering equation method 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 and horizontal interconnects. We decompose the modes effects inside the target structures into modes of cavity with multiple vertical interconnects and modes of horizontal interconnects which are traces. The coupling among vertical interconnects are solved by applying Foldy-Lax multiple scattering equation. The waveguide and cavity modes are decoupled in the Foldy-Lax equations. The modes effects of vertical interconnects and horizontal interconnects are finally integrated together to obtain the scattering matrix of off-chip interconnects. Numerical results for the method are in good agreement with a commercial full wave numerical tool up to 40 GHz.