A new efficient method for modeling dense via arrays with 1D discretization in 2D method of moment and group T matrix

In this paper, a new efficient methodology is used to model dense via arrays in 3D integrated circuit and package system, which also can include the layout of multiple vias sharing the same antipad. In order to accurately calculate all the effects of high order waveguide modes and azimuthal modes for complete signal integrity analysis of multiple closely spaced vias, we make use of transformation that converts the surface integration of magnetic surface currents into 1-dimensional line integration of surface charges on the vias and on the ground plane. We also use group T matrix to represent a group of vias to account for the scattering among different groups of vias. Numerical results illustrate physics that, after including high order mode effects using 1D line integration and group T matrix, the new method has great accuracy and efficiency for modeling multiple closely spaced vertical vias.