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Modeling and analysis of interconnects within a package incorporating vias and a perforated ground plane

Frequently multichip modules (MCM) have perforated ground and power planes as opposed to solid ground and power planes. The periodic apertures in the planes alter how electromagnetic waves propagate in the system, and therefore must be taken into account when analyzing the system. The characteristic behavior of interconnects above a perforated ground plane is affected by the size, shape, and orientation of the apertures. To accurately model the interconnects over perforated ground planes requires the use of the periodic 3D Green's function. The Green's functions comprises two infinite series both of which converge extremely slowly, and this slow convergence of the periodic Green's function has hampered previous analysis. To overcome this obstacle a mixed domain representation of the Green's function based on the error function transformation is used. This representation of the Green's function converges exponentially in both the spatial and spectral domains. Using this representation, the Green's function can be computed accurately and in a short amount of time. Modeling the gridded ground plane is just the first step in modeling an entire system. In addition to being able to accurately model the ground plane, one must be able to model a wide variety of structures, such as multiple interconnects, discontinuities, and conformal vias. All of these models need to be verified with measurements of actual devices. Finally, in order to be effective in post-layout verification, the developed models must interface with a circuit simulator.