Exploiting structure periodicity and symmetry in capacitance calculations for three dimensional multiconductor systems

The structure periodicity and symmetry usually encountered in the design and packaging of integrated circuits are utilized to alleviate the computation cost in the capacitance calculations for three-dimensional multiconductor systems by the integral equation method. For periodic structures, the region of unknowns is reduced to the base period by the use of a modified Green's function which circumvents the periodicity singularity. For structure with s orthogonal planes of symmetry, where s=1, 2, or 3, the region of unknowns is reduced to 1/2/sup s/ of the original whole space by even- and odd-mode decomposition techniques. Both algorithms are embedded into a general three-dimensional capacitance calculation program by which a numerical calculation for the via capacitance in a multilayer ceramic environment is presented and compared with the experimental measurements.>