Exponential expansion for field computation and capacitance extraction

We report a new numerical technique based on the exponential expansion of the Green's function 1/r for accurate and rapid computation of the three-dimensional potential field, its gradient, and the charge density distribution needed for capacitance extraction in multiple-dielectric-multiconductor systems. The exponential expansion provides a computational efficient alternative to the commonly used technique based on multipole expansion of spherical harmonics. With exponential expansion, the memory requirement is independent of the desired degree of accuracy and different forms of parallelism are available for both remotely distributed networks and closely coupled parallel systems. These features permit large-scale simulation, involving panel (element) count in the range of a few hundred thousand to several million, needed for extraction of the parasitic coupling capacitance in VLSI interconnects, including large-area amorphous silicon electronics, as well as for analysis of electrostatic interaction in micro-electro-mechanical systems (MEMS).