A novel dimension reduction technique for the capacitance extraction of 3D VLSI interconnects

In this paper, we present a new capacitance extraction method named Dimension Reduction Technique (DRT) for 3D VLSI interconnects. The DRT converts a complex 3D problem into a series of cascading simple 2D problems. Each 3D problem is solved separately, so we can choose the most efficient method according to the arrangement of conductors. More importantly, it is very easy to obtain the analytical solutions of 2D problem in many layers such as the pure dielectric layers and the layers with parallel signal lines. Therefore, the domain that has to be analyzed numerically is minimized. This leads to the drastic reduction of the computing time and memory needs. We have used the DRT to extract the capacitances of multilayered and multiconductor cross-overs, bends, via with signal lines and open-end. The results are in good agreement with those of Ansoft´s SPICELINK and MIT´s FastCap, but the computing time and memory size used by the DRT are several even tens times less than those used by SPICELINK and FastCap.