A divide-and-conquer method for 3D capacitance extraction

Abstract

This thesis describes a divide-and-conquer algorithm to improve the 3D boundary element method (BEM) for capacitance extraction. We divide large interconnect structures into small sections, set new boundary conditions using the borderfor each section, solve each section, and then combine the results to derive the capacitance. The target application is critical nets where 3D accuracy is required. The new algorithm is a significant improvement over the traditional BEMs and their enhancements, such as the "window" method where conductors far away are dropped, and the "shield" method where conductors hidden behind other conductors are dropped. Experimental results show that our algorithm is 25 times faster than the traditional BEM and 5 times faster than the window+shield method, for medium to large structures. The error of the capacitance computed by the new algorithm is within 2% for self capacitance and 7% for coupling capacitance, compared with the results obtained by solving the entire system using BEM. Furthermore, our algorithms gives accurate distributed RC, where none of the previous 3D BEM algorithms and their enhancements can.