Fast capacitance extraction of actual 3-D VLSI interconnects using quasi-multiple medium accelerated BEM

A quasi-multiple medium (QMM) method based on the direct boundary element method (BEM) is presented to extract the capacitance of three-dimensional (3-D) very large scale integration interconnects with multiple dielectrics. QMM decomposes each dielectric layer into a few fictitious medium blocks, and generates an overall coefficient matrix with high sparsity. With the storage technique of a sparse blocked matrix and iterative equation solver generalized minimal residual, the QMM can greatly reduce the CPU time and memory usage of large-scale direct BEM computation. Numerical examples of 3-D multilayered and multiconductor structures cut from actual layout show the efficiency of the QMM method for capacitance extraction. We also compared the QMM accelerated BEM with geometry independent measured equation of invariance (GIMEI) and Zhu's overlapping domain decomposition method (ODDM).