Fast 3-D inductance extraction in lossy multi-layer substrate

A mixed potential integral equation (MPIE) technique combined with fast multi-layer Green's functions and Gaussian Jacobi high order techniques is used to compute the 3-D frequency dependent inductances and resistances in lossy multi-layered substrates. Compared to FastHenry, a multipole-accelerated 3-D inductance extraction program, the algorithm presented here is more accurate and faster for lossy multi-layer structures for two reasons. First, substrate and optional ground plane loss and coupling effect are efficiently modeled by multilayer Green's functions, while the Green's functions are efficiently calculated via a window-based acceleration technique. Second, Gaussian Jacobi-based high order techniques are used to capture the singularity of the current distribution at metal edges, leading to significant reduction of problem size and speed-up of computation.