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 substrate. Compared to FastHenry, a multipole-accelerated 3-D inductance extraction program, the algorithm presented here is more accurate and faster for lossy multilayer structures due to two reasons. First, substrate and optional ground plane's lose and coupling effect are efficiently modeled by multilayer Green's functions, while the Green's functions are efficiently calculated via 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.