Three-dimensional on-chip inductance and resistance extraction

Abstract

An efficient three-dimensional finite element frequency domain method to extract the inductance and resistance of small structures like on-chip interconnects or on-chip inductors is presented. Skin effect and proximity effect are taken into account. The parameters are obtained from the field energy calculated from the magnetic field distribution in the simulation domain. The small dimensions of the domain of interest provide the opportunity of using the optimized model of dominant magnetic field even at very high operating frequencies. Vector and scalar shape functions are used for finite element equation system assembling. Series of simulations for an instancing on-chip inductor at frequencies between 1 MHz and 100 GHz are performed to extract the parameters and to visualize the field distributions in the simulation area.