Finite-thickness conductor models for full-wave analysis of interconnects with a fast integral equation method

In this paper, a fast electromagnetic integral equation solution methodology is proposed for the frequency-domain modeling of lossy, interconnect structures. The proposed method utilizes a two-layer model for thick conductors where the unknown current density inside the rectangular wire strips is approximated in terms of equivalent surface currents placed at the top and bottom sides of the strip which, for the purposes of this paper, are assumed to be substantially larger than the side strips. A matrix impedance relationship, which depends on the conductor thickness and its material properties, is established between the two surface current densities to account for the skin effect behavior of the field within the conductor. The selected assignment of the unknown current densities on the planes associated with the top and bottom sides of the metallization, combined with the planarity of multilayered interconnect structures, makes possible the application of the conjugate gradient fast Fourier transform (FFT) algorithm for the computationally efficient prediction of the electromagnetic response of multiport interconnect structures. Applications of the resulting fast integral equation solver to the electromagnetic modeling of interconnect circuits with thick lossy conductors from near dc to multigigahertz frequencies are used to demonstrate the validity of the method and quantify its computational efficiency.