Electromagnetic modeling for lossy interconnect structures based on hybrid surface integral equations

Electromagnetic (EM) modeling is essential to extract equivalent circuit parameters for interconnect structures in signal integrity. The modeling can be formulated by integral equation approach and surface integral equations (SIEs) are preferred whenever available. If conducting interconnects are lossy, the loss needs to be carefully considered for accurate modeling. Traditionally, the loss is approximately accounted for by a surface impedance for simplicity, but such an approximation may not be valid when the skin depth of current is large due to the small conductivity or low operating frequency of interconnects. We propose a different scheme to model the structures by treating the lossy interconnects as penetrable media and using a hybrid surface integral equations (HSIEs) to describe them. The HSIEs are solved with the method of moments (MoM), but we employ a dual basis function (DBF) to expand the magnetic current density so that the conditioning of system matrix can be greatly improved. A numerical example is presented to demonstrate the scheme and good results have been obtained.