Reduced order models for HF interconnect over lossy semiconductor substrate

The paper describes an effective procedure to extract the reduced order models of multi-wire on-chip interconnects. These models take into consideration effects of the high frequency electromagnetic field, such as propagation, skin effect, substrate losses, etc. The frequency dependent p.u.l. line parameters are extracted by solving with finite integral technique (FIT) two field problems with appropriate boundary conditions: 2D-EQS field for Y1(omega) and EMQS-TM field for Z1(omega). After the line extension, the reduced model is extracted by vector fitting (VFIT), and then the equivalent compact spice sub-circuit is synthesized by differential-equation method (DEM).