On the frequency-dependent line capacitance and conductance of on-chip interconnects on lossy silicon substrate

In this paper a method for analysis and modelling of transmission interconnect lines with zero or nonzero thickness on Si-SiO2 substrate is presented. The analysis is based on semi-analytical expressions for the frequency-dependent transmission line admittances. The electromagnetic concept of free charge density is applied. It allows us to obtain integral equations between electric scalar potential and charge density distributions. These equations are solved by the Galerkin procedure of the method of moments. This new model represents narrow and thick line interconnect behaviour over a wide range of frequencies up to 20 GHz. The accuracy of the developed method in this work is validated by comparing with the rigorous simulation data obtained by full-wave electromagnetic solver and CAD-oriented equivalent-circuit modelling approach. The response of the proposed model is shown to be in good agreement with the frequency-dependent capacitance and conductance characteristics of general coupled multiconductor on-chip interconnects.