Admittance matrix calculations of on-chip interconnects on lossy silicon substrate using multilayer Green´s function

In this paper, a simple method for computation of the shunt admittance matrix of multiconductor interconnects on a general lossy multilayer substrate at high bit rates is presented. The analysis is based on the semi-analytical Green´s function approach and the recurrence relation between the coefficients of potential in n and n+1 layers. 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. The new approach is especially suited to modeling 2D layered structures with planar boundaries for frequencies up to 20 GHz (quasi-stationary field approach). The transmission line parameters (capacitance and conductance per unit length) for the given interconnect multilayer geometry are computed. A discussion of the calculated line admittance matrix in terms of technological and geometrical parameters of the structure is given. A comparison of the numerical results from the new procedure with the techniques presented in the previous publications are also provided.