Partial element equivalent circuit method modeling of silicon interconnects

A new integral-equation-based formulation is presented enabling the modeling of lossy dielectrics, such as silicon, in the framework of the partial element equivalent circuit (PEEC) method, in the time domain. Due to the reduced value of conductivity of the lossy dielectric, charge is not restricted to its surface, e.g., the relaxation time is not as small as in standard conductors. This requires the PEEC method to be reformulated in order to consider both the conductivity of the dielectric material and the reduced value of the electrical conductivity, which prevents the charge to be located only on the surfaces. The proposed new PEEC model is validated through comparison with results available from the theory and commercial software. Then, the proposed method is used to analyze two silicon interconnects showing how the finite even small electrical conductivity of silicon may have a significant impact on the results compared with the ideal behavior of the dielectric.