A Novel Technique for Evaluating the Effective Permittivity of Inhomogeneous Interconnects Based on the Monotonicity Property

This paper presents a novel homogenization technique to retrieve the effective permittivity of an interconnect embedded in inhomogeneous dielectrics, with an arbitrary number of conductors. The technique is based on the monotonicity property of suitable matrices associated with the transmission line model. The effective permittivity values are obtained by checking an index related to the eigenvalues of such matrices. The technique requires only the knowledge, at a single frequency point, of any of the terminal matrices describing the original line (e.g., impedance, admittance, or scattering matrices), either obtained by measurements or by simulations. Depending on the applications, the technique can identify one or two values for the effective permittivity. In the first case, the original inhomogeneous line can be replaced by an equivalent line, embedded in a homogeneous dielectric. In the second case, two equivalent homogeneous lines are identified, which cannot replace the inhomogeneous line, but can be used to obtain the lower and upper bounds to its performance (in terms of significant physical signatures, such as stored energy, propagation velocities, delay times, and characteristic impedance). The mathematical theorems supporting the technique are rigorously proven. The technique is shown to be consistent with the existing results in the literature and is experimentally validated. Several case studies are carried out, including cables, microstrips, and multilayered interconnects.