Analysis and Application of a Surface Admittance Operator for Combined Magnetic and Dielectric Contrast in Emerging Interconnect Topologies

In state-of-the-art interconnect design, topologies including magnetic materials, such as the so-called superlattice conductors, are rapidly emerging as a novel strategy to handle the challenges associated with the evolution toward higher operating frequencies and integration densities. Consequently, it is imperative that the newly developed full-wave electromagnetic solvers rigorously model these innovative materials and still accurately capture phenomena such as the skin and proximity effect in good conductors. In this article, we propose such a method to rigorously characterize this important class of interconnects with arbitrary, possibly frequency-dependent, material properties, including combined dielectric and magnetic contrast. To that end, a 2-D differential surface admittance (DSA) operator is used, which invokes a single-source equivalence theorem to model both nonmagnetic and magnetic conductors efficiently. This operator is combined with the electric field integral equation (EFIE), yielding a comprehensive formalism to extract the pertinent per-unit-of-length (p.u.l.) resistance and inductance parameters of the modeled structures. The numerical properties of our technique are studied in detail, with particular attention to the influence of magnetic materials. Finally, various relevant application examples are considered to establish its correctness and versatility.