Full-Wave Broadband Characterization of On-Chip Passives Subject to Etching Effects Using a Vectorial Unified Transform for Polyhedral Geometries

This paper presents a generalized formulation of the differential surface admittance (DSA) operator for three-dimensional electromagnetic analysis of arbitrary polyhedral geometries. Motivated by the increasing need for accurate signal integrity modeling in high-frequency integrated circuits and printed circuit boards, the proposed approach enables efficient characterization of intricate passive interconnect structures. Therefore, a novel vectorial unified transform for Maxwell’s equations is proposed, allowing the systematic construction of a Dirichlet-to-Neumann (DtN) operator without requiring Green’s function evaluations within the material domain. The formulation is first developed for convex polyhedra and subsequently extended to arbitrary non-convex geometries. The resulting DSA operator is integrated into a boundary integral equation framework via projection onto Rao–Wilton–Glisson (RWG) basis functions and coupled with the electric field integral equation (EFIE) for solving the exterior problem. Numerical results demonstrate excellent agreement with state-of-the-art full-wave solvers across a broad range of material parameters. The novel method further enables accurate and efficient extraction of broadband impedance responses for advanced on-chip passive components subject to etching-induced variations, highlighting its potential for high-frequency design and analysis.