A Combined-Field Boundary Element Formulation for the Electromagnetic Modeling of Multiscale Interconnects and Integrated Passive Components From DC to Millimeter-Wave Frequencies

Abstract

Full-wave electromagnetic simulation is essential in the semiconductor and packaging industry, for the design and signal integrity analysis of high-speed interconnects and integrated passive components. These applications often entail broadband simulations of multiscale structures from DC to millimeter-wave frequencies, which requires the accurate modeling of conductor losses and the skin effect, and poses a substantial challenge to computational techniques. The boundary element method is an appealing candidate to address this challenge, because it offers a two-dimensional representation of a three-dimensional problem using a surface integral formulation of Maxwell's equations. However, this often comes at the cost of ill-conditioned matrices at low frequencies and for multiscale structures. In this work, a new boundary element formulation is developed, where the underlying surface integral equations are inherently valid from statics to full-wave electrodynamics. A discretization scheme is proposed which leads to a system of equations that (a) is immune to low-frequency breakdown and solvable from exactly DC to millimeter-wave frequencies, even for multiscale geometries, (b) models the skin effect rigorously, and (c) does not require a barycentric refinement or intermediate matrix factorization, unlike existing methods. Realistic and representative numerical examples drawn from the target application areas demonstrate the accuracy and effectiveness of the proposed method.