Electromagnetic Modeling of Lossy Interconnects From DC to High Frequencies With a Potential-Based Boundary Element Formulation

TL;DR

This paper introduces a novel potential-based boundary element method for accurately modeling lossy interconnects across a broad frequency spectrum, from DC to high frequencies, ensuring stability and improved accuracy over existing methods.

Contribution

A new full-wave boundary element formulation based on potentials with simple boundary conditions and a modified Lorenz gauge, stable from DC to high frequencies, and capable of coupling with circuit models.

Findings

Accurately models lossy conductors from DC to high frequencies.

Ensures stable condition number down to DC.

Demonstrates improved accuracy and stability over existing BEM methods.

Abstract

The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling because it can capture the frequency-dependent variation of skin depth with only a surface-based discretization of the structure. Conventional BEM formulations rely on the mutual coupling of electric and magnetic fields, and can become inaccurate or unstable at low frequencies. We develop a new full-wave BEM formulation based on potentials which can accurately model lossy conductors from exactly DC to very high frequencies. A new set of simple boundary conditions is proposed along with a modified Lorenz gauge to ensure that the proposed formulation has a stable condition number down to DC. Moreover, coupling the potential-based integral equations to a circuit model allows the straightforward extraction of network parameters. Realistic numerical examples at both the chip and package level demonstrate the accuracy and stability of the proposed method from DC to high frequencies, beyond the capabilities of state-of-the-art BEM formulations based on fields.