An SIE Formulation with Triangular Discretization and Loop Analysis for Parameter Extraction of Arbitrarily Shaped Interconnects

TL;DR

This paper introduces a novel surface integral equation formulation with triangular discretization and loop analysis, enabling efficient and accurate modeling of complex arbitrarily shaped interconnects in electronic packages.

Contribution

It presents a new SIE formulation combined with loop analysis and acceleration techniques, improving modeling accuracy and computational efficiency for complex interconnect geometries.

Findings

Accurate modeling of complex interconnects demonstrated

Significant reduction in computation time with pFFT acceleration

Flexible approach validated on various practical examples

Abstract

A surface integral equation (SIE) formulation under the magneto-quasi-static assumption is proposed to efficiently and accurately model arbitrarily shaped interconnects in packages. Through decently transferring all electromagnetic quantities into circuit elements, the loop analysis is used to carefully construct matrix equations with an independent and complete set of unknowns based on graph theory. In addition, an efficient preconditioner is developed, and the proposed formulation is accelerated by the pre-corrected Fast Fourier Transform (pFFT). Four practical examples, including a rectangular metallic interconnect, bounding wire arrays, interconnects in a real-life circuit and the power distribution network (PDN) used in packages, are carried out to validate its accuracy, efficiency and scalability. Results show that the proposed formulation is accurate, efficient and flexible to model complex interconnects in packages.