[Paper Review] A Complete Surface Integral Method for Broadband Modeling of 3D Interconnects in Stratified Media

Shashwat Sharma, Utkarsh R. Patel+2 more|arXiv (Cornell University)|Oct 9, 2018

Electromagnetic Scattering and Analysis38 references4 citations

TL;DR

This paper presents a complete surface integral method for broadband electromagnetic modeling of 3D interconnects in stratified multilayer media. It introduces a novel Taylor expansion-based technique to accelerate multilayer Green's function computation, extends the differential surface admittance operator for skin effect in arbitrary conductors, and develops a generalized adaptive integral method for efficient, grid-free simulation across a wide frequency range, validated against finite element methods with high accuracy.

ABSTRACT

A surface integral equation solver is proposed for fast and accurate simulation of interconnects embedded in stratified media. A novel technique for efficient computation of the multilayer Green's function is proposed. Using the Taylor expansion of Bessel functions, the computation of Sommerfeld integrals during the method of moments procedure is reduced to simple algebraic operations. To model skin effect in conductors, the single-source differential surface admittance operator is extended to conductors in stratified media. To handle large realistic structures, the adaptive integral method is developed for a multilayer environment in a generalized manner that poses no restrictions on layout of conductors, and requires no special grid refinement, unlike previous works. The proposed method is made robust over a wide frequency range with the augmented electric field integral equation. Realistic structures of different shapes and electrical sizes are successfully analyzed over a wide frequency range, and results are validated against a commercial finite element tool.

Motivation & Objective

• To enable fast and accurate broadband electromagnetic modeling of 3D interconnects in multilayered integrated circuits.
• To overcome the high computational cost of computing multilayer Green's functions via Sommerfeld integrals.
• To extend surface-based modeling to handle skin effects in arbitrary conductor geometries within stratified media.
• To develop a generalized adaptive integral method that imposes no restrictions on conductor layout or grid refinement.
• To ensure robustness across a wide frequency range, including low frequencies, through charge neutrality enforcement and preconditioning.

Proposed method

• A Taylor expansion of Bessel functions is used to transform complex Sommerfeld integrals into simple algebraic operations, drastically reducing computation time for multilayer Green's functions.
• The single-source differential surface admittance operator is extended to model skin and proximity effects in conductors embedded in stratified media.
• A generalized adaptive integral method (AIM) is developed for multilayer environments, enabling efficient matrix-vector products without special grid refinement or layout constraints.
• The augmented electric field integral equation (aEFIE) is employed to maintain robustness at low frequencies, particularly in the presence of charge neutrality issues.
• A sparse right-preconditioner based on the Schur complement is applied to accelerate iterative solution of the large linear system using restarted GMRES.
• Charge neutrality is enforced via mapping matrices F and B that reduce unknowns by eliminating redundant charge density degrees of freedom on isolated conductor sets.

Experimental results

Research questions

• RQ1 How can the computation of multilayer Green's functions be accelerated without relying on expensive numerical integration or interpolation?
• RQ2 Can the differential surface admittance operator be generalized to model skin effects accurately in arbitrary 3D conductor geometries within stratified media?
• RQ3 How can the adaptive integral method be extended to multilayered environments without requiring special grid refinement or layout constraints?
• RQ4 What techniques ensure numerical robustness across the full broadband spectrum, including low-frequency regimes?
• RQ5 How can preconditioning be effectively applied to accelerate iterative solution of the large, sparse linear system arising from the method of moments?

Key findings

• The proposed Taylor expansion technique reduces the computational cost of multilayer Green's function evaluation by replacing numerical integration of Sommerfeld integrals with fast algebraic operations.
• The extended differential surface admittance operator enables accurate modeling of skin and proximity effects in arbitrary 3D conductor shapes within stratified dielectrics.
• The generalized adaptive integral method achieves high efficiency and scalability for large, complex interconnect structures without requiring special grid refinement or layout restrictions.
• The use of the augmented electric field integral equation ensures numerical stability and accuracy at low frequencies, resolving rank deficiency due to charge neutrality.
• The preconditioned iterative solver achieves fast convergence, enabling large-scale simulations with high computational efficiency.
• Validation against a commercial finite element tool confirms high accuracy across a broad frequency range, from DC to tens of gigahertz, for various realistic interconnect geometries.