电子学报2025，Vol.53Issue(6)：1874-1884,11.DOI:10.12263/DZXB.20240834
基于双区域增强体-面积分方程的有损互连结构的低频分析
Low-Frequency Analysis of Lossy Interconnect Structures Based on Two-Region Augmented Volume-Surface Integral Equations
摘要
Abstract
Real conductors of interconnect structures are lossy and their skin depth becomes large at low frequencies.The traditional one-region formation with the approximation of perfect electric conductor(PEC)or surface impedances may not be valid anymore,and two-region integral equation formations are needed in the integral equation approach.Also,the electric feld integral equation(EFIE)tend to break down at low frequencies and augmented electric field integral equations(AEFIEs)have been proposed to remedy the problem.In this work,we treat lossy conductors as penetrable objects and pro-pose two-region augmented hybrid field integral equations(AHFIEs)for low-frequency analysis.The hybrid field integral equations(HFIEs)consist of the EFIE of describing the exterior of a conductor and the magnetic field integral equation(MFIE)of describing its interior.Since the magnetic current density appears in the L operator in the HFIEs,we select the magnetic charge density as a new unknown function to be solved and introduce the continuity equation of magnetic current density as an extra equation.By incorporating the volume integral equations(VIEs)of describing the substrate with arbi-trary penetrable media in the interconnect structures,the two-region augmented volume-surface integral equations(AV-SIEs)are formulated for entire structures.The traditional method based on the AEFIEs can only be used for solving the problems including PEC interconnects and isotropic and homogeneous substrates while the proposed method based on the AVSIEs can applied to solve the problems with arbitrary materials so the capability of solving problems has been signifi-cantly enhanced.The AVSIEs are solved by the method of moments(MoM)where the Rao-Wlton-Glisson(RWG)and Schaubert-Wilton-Glisson(SWG)basis functions are used to represent the surface current densities of AHFIEs and volume current densities of VIEs,respectively,while a pulse basis function is employed to represent the charge densities of AH-FIEs.Numerical examples are presented to illustrate the approach and good results have been obtained.关键词
增强体-面积分方程/有损导体/互连结构/低频崩溃/双区域Key words
augmented volume-surface integral equations(AVSIEs)/lossy conductor/interconnect structure/low-frequency breakdown/two-region分类
信息技术与安全科学引用本文复制引用
张黎,童美松..基于双区域增强体-面积分方程的有损互连结构的低频分析[J].电子学报,2025,53(6):1874-1884,11.基金项目
国家自然科学基金(No.62071331) （No.62071331）
上海市科技委员会(No.21500714400) National Natural Science Foundation of China(No.62071331) （No.21500714400）
Shanghai Science and Technol-ogy Commission(No.21500714400) （No.21500714400）
