互连封装结构电特性分析中的改进PEEC三维建模

A Modified 3-D PEEC Model in Interconnect and Packaging Electric Analysis

本文提出了一种改进的PEEC模型 ,为便于在大规模互连封装结构分析中利用规模缩减技术 ,它以描述系统的状态方程代替了具体的等效电路 .为此它以矢量磁位的积分表达式和洛仑兹规范代替了矢量磁位和标量电位的积分表达式 ,对积分方程进行展开 .这样做可以避免复杂介质结构中的电容矩阵提取 ,大大节省了计算时间 .这一模型可方便地嵌入更大的系统进行分层次的综合分析和利用PVL等规模缩减技术 .数值计算的结果与其他文献吻合较好 。

A modified PEEC model is introduced in this paper.For the convenience of utilization the reduction technology in large scale interconnect and packaging electric analysis,this model present the state equations instead of the equivalent circuit.To do that,the integral definition of vector magnetic potential and the Lorentz gauge is used to expand the integral equation of the PEEC model.This avoids the using of the integral definition of the scalar electric potential and consequently avoids the capacitance matrix extraction in complex dielectric structures,which can save a large part of computing time.This model is suitable for hierarchical electromagnetic modeling and reduction technology like PVL.The numerical results show the validity of the presented model.