寄生参数提取中不协调有限元网格的分析  

Non-conforming mesh for finite element method in interconnect parasitic extraction

作　　者：殷英 徐小宇[1,3] 闫帅 吕鹏飞[1,3] 任卓翔 YIN Ying;XU Xiao-yu;YAN Shuai;LV Peng-fei;REN Zhuo-xiang(Institute of Microelectronics of Chinese Academy of Sciences,Beijing 100029,China;University of Chinese Academy of Sciences,Beijing 100049,China;Beijing Key Laboratory of 3D & Nano IC EDA Technologies,Beijing 100029,China)

机构地区：[1]中国科学院微电子研究所,北京100029 [2]中国科学院大学,北京100049 [3]三维及纳米集成电路设计自动化北京市重点实验室,北京100029

出　　处：《电子设计工程》2019年第1期9-13,共5页Electronic Design Engineering

基　　金：国家重点研发计划专项(2017YFB0203500);国家自然科学基金项目(51407181)

摘　　要：纳米尺度的超大规模集成电路结构复杂,对集成电路设计带来巨大的挑战。互联线寄生参数提取是设计中的重要课题之一,须借助有限元法等电磁场求解器。有限元法需要协调性网格来保证稳定地建立代数系统。然而由于分离部件设计、局部网格细化等原因,经常会出现不匹配网格的情况。本文提出了一种灵活通用的方法来高效地粘连与分析不协调网格。该方法自然地连接起各种网格,形成多边形或多面体单元,这些单元经常退化成诸如三角形或四面体的单纯型,然后基于有限元法框架,通过退化的广义重心坐标和分段插值处理这些单元,得到网格单元上的分段形函数。此方法避免了对网格的重新划分,避免其他重心坐标法的复杂性,并获得良好的精度。论文选用位于衬底上方的三导体静电系统的电容参数提取作为算例,验证了所述方法的可行性与准确性。Nanoscale VLSI has very complicated structure,which brings out tremendous challenge to integrated circuit(IC)designs.As an importance issue in IC design,interconnect parasitic extraction is based on electromagnetic solver such as finite element method(FEM),which usually requires conforming meshes to reliably build algebra systems.However,due to many facts such as separate component design,local mesh refinement,non-matching meshes exist commonly.The purpose of this paper is to present a flexible method to glue non-conforming meshes efficiently.The method naturally connects meshes to form polygon or polytope elements,which are often degenerated into simplexes such as triangles or tetrahedrons,and the piecewise shape functions over the elements,are derived through degenerated generalized barycentric coordinates(GBCs)and piecewise interpolation within the framework of FEM.The method avoids re-meshing of computational domain and reduces complexity and is with high precision.A parasitic extraction example of a multi-conduct electrostatic system is presented.The result shows that it is feasible and accurate.

关 键 词：寄生参数提取 有限元法 广义重心坐标 不协调网格 分段插值 

分 类 号：TN402[电子电信—微电子学与固体电子学]