Capacitance Extraction of Three-Dimensional Interconnects Using Element-by-Element Finite Element Method (EBE-FEM) and Preconditioned Conjugate Gradient (PCG) Technique

Capacitance Extraction of Three-Dimensional Interconnects Using Element-by-Element Finite Element Method (EBE-FEM) and Preconditioned Conjugate Gradient (PCG) Technique
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DOI：
10.1093/ietele/e90-c.1.179
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发表时间：
2007
期刊：
IEICE Trans. Electron.
影响因子：
--
通讯作者：
Jianfeng Xu;Hong Li;W. Yin;J. Mao;Le-Wei Li
Jianfeng Xu;Hong Li;W. Yin;J. Mao;Le-Wei Li
中科院分区：
其他
文献类型：
--
作者：
Jianfeng Xu;Hong Li;W. Yin;J. Mao;Le-Wei Li

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采用单元间有限元方法(EBEFE)和预条件共轭梯度法(PCG)相结合的方法，计算了多层高密度三维互连(3DIs)的耦合电容。考虑了所有几何和物理参数的影响，可以捕获所有的电容耦合3DIS。数值计算表明，与商用有限元软件Maxwell 3D或Ansys相比，采用这种混合方法提取电容可以得到拉普拉斯方程有效而准确的收敛解，且所需内存和CPU时间都较少。关键词：三维互连(3DIS)、电容提取、逐元有限元方法、预条件共轭梯度技术
The element-by-element finite element method (EBEFEM) combined with the preconditioned conjugate gradient (PCG) technique is employed in this paper to calculate the coupling capacitances of multi-level high-density three-dimensional interconnects (3DIs). All capacitive coupling 3DIs can be captured, with the effects of all geometric and physical parameters taken into account. It is numerically demonstrated that with this hybrid method in the extraction of capacitances, an effective and accurate convergent solution to the Laplace equation can be obtained, with less memory and CPU time required, as compared to the results obtained by using the commercial FEM software of either MAXWELL 3D or ANSYS. key words: three-dimensional interconnects (3DIs), capacitance extraction, element-by-element finite element method (FEM), pre-conditioned conjugated gradient technique