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

Jianfeng XU  Hong LI  Wen-Yan YIN  Junfa MAO  Le-Wei LI  

IEICE TRANSACTIONS on Electronics   Vol.E90-C   No.1   pp.179-188
Publication Date: 2007/01/01
Online ISSN: 1745-1353
DOI: 10.1093/ietele/e90-c.1.179
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Integrated Electronics
three-dimensional interconnects (3DIs),  capacitance extraction,  element-by-element finite element method (FEM),  pre-conditioned conjugated gradient technique,  

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The element-by-element finite element method (EBE-FEM) 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.