Substrate Resistance Modeling by Combination of BEM and FEM Methodologies
In present-day IC’s, substrate noise can have a significant impact on performance. Thus, modeling the noise-propagation characteristics of the substrate is becoming ever more important. Two ways of obtaining such a model are the Finite Element Method (FEM) and the Boundary Element Method (BEM). The FEM makes a full 3D discretization of the entire substrate and is very accurate and flexible, but, in general, it is also slow. The BEM only discretizes contact areas on the substrate-boundary, and is usually faster, but less flexible, because it assumes the substrate to consist of uniform layers. Sometimes, layout-dependent doping patterns near the top of the substrate may also play a significant role in noise-propagation. The FEM would easily be able to model such patterns, but it can often be too slow. The BEM, on the other hand, might not always be accurate enough. This paper describes a combination between BEM and FEM, which results in a method that is faster than FEM but more accurate than BEM. Through a number of experiments, the method is validated and successfully verified against 2 commercially available tools.
KeywordsBoundary Element Method Voronoi Polygon Finite Element Meet Method Interface Mesh Impose Dirichlet Boundary Condition
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