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A rigorous approach for the modeling of through-silicon via pairs using multipole expansions

: Duan, X.M.; Dahl, D.; Ndip, I.; Lang, K.D.; Schuster, C.


IEEE transactions on components, packaging and manufacturing technology 6 (2016), No.1, pp.117-125
ISSN: 2156-3950
Journal Article
Fraunhofer IZM ()

This paper presents a novel multipole expansion method for the rigorous analysis of wave propagation along a through-silicon-via (TSV) pair. TSV models are often constructed using equivalent circuits under the assumption that the interfaces between different media are equipotential. In comparison with that, the proposed method is a rigorous full-wave solution of the propagation mode. It takes advantage of cylindrical wave expansion functions and matches the boundary conditions at both the metal-to-insulator and insulator-to-silicon interfaces exactly. The method is validated against a full-wave finite-element method solver, and analysis examples using the method are demonstrated in a frequency range up to 100 GHz.