A Rigorous Approach for the Modeling of Through-Silicon-Via Pairs Using Multipole Expansions

Abstract

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.