Wideband Electromagnetic Modeling of Coaxial-Annular Through-Silicon Vias

A wideband equivalent-circuit model of coaxialannular through-silicon vias (TSVs) for three-dimensional (3-D) integrated circuits is proposed in this paper. Rigorous closed-form formulas for the resistance and inductance of coaxial-annular TSVs are derived by computing the longitudinal electrical field in Cu and the longitudinal magnetic vector potentials in SiO
₂
and Si substrate with Bessel functions. The equivalent-circuit model can appropriately capture the skin effect in Cu as well as eddy-current effect in Si substrate. The proposed model is verified using 3-D full-wave field solver high frequency simulator structure, showing that it can yields highly accurate results up to 100 GHz.