Wideband Impedance Model for Coaxial Through-Silicon Vias in 3-D Integration

Coaxial through-silicon via (TSV) is a promising 3-D integration solution, which can offer lower coupling with its surrounding environment and achieve better electromagnetic compatibility and signal integrity than other TSV structures. In this paper, an analytical wideband equivalent circuit model is proposed for the impedance modeling of coaxial TSVs in 3-D integration. Closed-form formulas for calculations of the per-unit-length resistance and the inductance of both the isolation dielectric filled and silicon filled coaxial TSVs are derived from the theory of quasi-magnetostatic fields. These formulas appropriately capture the skin effect in metal as well as the eddy current effect in silicon. Therefore, they yield accurate results comparable with the full-wave solutions in a wideband frequency range.