Wideband Modeling and Characterization of Differential Through-Silicon Vias for 3-D ICs

This paper presents the wideband modeling and analysis of differential through-silicon vias (D-TSVs) in 3-D ICs. An equivalent-circuit model of the ground-signal-signal-ground-type D-TSVs is given and validated against a commercial full-wave electromagnetic simulation tool. The common- and differential-mode impedances are extracted using the partial-element equivalent-circuit method, while the admittances are calculated analytically, with the MOS effects considered and treated appropriately. The circuit model can also be used for studying the differential annular TSVs (ATSVs). It is shown that the ATSVs are more suitable for transmitting differential signals in comparison with the cylindrical TSVs. Based on the equivalent-circuit model, the characteristic impedances and the forward transmission coefficients of the D-TSVs made of Cu and carbon nanotubes are characterized and compared under different settings of frequencies and temperatures.