Qijun Lu

Electrical Modeling and Characterization of Shield Differential Through-Silicon Vias

An equivalent-circuit model of shield differential through-silicon vias (SDTSVs) in 3-D integrated circuits (3-D ICs) is proposed in this paper. The proposed model is verified using the 3-D full-wave field solver High Frequency Simulator Structure, showing that it is highly accurate up to 100 GHz. Furthermore, a full-wave extraction method for the resistance-inductance-capacitance-conductance (RLCG) parameters of SDTSVs is also proposed in this paper, which can be applied to all of differential transmission lines. It is shown that the results of the RLCG parameters obtained from the full-wave extraction method agree well with that from the analytical calculation up to 100 GHz, further validating the accuracy of the proposed model. Finally, using the proposed model, a deep analysis of electrical characteristics of SDTSVs is carried out to provide helpful design guidelines for them in future 3-D ICs.

Accurate Formulas for the Capacitance of Tapered-Through Silicon Vias in 3-D ICs

This letter first proposes novel formulas for the calculation of the oxide capacitance and the silicon substrate capacitance in Tapered-Through Silicon vias (T-TSVs). The electric field is non-uniform distribution in T-TSVs due to its non-uniform three-dimensional structure. In order to get accurate formulas for the capacitance of T-TSVs, the conformal mapping method was used properly based on the analytical results of the local electric field structure in T-TSVs. When the slope angle equals to zero, the obtained formulas can be reduced to the formulas of cylindrical TSVs. The comparison between the results of the proposed formulas and the three-dimensional quasi-static field solver shows that the proposed formulas have very high accuracy, with maximum errors of 1% and 3% for the oxide capacitance and the silicon substrate capacitance, respectively.

Analysis of propagation delay and repeater insertion in single-walled carbon nanotube bundle interconnects

A new closed-form expression of 50% propagation delay for distributed RLC interconnects is proposed using the multivariable curve fitting method, with a maximum error of 4% with respect to SPICE results. Then accurate closed-form solutions for the optimum repeater number and size to minimize the propagation delay are further derived. The performance of single-walled carbon nanotube (SWCNT) bundle interconnects is evaluated using the proposed models in the intermediate and global levels at the 22- and 32-nm technology nodes, and compared against traditional Cu interconnects. It is shown that the performance of SWCNT bundle interconnects in propagation delay can outperform Cu interconnects, and the improvement will be enhanced with technology scaling and wire length increasing. On the other hand, the propagation delay of SWCNT bundle interconnects is super-linearly dependent on the wire length similar to Cu interconnects, indicating that the method of repeater insertion to reduce the propagation delay can also apply to SWCNT bundle interconnects. The results shown that repeater insertion can really reduce the propagation delay of SWCNT bundle interconnects effectively, and the optimum repeater number is much smaller than that of Cu interconnects.

Electrical Modeling and Analysis of Cu-CNT Heterogeneous Coaxial Through-Silicon Vias

An equivalent-circuit model of Cu-carbon nanotube heterogeneous coaxial through-silicon vias (HCTSVs) in 3-D integrated circuits (3-D ICs) is proposed in this paper. Based on the complex effective conductivity method, the resistances and inductances of Cu-single walled carbon nanotube (SWCNT) HCTSVs and Cu-multi walled carbon nanotube (MWCNT) HCTSVs are compared with that of Cu coaxial through-silicon vias (CTSVs). Furthermore, using the proposed model, the magnitudes of their insertion losses are compared. It is shown that the transmission performance of Cu-SWCNT HCTSVs with higher metallic fraction and Cu-MWCNT HCTSVs is better than that of Cu CTSVs, and the improvement of Cu-MWCNT HCTSVs is more obvious at high frequencies. Finally, the transmission characteristics of Cu-MWCNT HCTSVs are analyzed deeply to provide helpful design guidelines for them in future high-speed 3-D ICs.