Compact AC modeling and analysis of Cu, W, and CNT based through-silicon vias (TSVs) in 3-D ICs

This paper introduces the first accurate compact RLCG model for through-silicon vias (TSVs) in 3-D ICs valid for both low- and high-frequency regime, with consideration of MOS effect in silicon, AC conduction in silicon, skin effect in TSV metal and eddy currents in silicon substrate. The model is verified against a commercial full-wave electromagnetic (EM) simulation tool and subsequently employed for various performance (delay) analyses. The compact model is also applicable to TSVs made of carbon nanotube (CNT) bundles, once a small modification (making the effective resistivity complex) is made. Various geometries (as per the ITRS) and prospective materials (Cu, W, and Single-Walled (SW)/Multi-Walled (MW) -CNTs) are evaluated and comparative performance analysis is presented. It is shown that MWCNT bundle based TSVs can offer smaller or comparable high-frequency resistance than those of other materials due to reduced skin-effect in CNT bundle structures. On the other hand, performance (delay) analysis indicates that the performance differences among different TSV materials are rather small. However, since CNTs have other benefits over Cu and W (e.g., much higher thermal conductivity and better robustness and thermal stability), they could be the material of choice for TSVs in emerging 3-D ICs.