Compact AC Modeling and Performance Analysis of Through-Silicon Vias in 3-D ICs

Abstract

This paper introduces the first comprehensive and accurate compact resistance-inductance-capacitance-conductance ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLCG</i> ) model for through-silicon vias (TSVs) in 3-D ICs valid from low- to high-frequency regimes, with consideration of the MOS effect in silicon, the alternating-current (ac) conduction in silicon, the skin effect in TSV metal, and the eddy currents in the silicon substrate. The model is verified against electrostatic measurements as well as a commercial full-wave electromagnetic 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 slight modification (making the effective conductivity complex) is made. Various geometries (as per the International Technology Roadmap for Semiconductors) and prospective materials (Cu, W, and single-walled/multiwalled CNTs) are evaluated, and a comparative performance analysis is presented. It is shown that CNT-bundle-based TSVs can offer smaller or comparable high-frequency resistance than those of other materials due to the reduced skin effect in CNT bundle structures. On the other hand, the performance (delay) analysis indicates that the performance differences among different TSV materials are rather small. However, it is shown that CNTs provide an improved heat dissipation path due to their much higher thermal conductivity. In addition, the improved mechanical robustness and thermal stability of CNTs also favor their selection as TSV materials in emerging 3-D ICs.