Modeling of Carbon Nanotube Vertical Interconnects as Transmission Lines

Metallic carbon nanotubes (CNTs) have received worldwide attention as potential substitutions for traditional vertical interconnect (via) materials due to their excellent inherent electrical and thermal properties. In this paper, we present a RLC transmission line model for a single single-walled CNT (SWCNT) via. The resistance of a CNT is dependent on both the magnitude of the applied bias voltage and its length. Due to the low-bias nature of via application, weak electron scattering (acoustic phonons) dominates and the electron mean free path can be as large as a few micrometers. For 1-D nanoelectronic systems, the kinetic (or quantum) inductance dominates the magnetic (or continuum) inductance. As the CNT via is designed to be shielded by a grounded ring, the electrostatic capacitance between the via and the ring is considered. Subsequently, this single SWCNT model is further developed to include a bundled SWCNT via as a result of the weak intertube coupling. Established theoretical modeling results and experimental findings conclude that only the outer tube of the multi-walled CNT (MWCNT) contributes to its conductance. From this, we infer that our modeling approach can also be used for predicting the performance of single and bundled MWCNT-based vias.