Fundamental Limits of Current Flow in One-dimensional Carbon Nanomaterials

Carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) carry very high current densities given their strong sp2 bonds and high carrier mobility. However, the fundamental limitations to their maximum current flow are still not well understood. We measured the maximum current flow of CNTs and GNRs in substrate-supported configurations in ambient air where devices break from Joule heating at $\sim $600 C [1,2], revealing information about their power dissipation. Interestingly, thermal coupling with the substrate increases with CNT diameter but decreases with GNR width, due to competing roles of thermal boundary resistance and heat spreading into the substrate. To further study quasi-metallic single-wall CNTs at very high fields, we performed measurements in vacuum. We found some devices show current saturation as expected [3], but in many the current continues to increase with a constant slope of $\sim $~1~$\mu $A/V at fields $>$10 V/$\mu $m. This is observed even in small-diameter ($\sim $1.2 nm) CNTs whose dimensions were verified by AFM and Raman spectroscopy. We suggest such behavior can be explained by a combination of better heat coupling with the substrate and higher subband conduction. [1] A. Liao \textit{et al}, PRB \textbf{82}, 205406 (2010). [2] A. Liao \textit{et al}, PRL \textbf{106}, 256801 (2011). [3] Z. Yao \textit{et al}, PRL \textbf{84}, 2941 (2000).