Theoretical Estimation of Electromigration in Metallic Carbon Nanotubes Considering Self-Heating Effect

In this paper, we estimate the solution of the electromigration diffusion equation (EMDE) in isotopically pure and impure metallic single-walled carbon nanotubes (CNTs) (SWCNTs) by considering self-heating. The EMDE for SWCNT has been solved not only by invoking the dependence of the electromigration flux on the usual applied static electric field across its two ends but also by considering a temperature-dependent thermal conductivity $(\kappa )$ which results in a variable temperature distribution $(T)$ along its length due to self-heating. By changing its length and isotopic impurity, we demonstrate that there occurs a significant deviation in the SWCNT electromigration performance. However, if $\kappa$ is assumed to be temperature independent, the solution may lead to serious errors in performance estimation. We further exhibit a tradeoff between length and impurity effect on the performance toward electromigration. It is suggested that, to reduce the vacancy concentration in longer interconnects of few micrometers, one should opt for an isotopically impure SWCNT at the cost of lower $\kappa$ , whereas for comparatively short interconnects, pure SWCNT should be used. This tradeoff presented here can be treated as a way for obtaining a fairly well estimation of the vacancy concentration and mean time to failure in the bundles of CNT-based interconnects.