Modeling of Joule Heating Induced Effects in Multiwall Carbon Nanotube Interconnects

Abstract

Electrothermal performance of multiwall carbon nanotubes (MWCNT)-based interconnects has been studied under the influence of self-heating. The interlayer insulator is a low-k ( $\varepsilon _{r}\sim 2$ ) dielectric. Various geometries have been studied for the normal operation and breakdown conditions. Electrothermal coupled equations have been solved iteratively by solving Fourier heat diffusion equation with a finite-element method. Within the relaxation time approximation, mean free path of the electron has been calculated under different scattering mechanisms. Landauer–Buttiker formalism resistance has been used for calculating electrical resistance. Breakdown voltages for varying MWCNT lengths have been calculated and found to be higher in MWCNT with a shorter length. Breakdown voltage varies from 8.2 to 12 V for inner diameters 10–40 nm of 5- $\mu \text{m}$ interconnect length and 50-nm outer diameter. Breakdown voltage decreases with the increase in the length of interconnect. For a 5- $\mu \text{m}$ long interconnect, the breakdown voltage is nearly 8 V whereas for the same diameter $1~\mu \text{m}$ long interconnect it is nearly 22 V. Breakdown current density depends on the geometry $\vphantom {_{\int }} $ of the MWCNT and is estimated on the order of $10^{8}$ A $\cdot $ cm−2.