Frequency- and electric-field-dependent conductivity of single-walled carbon nanotube networks of varying density

Abstract

We present measurements of the frequency- and electric-field-dependent conductivity of single-walled carbon nanotube (SWCNT) networks of various densities. The ac conductivity as a function of frequency is consistent with the extended pair approximation model and increases with frequency above an onset frequency ${\ensuremath{\omega}}_{0}$ which varies over seven decades with a range of film thickness from submonolayer to $200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The nonlinear electric-field-dependent dc conductivity shows strong dependence on film thickness as well. Measurement of the electric field dependence of the resistance $R(E)$ allows for the determination of a length scale ${L}_{E}$ possibly characterizing the distance between tube contacts, which is found to systematically decrease with increasing film thickness. The onset frequency ${\ensuremath{\omega}}_{0}$ of ac conductivity and the length scale ${L}_{E}$ of SWCNT networks are found to be correlated, and a physically reasonable empirical formula relating them has been proposed. Such studies will help the understanding of transport properties and benefit the applications of this material system.