In this work, we use contrast image processing to estimate the concentration of multi-wall carbon nanotubes (MWCNT) in a given network. The fractal dimension factor (D) of the CNT network that provides an estimate of its geometrical complexity, is determined and correlated to network resistance. Six fabricated devices with different CNT concentrations exhibit D factors ranging from 1.82 to 1.98. The lower D-factor was associated with the highly complex network with a large number of CNTs in it. The less complex network, having the lower density of CNTs had the highest D factor of approximately 2, which is the characteristic value for a two-dimensional network. The electrical resistance of the thin MWCNT network was found to scale with the areal mass density of MWCNTs by a power law, with a percolation exponent of 1.42 and a percolation threshold of 0.12 μg/cm2. The sheet resistance of the films with a high concentration of MWCNTs was about six orders of magnitude lower than that of less dense networks; an effect attributed to an increase in the number of CNT-CNT contacts, enabling more efficient electron transfer. The dependence of the resistance on the areal density of CNTs in the network and on CNT network complexity was analyzed to validate a two-dimension percolation behavior.
Keywords: carbon nanotubes; electron transport; fractal dimension; multi-walled; packing density; percolation limits; tunneling.