Computational study of geometry-dependent resistivity scaling in single-walled carbon nanotube films

We study the geometry-dependent resistivity scaling in single-walled carbon nanotube films as a function of nanotube and device parameters using Monte Carlo simulations. We first demonstrate that these simulations can model and fit recent experimental results on the scaling of nanotube film resistivity with device width. Furthermore, we systematically study the effect of four parameters; namely, tube-tube contact resistance to nanotube resistance ratio, nanotube density, nanotube length, and nanotube alignment on the film resistivity and its scaling with device width. Stronger width scaling is observed when the transport in the nanotube film is dominated by tube-tube contact resistance. Increasing the nanotube density decreases the film resistivity strongly and results in a higher critical exponent and a lower critical width. Increasing the nanotube length also reduces the film resistivity, but increases both the critical exponent and the critical width. In addition, the lowest resistivity occurs for a partially aligned rather than perfectly aligned nanotube film. Increasing the degree of alignment reduces both the critical exponent and the critical width. We systematically explain these observations, which are in agreement with previous experimental results, by simple physical and geometrical arguments. We also observe that, near the percolation threshold, the resistivity of the nanotube film exhibits an inverse power-law dependence on all of these parameters, which is a distinct signature of percolating conduction. However, the strength of resistivity scaling for each parameter is different, and it depends on how strongly a particular parameter changes the number of conduction paths in the film. Monte Carlo simulations, as presented in this paper, can help elucidate the effects of various parameters on percolating transport in films made up of one-dimensional conductors, which is an essential step towards understanding and characterizing the performance of these nanomaterials in electronic and optoelectronic devices.