1 Department of Micro- and Nanotechnology, Technical University of Denmark2 Experimental Surface and Nanomaterials Physics, Department of Physics, Technical University of Denmark3 Silicon Microtechnology, Department of Micro- and Nanotechnology, Technical University of Denmark4 Nanointegration, Department of Micro- and Nanotechnology, Technical University of Denmark5 Center for Nanostructured Graphene, Center, Technical University of Denmark6 Department of Physics, Technical University of Denmark
The presence of defects in graphene have for a long time been recognized as a bottleneck for its utilization in electronic and mechanical devices. We recently showed that micro four-point probes may be used to evaluate if a graphene film is truly 2D or if defects in proximity of the probe will lead to a non-uniform current flow characteristic of lower dimensionality. In this work, simulations based on a finite element method together with a Monte Carlo approach are used to establish the transition from 2D to quasi-1D current transport, when applying a micro four-point probe to measure on 2D conductors with an increasing amount of line-shaped defects. Clear 2D and 1D signatures are observed at low and high defect densities, respectively, and current density plots reveal the presence of current channels or branches in defect configurations yielding 1D current transport. A strong correlation is found between the density filling factor and the simulation yield, the fraction of cases with 1D transport and the mean sheet conductance. The upper transition limit is shown to agree with the percolation threshold for sticks. Finally, the conductance of a square sample evaluated with macroscopic edge contacts is compared to the micro four-point probe conductance measurements and we find that the micro four-point probe tends to measure a slightly higher conductance in samples containing defects. (C) 2014 AIP Publishing LLC.