# Revealing origin of quasi-one dimensional current transport in defect rich two dimensional materials

## Abstract

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 probemore »

- Authors:

- Center for Nanostructured Graphene (CNG), Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech Building 345 East, DK-2800 Kgs. Lyngby (Denmark)
- Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech Building 345 East, DK-2800 Kgs. Lyngby (Denmark)
- (CINF), Technical University of Denmark, DK-2800 Kgs. Lyngby (Denmark)
- (Denmark)

- Publication Date:

- OSTI Identifier:
- 22314511

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Physics Letters; Journal Volume: 105; Journal Issue: 5; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; DEFECTS; ELECTRIC CURRENTS; FINITE ELEMENT METHOD; GRAPHENE; MONTE CARLO METHOD; ONE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Lotz, Mikkel R., Boll, Mads, Bøggild, Peter, Petersen, Dirch H., E-mail: dirch.petersen@nanotech.dtu.dk, Hansen, Ole, Danish National Research Foundation's Center for Individual Nanoparticle Functionality, Kjær, Daniel, and CAPRES A/S, Scion-DTU, Building 373, DK-2800 Kgs. Lyngby.
```*Revealing origin of quasi-one dimensional current transport in defect rich two dimensional materials*. United States: N. p., 2014.
Web. doi:10.1063/1.4892652.

```
Lotz, Mikkel R., Boll, Mads, Bøggild, Peter, Petersen, Dirch H., E-mail: dirch.petersen@nanotech.dtu.dk, Hansen, Ole, Danish National Research Foundation's Center for Individual Nanoparticle Functionality, Kjær, Daniel, & CAPRES A/S, Scion-DTU, Building 373, DK-2800 Kgs. Lyngby.
```*Revealing origin of quasi-one dimensional current transport in defect rich two dimensional materials*. United States. doi:10.1063/1.4892652.

```
Lotz, Mikkel R., Boll, Mads, Bøggild, Peter, Petersen, Dirch H., E-mail: dirch.petersen@nanotech.dtu.dk, Hansen, Ole, Danish National Research Foundation's Center for Individual Nanoparticle Functionality, Kjær, Daniel, and CAPRES A/S, Scion-DTU, Building 373, DK-2800 Kgs. Lyngby. Mon .
"Revealing origin of quasi-one dimensional current transport in defect rich two dimensional materials". United States.
doi:10.1063/1.4892652.
```

```
@article{osti_22314511,
```

title = {Revealing origin of quasi-one dimensional current transport in defect rich two dimensional materials},

author = {Lotz, Mikkel R. and Boll, Mads and Bøggild, Peter and Petersen, Dirch H., E-mail: dirch.petersen@nanotech.dtu.dk and Hansen, Ole and Danish National Research Foundation's Center for Individual Nanoparticle Functionality and Kjær, Daniel and CAPRES A/S, Scion-DTU, Building 373, DK-2800 Kgs. Lyngby},

abstractNote = {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.},

doi = {10.1063/1.4892652},

journal = {Applied Physics Letters},

number = 5,

volume = 105,

place = {United States},

year = {Mon Aug 04 00:00:00 EDT 2014},

month = {Mon Aug 04 00:00:00 EDT 2014}

}