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 probe conductance measurements and we find that the micro four-point probe tends to measure a slightly higher conductance in samples containing defects.

Terahertz wafer-scale mobility mapping of graphene on insulating substrates without a gate

“…4, the spread in σ s,dc , µ Hall , and N s,Hall measured in vdP structures is quite large compared to the significantly smaller spread in σ s,dc , µ drift , and N s measured by THz-TDS. As we have shown in previous correlation studies [13,18], however, defects on the scale of the device dimensions can greatly affect the electronic parameters determined by vdP device measurements [22,23,36], while the THz-TDS outcome is much less affected, due to its much smaller characteristic carrier transport length (tens to hundreds of nm). The ratio of resistances R A /R C , measured in two different electrode configurations provides a unique signature of the presence of such extended defects in the devices, where a device with a continuous active region, free from such extended defects will fulfil the criterion of electrical continuity [18], which in this case is 1 A C…”

“…The graphene film was patterned by picosecond laser ablation into 5 mm wide square van der Pauw (vdP) devices, suitable for dual-configuration sheet conductance and Hall effect measurements to extract carrier mobility and carrier density [19]. Dual configuration measurements suppress geometrical errors in both sheet conductance [20] and Hall effect measurements [21] and allow the electrical continuity to be determined [13,18,22,23]. With a constant applied external magnetic field of B ext = 255 mT, the resistances R A , R B and R C were measured in the three electrode configurations, defined from Fig.…”

Mesoscopic current transport in two-dimensional materials with grain boundaries: Four-point probe resistance and Hall effect

“…23,24 Initially, a coarse triangular mesh was applied; then two adaptive mesh refinement steps followed to optimize the mesh by increasing the mesh resolution in locations with large potential gradients, such as close to the current inlets. As shown in our previous publication, 18 two mesh-refinement steps were sufficient to ensure a relative error of less than 1% of the fully converged solution. For questions concerning the validity of this method of modelling M4PP measurements, we also refer to a previous publication, Ref .…”

“…The resistance ratio RÃ= RB has previously been shown to assume values that differ significantly between 2D and quasi-1D materials, 15,18,19 and here, we study the distribution on the grainy material.…”

“…14 M4PP metrology can be used to measure the sheet resistance (or sheet conductance), and in addition, the method allows for extraction and evaluation of geometry related parameters such as the resistance ratio 15,16 and the Hall effect signal caused by the Lorentz force. 17 In previous work, 18 we developed a finite element (FE) model to investigate how the M4PP signature differs for measurements on 2D and quasi-1D materials; these signatures had already been observed experimentally. 15,16 We successfully validated the FE approach by comparing calculations for a single line defect to the analytical result.…”