Sensitivity analysis explains quasi-one-dimensional current transport in two-dimensional materials

Abstract

We demonstrate that the quasi-one-dimensional (1D) current transport, experimentally observed in graphene as measured by a collinear four-point probe in two electrode configurations A and B, can be interpreted using the sensitivity functions of the two electrode configurations (configurations A and B represents different pairs of electrodes chosen for current sources and potential measurements). The measured sheet resistance in a four-point probe measurement is averaged over an area determined by the sensitivity function. For a two-dimensional conductor, the sensitivity functions for electrode configurations A and B are different. But when the current is forced to flow through a percolation network, e.g., graphene with high density of extended defects, the two sensitivity functions become identical. This is equivalent to a four-point measurement on a line resistor, hence quasi-1D transport. The sensitivity analysis presents a formal definition of quasi-1D current transport, which was recently observed experimentally in chemical-vapor-deposition graphene. Our numerical model for calculating sensitivity is verified by comparing the model to analytical calculations based on conformal mapping of a single extended defect.

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.…”

Case studies of electrical characterisation of graphene by terahertz time-domain spectroscopy

“…A(I 1,4 , V 2,3 ) and B(I 1,3 , V 2,4 ), following the notation described in detail elsewhere [14]. If R A /R B = 1 the current flow is said to be 1D-like, while a uniform conductor will exhibit R A /R B ≈ 1.26 [72][73][74]. Figure 4(c) shows a line plot of the R A /R B resistance ratio across the same line as in figure 4(b).…”

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

“…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.…”

“…15,16 We successfully validated the FE approach by comparing calculations for a single line defect to the analytical result. 19 The model was limited in its scope since only samples with insulating line defects were studied, which may be a reasonable representation of 2D materials in which current transport is dominated by transfer defects such as rips and tears. However, with improvements in fabrication of 2D materials, today transfer defects can now often be neglected.…”