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

Abstract

Anomalous Hall resistivity due to grain boundary in manganite thin films J. Appl. Phys. 93, 8107 (2003) We have studied the behavior of micro four-point probe (M4PP) measurements on two-dimensional (2D) sheets composed of grains of varying size and grain boundary resistivity by Monte Carlo based finite element (FE) modelling. The 2D sheet of the FE model was constructed using Voronoi tessellation to emulate a polycrystalline sheet, and a square sample was cut from the tessellated surface. Four-point resistances and Hall effect signals were calculated for a probe placed in the center of the square sample as a function of grain density n and grain boundary resistivity q GB . We find that the dual configuration sheet resistance as well as the resistance measured between opposing edges of the square sample have a simple unique dependency on the dimension-less parameter ffiffi ffi n p q GB G 0 , where G 0 is the sheet conductance of a grain. The value of the ratio R A =R B between resistances measured in A-and B-configurations depends on the dimensionality of the current transport (i.e., one-or two-dimensional). At low grain density or low grain boundary resistivity, two-dimensional transport is observed. In contrast, at moderate grain density and high grain resistivity, one-dimensional transport is seen. Ultimately, this affects how measurements on defective systems should be interpreted in order to extract relevant sample parameters. The Hall effect response in all M4PP configurations was only significant for moderate grain densities and fairly large grain boundary resistivity. Published by AIP Publishing. [http://dx

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“…In contrast, a M4PP measurement with 300 μm probe pitch (see illustration in Supporting Information Figure S1) is measuring the 2D conductance, which is highly sensitive to any obstructions of the current flow, and only identical to the 2D conductivity for a perfectly uniform conducting film of constant thickness. 24,28,29 CLSM, KPFM, and Raman spectroscopic mapping were carried out in all three regions, R1, R2, and R3, to further understand the differences in σ dc observed in Figure 1. The CLSM images reveal clear topographical differences between the three regions as shown in Figure 2a−c.…”

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“…From the M4PP resistance ratio ( R A / R B ), it is possible to determine whether the current flow in the sample is qualitatively one- or two-dimensional (1D or 2D). If R A / R B = 1, the current flow is 1D-like, typical for damaged regions where the source-drain current flow is restricted to narrow pathways, whereas R A / R B ≈ 1.26 corresponds to an uninhibited current flow, where the sample is homogeneously conducting in two dimensions. , The M4PP measurements were conducted with the probes aligned horizontally in all images shown as indicated by the probe positions in Supporting Information Figure S1.…”

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“…Moreover, STP has received interest from theory in recent years. More recent approaches consider graphene‐specific geometries and defects and extend general treatments that were started over two decades ago …”

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“…It is well known that the experimental measurements of electrical conductivity are not so complicated; this is done with a four-point method to measure the sheet resistivity or conductivity [1,2]. However, making a theoretical estimate of the electrical conductivity requires complicated mathematical elements, e.g., Lippmann-Schwinger equation [3,4].…”