Joachim Dahl Thomsen

Quality assessment of graphene: Continuity, uniformity, and accuracy of mobility measurements

With the increasing availability of large-area graphene, the ability to rapidly and accurately assess the quality of the electrical properties has become critically important. For practical applications, spatial variability in carrier density and carrier mobility must be controlled and minimized. We present a simple framework for assessing the quality and homogeneity of large-area graphene devices. The field effect in both exfoliated graphene devices encapsulated in hexagonal boron nitride and chemical vapor-deposited (CVD) devices was measured in dual current–voltage configurations and used to derive a single, gate-dependent effective shape factor, β, for each device. β is a sensitive indicator of spatial homogeneity that can be obtained from samples of arbitrary shape. All 50 devices investigated in this study show a variation (up to tenfold) in β as a function of the gate bias. Finite element simulations suggest that spatial doping inhomogeneity, rather than mobility inhomogeneity, is the primary cause of the gate dependence of β, and that measurable variations of β can be caused by doping variations as small as 1010 cm−2. Our results suggest that local variations in the position of the Dirac point alter the current flow and thus the effective sample shape as a function of the gate bias. We also found that such variations lead to systematic errors in carrier mobility calculations, which can be revealed by inspecting the corresponding β factor.

Conductance quantization suppression in the quantum Hall regime

Conductance quantization is the quintessential feature of electronic transport in non-interacting mesoscopic systems. This phenomenon is observed in quasi one-dimensional conductors at zero magnetic field B, and the formation of edge states at finite magnetic fields results in wider conductance plateaus within the quantum Hall regime. Electrostatic interactions can change this picture qualitatively. At finite B, screening mechanisms in narrow, gated ballistic conductors are predicted to give rise to an increase in conductance and a suppression of quantization due to the appearance of additional conduction channels. Despite being a universal effect, this regime has proven experimentally elusive because of difficulties in realizing one-dimensional systems with sufficiently hard-walled, disorder-free confinement. Here, we experimentally demonstrate the suppression of conductance quantization within the quantum Hall regime for graphene nanoconstrictions with low edge roughness. Our findings may have profound impact on fundamental studies of quantum transport in finite-size, two-dimensional crystals with low disorder.Conductance quantization is the hallmark of non-interacting confined systems. The authors show that the quantization in graphene nanoconstrictions with low edge disorder is suppressed in the quantum Hall regime. This is explained by the addition of new conductance channels due to electrostatic screening.

Quantitative optical mapping of two-dimensional materials

The pace of two-dimensional materials (2DM) research has been greatly accelerated by the ability to identify exfoliated thicknesses down to a monolayer from their optical contrast. Since this process requires time-consuming and error-prone manual assignment to avoid false-positives from image features with similar contrast, efforts towards fast and reliable automated assignments schemes is essential. We show that by modelling the expected 2DM contrast in digitally captured images, we can automatically identify candidate regions of 2DM. More importantly, we show a computationally-light machine vision strategy for eliminating false-positives from this set of 2DM candidates through the combined use of binary thresholding, opening and closing filters, and shape-analysis from edge detection. Calculation of data pyramids for arbitrarily high-resolution optical coverage maps of two-dimensional materials produced in this way allows the real-time presentation and processing of this image data in a zoomable interface, enabling large datasets to be explored and analysed with ease. The result is that a standard optical microscope with CCD camera can be used as an analysis tool able to accurately determine the coverage, residue/contamination concentration, and layer number for a wide range of presented 2DMs.