Microscale multi-point probes fabricated by Capres A/S. (a) Twelve-point probes based on individual metal-coated SiO2 cantilevers. (b) Mono-cantilever probes which support metal wires as contacts. 20 Both types of probes are commercially available.
(a) Four possible measurement configurations for a non-equidistant twelve-point probe, along with the resultant corrected spacing. The top-left corresponds to a traditional equidistant arrangement, the top-right is a bridging configuration, and the two lower are exterior configurations. (b) Corrected resistance vs. corrected spacing for three hypothetical systems measured with this probe: a semi-infinite 3D bulk with ρ b = 5000 Ωm, a 2D sheet with ρ s = 50 × 10−3 Ω/□, and the two in parallel.
Cut-away diagram of the multi-point probe instrument. The upper-right inset shows the circuit board used for mounting and connecting the probes shown in Fig. 1 .
(a) Corrected resistance vs. corrected spacing for a monolayer of epitaxial graphene on silicon carbide. 11 (b) Corrected resistance vs. corrected spacing for degenerately doped Bi2Se3.
(a) Corrected resistance vs. corrected spacing for quasi free-standing hydrogen-intercalated graphene on silicon carbide. Note the greatly increased scatter compared to Fig. 4(a) . (b) Comparison of two sequences of I/V measurements taken from the same location, separated by approximately 40 min.
(a) Example of a randomly generated conductivity map used for simulations. Black areas are of high resistivity, white areas are of low resistivity. (b) Corrected resistance vs. corrected spacing for the quasi free-standing monolayer graphene sample (from Fig. 5 ) together with simulated data. (c) Histograms of corrected resistance for simulations and both graphene samples (Figs. 4(a) and 5(a) ). The height of the histograms has been rescaled for clarity.
(a) Corrected spacing, plotted in grayscale, versus the positions of the two voltage contacts. The distance between the current-carrying contacts is 3s and the resulting corrected spacing is also given in units of s. The x and y axes denote the position of the voltage probes (both in units of s), and are hence allowed to be negative. Contours indicate bounds of relative error. While the diagram for the corrected spacing can be scaled freely, these contours have been calculated by assuming a contact positional error of 500 nm and 3s = 10 μm. Note the areas of very significant error associated with some bridging configurations. (b) Overview of configurations as represented in these plots.
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