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Schematic of the Kelvin probe force measurement setup. The applied voltages and are indicated.
(a) Topography of the epitaxially grown graphene. Terrace sizes of approximately in diameter are visible. Wrinkles (bright lines) and pits (dark holes) can be seen. (b) Surface potential map at the same location. Discrete values of surface potential can be seen corresponding to the number of graphene layers on the surface. (c) Larger topography of the graphene surface between the contacts. (d), (e) The potential maps with the applied bias voltage of , respectively. (f), (g) The corresponding, averaged cross section of (d) and (e) with linear fits showing slopes of and
(a) Topography at the edge of one of the gold electrodes. (b), (c)Corresponding potential maps at applied biases of , respectively. (d) Color coded cross sections of the maps in (a), (b), and (c). The shaded area indicates the position of the contact. The linear fits of thesurface potential show slopes of and respectively.
(a) The potential resulting from the charge transport through the graphene layer extracted from the measurements in Fig. 4(a) along with the graph of the simulated graphene layer potential for contact resistivities of and The dark shaded area is again the position of the gold contact according to the topographic measurements. The potential resulting from the charge transport through the graphene layer extracted from the measurements in Fig. 4(a) along with the graph of the simulated graphene layer potential for contact resistivities of and The dark shaded area is again the position of the gold contact according to the topographic measurements. The inset line graph shows the distribution of current density along the graphene-gold contact interface using the same x-axis as the original plot. Colored symbols represent the results of the simulation, and solid lines represent the analytical solution after 33 using the experimental results as input parameters. The color plot represents the electric potential distribution across the whole gold contact, 260 μm in length and 100 nm in height and the underlying graphene sheet as result of the simulation for a contact resistivity of The graphene layer is displayed broadened for better visualization. (b) Schematic of the resistor network used for the simulation. The gold colored resistors on the top represent the gold contacts; the dark gray ones on the bottom represent the graphene layer. Red resistors represent the contact resistivity between the two. Dashed lines indicate successive resistors. A voltage corresponding to the experiments is applied to the top of the contacts.
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