(a) Schematic of the fabricated device structure with several electrodes and different inter-electrode spacings L, on a single flake of graphene. (b) Schematic of the TLM. A contact resistance can be extracted from an intercept at L = 0 for a linear fitting of the two-terminal resistance, R, versus L plot.
(a) and (b) Transfer characteristics of Ag-contacted graphene FETs with different channel lengths (L = 2.5 to 0.5 μm) fabricated on the same graphene flake. The characteristics in (b) are replots of (a) against the normalized gate voltage, V G − V NP. (c) R-L plot of the Ag-contacted devices at V G = V NP. The straight line is the result of a least-squares fit, which indicates an apparently negative contact resistance.
Dependence of the contact resistance on the gate voltage extracted using the TLM for (a) Ag, (b) Cu, and (c) Au contacts. The solid lines represent the best-fit lines of calculations using the proposed model. Deviation of the fitting lines from the experimental curves may be due to partial depinning of the metal contacts.16
(a) Gate-voltage dependence of the charge-density profile for the model calculation. The vertical axis is a gate-voltage equivalent, and positive (negative) values correspond to electron (hole) doping. Linearly graded doping occurs from the metal contact edges (x = 0, L) to the distance into the graphene channel, L D. The charge density at the metal contacts is uncontrollable with the application of gate voltages. (b) Two possible contributions to the contact resistances extracted by the TLM or four-terminal measurement are (1) the actual contact resistance precisely at the contact, R CI (most simply, ascribable to a tunneling process5), and (2) the apparently-appeared contact resistance due to the potential variation induced by the metal contact, R CD.
Simulated R CD-V G characteristics with variation of the (a) polarity of doped carriers, (b) L D, (c) μ, and (d) n D. The fixed parameters were set to L D = 0.2 μm, μ = 1.0 m2 V−1 s−1, and n D = 1.5 × 1012 cm−2. The solid and dashed lines in (a) indicate the results for positive (electron doping) and negative (hole doping) n D, respectively.
Comparison of the magnitudes of R CI and R CD at metal contacts to various systems. The condition |R CD| > R CI, which is necessary to observe the apparently negative R C as extracted in this study, is considered to be fulfilled at the interfaces of metals with Dirac-cone systems.
Simulated V G dependency of the two parts of R CI with various p. While the completely pinned contacts (p = 0) lead to no V G dependence, thefully or partially depinned contacts (finite p) induce a divergence at V G= −V D/p.
R C simulation parameters extracted by fitting to the experimentally obtained R C-V G characteristics shown in Figure 3.
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