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Measurement setup and frequency map as used for surface potential and quantum capacitance tracking. The charge carrier density in grounded graphene flakes is adjusted through . Likewise, the electrostatic force gradient between AFM tip and flake is modulated by an applied ac + dc voltage, , and detected by lock-in techniques at and on the frequency shift output of the PLL. The in-phase component of the fundamental harmonic is nullified by the KPFM feedback to yield the contact potential difference, , while the amplitude of the signal is recorded as a measure of the local capacitance.
Surface potential measurement on a monolayer flake during a gate voltage sweep plotted in parallel to fits obtained from the nearest-neighbor tight-binding model for 0 and 300 K. The inset shows a CPD image of 1LG at .
Surface potential measurement of a flake with 1 to 4 layers of graphene. For better comparison, the curves are shifted with respect to the charge neutrality point found from a 300 K fit of the monolayer data. Data of 2 to 4 layers are fitted to a 2DEG model in order to extract effective masses (see Table I ). (Inset: reflected light micrograph, enhanced contrast).
Simultaneously detected surface potential ( , bilayer offset by +0.1 V) and second sideband amplitude ( ) during a density sweep on a flake with monolayer and bilayer regions. Also shown is the quantum capacitance ( ) of monolayer and bilayer graphene as derived from NNTB calculations at 300 K (solid) and for (dashed). A parabolic approximation (2DEG) on the hyperbolic dispersion of bilayer graphene is only appropriate for very low energies or carrier densities (dotted). At room temperature, the behavior can be approximated by a mean effective mass due to pronounced thermal broadening. (Parameters are and the interlayer coupling, 27 .)]
Multilayer effective masses extracted from the linear fits in Fig. 3 .
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