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Probing the local surface potential and quantum capacitance in single and multi-layer graphene
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Image of FIG. 1.
FIG. 1.

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  +  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.

Image of FIG. 2.
FIG. 2.

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 .

Image of FIG. 3.
FIG. 3.

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).

Image of FIG. 4.
FIG. 4.

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, .)]


Generic image for table
Table I.

Multilayer effective masses extracted from the linear fits in Fig. 3 .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Probing the local surface potential and quantum capacitance in single and multi-layer graphene