Probing the local surface potential and quantum capacitance in single and multi-layer graphene

We report on local measurements of the surface potential and quantum capacitance in single layer graphene as well as multilayers thereof as a function of the carrier density by using frequency-modulated Kelvin probe force microscopy. We find excellent agreement to tight-binding calculations reported for graphene monolayers and extract the minimum quantum capacitance from density sweeps at room temperature. The surface potential of graphene multilayers is found to depend linearly on the carrier density, which suggests treating them as two-dimensional electron gases. In addition, we demonstrate that the simultaneously detected second harmonic of the Kelvin modulation, proportional to |∂2C/∂z2|, is directly sensitive to local changes in the quantum capacitance of graphene.