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

Abstract

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.

Probing Nanoscale Schottky Barrier Characteristics at WSe2/Graphene Heterostructures via Electrostatic Doping

“…The carrier density induced in graphene by electrostatic doping is expected to be widely modeled by the geometric capacitance, with little contribution from the quantum capacitance. [ 49 ]…”

“…The carrier density induced in graphene by electrostatic doping is expected to be widely modeled by the geometric capacitance, with little contribution from the quantum capacitance. [49] The estimated doping density relative to the CNP from the capacitor model can be converted into a Fermi level (E F ) in monolayer graphene with the expression [50,51,52]…”

Measurement of electrostatic tip–sample interactions by time-domain Kelvin probe force microscopy

“…The Kelvin system, i.e., the measurement system without the detector, has the state vector (12) Index k is the discrete sampling applied, t k = kΔt. The model assumes that the sample properties remain constant between two discrete measurements, thus (13) Deviations from this assumption, for example due to scan movement, are introduced by the vector (14) This vector, the so-called transition noise vector, is anticipated to be Gaussian white noise (0,Q K ) with the covariance matrix (15) The output of the Kelvin system is the scalar value of the intrinsic frequency shift . It is defined by (16)…”

“…The response at the second harmonic contains additional information about the capacitance gradient C ′′ = ∂ 2 C/∂z 2 . This signal is interesting in itself as it contains information about both geometric and electronic properties of tip and sample, e.g., the dielectric properties of a sample or the quantum capacitance [14]. Furthermore, this signal can be used to adjust the sensitivity of the KFM feedback loop [15].…”

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

“…Recently, KFM has been used to extract the surface state density and Schottky depletion region in semiconductor nanowires [4–5] or to determine the mean free path in carbon nanotubes [6]. KFM also allows one to determine intrinsic doping of two-dimensional crystals such as graphene [7–8], where surface potential and electronic properties depend on the number of layers.…”