Contrast inversion in electrostatic force microscopy imaging of trapped charges: tip-sample distance and dielectric constant dependence

Exploring surface charge dynamics: implications for AFM height measurements in 2D materials

An often observed artifact in atomic force microscopy investigations of individual monolayer flakes of 2D materials is the inaccurate height derived from topography images, often attributed to capillary or electrostatic forces. Here, we show the existence of a Joule dissipative mechanism related to charge dynamics and supplementing the dissipation due to capillary forces. This particular mechanism arises from the surface conductivity and assumes significance specially in the context of 2D materials on insulating supports. In such scenarios, the oscillating tip induces in-plane charge currents that in many circumstances constitute the main dissipative contribution to amplitude reduction and, consequently, affect the measured height. To investigate this phenomenon, we conduct measurements on monolayer flakes of co-deposited graphene oxide and reduced graphene oxide. Subsequently, we introduce a general model that elucidates our observations. This approach offers valuable insights into the dynamics of surface charges and their intricate interaction with the tip.

Characterizing Dielectric Permittivity of Nanoscale Dielectric Films by Electrostatic Micro-Probe Technology: Finite Element Simulations

Finite element simulations for detecting the dielectric permittivity of planar nanoscale dielectrics by electrostatic probe are performed to explore the microprobe technology of characterizing nanomaterials. The electrostatic force produced by the polarization of nanoscale dielectrics is analyzed by a capacitance gradient between the probe and nano-sample in an electrostatic detection system, in which sample thickness is varied in the range of 1 nm-10 μm, the width (diameter) encompasses from 100 nm to 10 μm, the tilt angle of probe alters between 0° and 20°, and the relative dielectric constant covers 2-1000 to represent a majority of dielectric materials. For dielectric thin films with infinite lateral dimension, the critical diameter is determined, not only by the geometric shape and tilt angle of detecting probe, but also by the thickness of the tested nanofilm. Meanwhile, for the thickness greater than 100 nm, the critical diameter is almost independent on the probe geometry while being primarily dominated by the thickness and dielectric permittivity of nanomaterials, which approximately complies a variation as exponential functions. For nanofilms with a plane size which can be regarded as infinite, a pertaining analytical formalism is established and verified for the film thickness in an ultrathin limit of 10-100 nm, with the probe axis being perpendicular and tilt to film plane, respectively. The present research suggests a general testing scheme for characterizing flat, nanoscale, dielectric materials on metal substrates by means of electrostatic microscopy, which can realize an accurate quantitative analysis of dielectric permittivity.

Charge distribution from SKPM images

Inferring the surface charge distribution from experimental Kelvin probe microscopy measurements is usually a hard task. Although several approximations have been proposed in order to estimate the effect of these charges, the real inverse problem has not been addressed so far. In this paper, we propose a fast and intuitive method based on Fast Fourier Transform algorithms that allows the surface charge distribution to be obtained directly from the experimental Kelvin voltage measurements. With this method, quantitative physical information such as the total charge and charge position is accessible even in complex charge distributions such as highly insulating polymer surfaces. Moreover, one of the strongest points is that sub-tip resolution is achieved, and therefore the usually unknown charge size can be estimated.

Localized charge imaging with scanning Kelvin probe microscopy

In this work, we propose an intuitive and easily implementable approach to model and interpret scanning Kelvin probe microscopy images of insulating samples with localized charges. The method, based on the image charges method, has been validated by a systematic comparison of its predictions with experimental measurements performed on charge domains of different sizes, injected in polymethyl methacrylate discontinuous films. The agreement between predictions and experimental lateral profiles, as well as with spectroscopy tip-sample distance curves, supports its consistency. The proposed procedure allows obtaining quantitative information such as total charge and the size of a charge domain and allows estimating the most adequate measurement parameters.