Numerical study of the lateral resolution in electrostatic force microscopy for dielectric samples

Intermittent-contact local dielectric spectroscopy of nanostructured interfaces

Local dielectric spectroscopy (LDS) is a scanning probe method, based on dynamic-mode atomic force microscopy (AFM), to discriminate dielectric properties at surfaces with nanometer-scale lateral resolution. Until now a sub-10 nm resolution for LDS has not been documented, that would give access to the length scale of fundamental physical phenomena such as the cooperativity length related to structural arrest in glass formers (2-3 nm). In this work, LDS performed by a peculiar variant of intermittent-contact mode of AFM, named constant-excitation frequency modulation, was introduced and extensively explored in order to assess its best resolution capability. Dependence of resolution and contrast of dielectric imaging and spectroscopy on operation parameters like probe oscillation amplitude and free amplitude, the resulting frequency shift, and probe/surface distance-regulation feedback gain, were explored. By using thin films of a diblock copolymer of polystyrene (PS) and polymethylmethacrylate (PMMA), exhibiting phase separation on the nanometer scale, lateral resolution of at least 3 nm was demonstrated in both dielectric imaging and localized spectroscopy, by operating with optimized parameters. The interface within lamellar PS/PMMA was mapped, with a best width in the range between 1 and 3 nm. Changes of characteristic time of the secondary (β) relaxation process of PMMA could be tracked across the interface with PS.

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.

Quantitative analysis of effective height of probes in microwave impedance microscopy

A quantitative approach is used to determine an effective height of probe beyond which the capacitance contribution is not significant in microwave impedance microscopy (MIM). We compare the effective height for three different modes of measurement, i.e., capacitance C(l) (l is the tip-sample distance), derivative of capacitance (C'(l)), and second derivative of capacitance (C″(l)). We discuss the effects of tip geometry and sample properties such as relative permittivity and sample height on the effective height with examples and analyze the implication on the spatial resolution of MIM. Finally, our results are verified by microwave impedance microscopy (MIM) measurement.

Nanoscale electric polarizability of ultrathin biolayers on insulating substrates by electrostatic force microscopy

We measured and quantified the local electric polarization properties of ultrathin (∼5 nm) biolayers on mm-thick mica substrates. We achieved it by scanning a sharp conductive tip (<10 nm radius) of an electrostatic force microscope over the biolayers and quantifying sub-picoNewton electric polarization forces with a sharp-tip model implemented using finite-element numerical calculations. We obtained relative dielectric constants εr = 3.3, 2.4 and 1.9 for bacteriorhodopsin, dioleoylphosphatidylcholine (DOPC) and cholesterol layers, chosen as representative of the main cell membrane components, with an error below 10% and a spatial resolution down to ∼50 nm. The ability of using insulating substrates common in biophysics research, such as mica or glass, instead of metallic substrates, offers both a general platform to determine the dielectric properties of biolayers and a wider compatibility with other characterization techniques, such as optical microscopy. This opens up new possibilities for biolayer research at the nanoscale, including nanoscale label-free composition mapping.

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

We present a numerical and analytical study of the behavior of both electrostatic force and force gradient created by a charge trapped below the surface of a dielectric on an atomic force microscope tip as a function of the dielectric constant and tip-sample distance. As expected, the force decreases monotonously when the dielectric constant increases. However, a maximum in the dielectric constant dependence of the force gradient is found. This maximum occurs in the typical experimental parameters' range and depends on the tip-sample distance and the sample thickness. The analytical study permits us to understand the physical origin of this phenomenon and is in good agreement with the numerical simulation for small tip-sample distances. We also report a study exemplifying a possible contrast inversion in electrostatic force microscopy (EFM) signals while scanning, at different heights, two charges trapped in a sample having heterogeneous dielectric domains. In addition to this particular contrast inversion effect, this study can be considered as a way to gain insight into the mechanisms of EFM image formation as a function of the dielectric constant and tip-sample.