Frequency Modulation Atomic Force Microscopy Research Articles

Development of scanning capacitance force microscopy using the dissipative force modulation method

We have developed scanning capacitance force microscopy (SCFM) using the dissipative force in frequency-modulation atomic force microscopy. An SCFM signal depends on the dopant density and polarity of semiconductors, whose evaluation is important for developing electronic devices. Thus, improving the force sensitivity of SCFM can prove effective for investigating these devices. In a previous report, the dissipative force modulation method was developed to increase the force sensitivity for Kelvin probe force microscopy. Thus, the force sensitivity of SCFM can be increased using this method. In this study, we determined the theoretical formula for SCFM by using dissipative force. Because this force was modulated using a multiplication signal with the same phase as that of a cantilever excitation signal, the SCFM signal was detected from the deflection of the cantilever by using a demodulation circuit. In the conventional method, the SCFM signal is detected using the second resonance frequency of the cantilever with a high-quality factor. The minimum detectable force of SCFM was calculated to be 0.74 fN from the Brownian motion of the cantilever, which is smaller than that obtained using the conventional method. The differential capacitance of a patterned silicon sample was measured using the proposed method and conventional one. The modulation signal amplitude was reduced from 3.0 V to 1.5 V in increments of 0.5 V. Using the proposed method, the differential dopant regions could be distinguished under a modulation signal amplitude of 1.5 V. However, using the conventional method, the regions could not be observed under the modulation signal amplitude of 2.0 V. Therefore, the proposed method could reduce the modulation signal amplitude from 2.5 V to 1.5 V. In addition, the signal-to-noise ratio and the spatial resolution of the proposed method were found to be higher than that of the conventional one.

Modelling and nanoscale force spectroscopy of frequency modulation atomic force microscopy

In this paper, a simulation model for frequency modulation atomic force microscopy (FM-AFM) operating in constant amplitude dynamic mode is presented. The model is based on the slow time varying function theory. The mathematical principles to derive the dynamical equations for the amplitude and phase of the FM-AFM cantilever-tip motion are explained and the stability and performance of its closed-loop controller to keep the amplitude at constant value and phase at 90° is analysed. Then, the performance of the theoretical model is supported by comparison of numerical simulations and experiments. Furthermore, the transient behaviour of amplitude, phase and frequency shift of FM-AFM is investigated and the effect of controller gains on the transient motion is analysed. Finally, the derived FM-AFM model is used to simulate the single molecule/nanoscale force spectroscopy and study the effect of sample viscosity, stiffness and Hamaker constant on the response of FM-AFM.

Multidimensional topography sensing simulating an AFM

Atomic force microscopy (AFM) is used in the semiconductor industry for inspection and quality control. Frequency modulated AFM (FM-AFM) extracts surface topography by measuring the frequency shift created by the Van der Waals (VdW) interaction forces between the tip and the sample. To improve the measurement speed and address complex geometries emerging in industrial microchip constructions, several enhancements are introduced. While most FM-AFM devices operate in a single vibrating mode, this article proposes a method for multidimensional sensing using frequency modulation of 2 orthogonal vibration modes, simultaneously. The concept was tested on a large-scale experimental system, where VdW forces were replaced by magnetic forces, using a magnetic tip and ferromagnetic samples. To emulate the VdW forces accurately, the designed ratio between the base frequency and frequency shift was kept to mimic a Nano-scale AFM. By utilizing an Autoresonance (AR) control scheme for faster locking onto resonance and a curve fitting frequency estimation algorithm it is possible to sense the minute changes in frequency experienced by several modes, simultaneously. Experimental results employ 3D relevant topographies such as inclined surfaces, steep walls and trenches that were reconstructed experimentally with 4 (μm) resolution or better. Downscaling to typical AFM dimensions would theoretically yield sub-nanometer resolution.

Layer-by-layer dissolution and recovery of KBr(001) surfaces covered with a nanometer-thick water film caused by a pressing tip controlled by frequency modulation atomic force microscopy

We observed KBr(001) surfaces covered with a nanometer-thick water film (NWF) using frequency modulation atomic force microscopy (FM-AFM) with stiff force sensors. The NWF with a thickness of ∼3 nm was prepared in humid air at 50%–60% RH. The Δf–Z curves measured by FM-AFM exhibited a series of peaks over the surface, corresponding to the hydration layers, and unique multiple oscillation peaks under the surface. The AFM images showed that layer-by-layer dissolution of KBr(001) planes under the NWF was induced by tip pressing, and quick recovery of the KBr planes was achieved after tip retraction.

Force spectroscopy using a quartz length-extension resonator

Frequency modulation atomic force microscopy detects the interaction force between the tip and the sample by measuring the change in the resonance frequency of an oscillating force sensor. Short-range interaction force can be selectively detected by a small oscillation amplitude. A quartz length-extension resonator (LER) offers the advantage of small-amplitude operation by virtue of its ultrahigh stiffness. Here, we demonstrate that an LER can accurately measure the short-range interaction force at cryogenic temperature even under a high magnetic field. We derive a formula for calculating the effective stiffness of an oscillating LER by using the theory of elasticity. The obtained dynamic stiffness is 1.23 times greater than the static stiffness, and this difference significantly affects the estimation of the interaction force. Using a properly calibrated LER, force curves are measured on Si(111)-(7 × 7) surfaces. The maximum attractive short-range forces above Si adatoms using several tip apex states are in the ranges of the values previously obtained by Si cantilevers.

Amplitude Dependence of Resonance Frequency and its Consequences for Scanning Probe Microscopy.

With recent advances in scanning probe microscopy (SPM), it is now routine to determine the atomic structure of surfaces and molecules while quantifying the local tip-sample interaction potentials. Such quantitative experiments using noncontact frequency modulation atomic force microscopy is based on the accurate measurement of the resonance frequency shift due to the tip-sample interaction. Here, we experimentally show that the resonance frequency of oscillating probes used for SPM experiments change systematically as a function of oscillation amplitude under typical operating conditions. This change in resonance frequency is not due to tip-sample interactions, but rather due to the cantilever strain or geometric effects and thus the resonance frequency is a function of the oscillation amplitude. Our numerical calculations demonstrate that the amplitude dependence of the resonance frequency is an additional yet overlooked systematic error source that can result in nonnegligible errors in measured interaction potentials and forces. Our experimental results and complementary numerical calculations reveal that the frequency shift due to this amplitude dependence needs to be corrected even for experiments with active oscillation amplitude control to be able to quantify the tip-sample interaction potentials and forces with milli-electron volt and pico-Newton resolutions.

Nanometer-Scale Distribution of a Lubricant Modifier on Iron Films: A Frequency-Modulation Atomic Force Microscopy Study Combined with a Friction Test.

Liquid lubricants used in mechanical applications are low-vapor-pressure hydrocarbons modified with a small quantity of polar compounds. The polar modifiers adsorbed on the surface of sliding solids dominate the friction properties when the sliding surfaces are in close proximity. However, a few methods are available for the characterization of the adsorbed modifiers of a nanometer-scale thickness. In this study, we applied frequency-modulation atomic force microscopy to evaluate the vertical and lateral density distributions of the adsorbed modifier in a real lubricant, namely, poly-α-olefin (PAO) modified with an orthophosphoric acid oleyl ester. The liquid-induced force on the probing tip was mapped on a plane that was perpendicular to the lubricant–iron interface with a force sensitivity on the order of 10 pN. The PAO in the absence of the ester modifier was directly exposed to the film, which produced a few liquid layers parallel to the film surface with layer-to-layer distances of 0.6–0.7 nm. A monomolecular layer of the modifier was intermittently adsorbed with increasing ester concentration in the bulk lubricant, with complete coverage seen at 20 ppm. The C18H35 chains of the oleyl esters fluctuating in the lubricant produced a repulsive force on the tip, which monotonically decayed with the tip-to-surface distance. The dynamic friction coefficient of sliding steel–lubricant–steel interfaces, which was separately determined using a friction tester, was compared with the force map determined on the iron film immersed in the corresponding lubricant. The complete monomolecular layer of the ester modifier on the static lubricant–iron boundary is a requirement for achieving smooth and stable friction at the sliding interface.

Highly sensitive AFM using self-excited weakly coupled cantilevers

In this article, we propose a method, using weakly coupled cantilevers, to enhance the sensitivity of atomic force microscopy (AFM) by several orders of magnitudes. There are two major dynamics AFM methods, i.e., amplitude modulation AFM and frequency modulation AFM (FM-AFM). In FM-AFM, which is based on the eigenfrequency shift of a single cantilever, the enhancement in sensitivity is restricted because of the limitations of miniaturization in the manufacturing process. By contrast, we used coupled cantilevers based on the eigenmode shift, which corresponds to the amplitude ratio between the cantilevers. This enabled us to increase the sensitivity by reducing the coupling stiffness between cantilevers without relying on further miniaturization. In addition, to detect the eigenmode shift, even in high-viscosity environments, we produced self-excitation in the weakly coupled cantilevers by feedback control. Using this prototype system of coupled macroscale cantilevers subjected to the magnetic force, which simulates the atomic force, we confirmed the high sensitivity of the proposed method.

Sequence-Dependent Deviations of Constrained DNA from Canonical B-Form.

Decades of crystallographic and NMR studies have produced canonical structural models of short DNA. However, no experimental method so far has been able to test these models in vivo, where DNA is long and constrained by interactions with membranes, proteins, and other molecules. Here, we employ high-resolution frequency-modulation AFM to image single long poly(dA)-poly(dT), poly(dG)-poly(dC), and lambda DNA molecules interacting with an underlying substrate that emulates the effect of biological constraints on molecular structure. We find systematic sequence-dependent variations in groove dimensions, indicating that the structure of DNA subject to realistic interactions may differ profoundly from canonical models. These findings highlight the value of AFM as a unique, single molecule characterization tool.

Adsorbed gas layers limit the mobility of micropancakes

In contrast to surface nanobubbles, the properties of atomically flat gas phases such as micropancakes remain unclear. In this study, we investigated nanoscopic gas phases existing at the interface between highly ordered pyrolytic graphite and air-supersaturated pure water using high-sensitivity frequency-modulation atomic force microscopy (AFM). Micropancakes appeared on a disordered gas layer overlying an ordered gas layer and moved in the direction of AFM scanning. Their movement stopped at the edge of the disordered gas layers, whereas the two gas layers did not move at all. The limited mobility of micropancakes is explained by assuming that the disordered and ordered gas layers, which are composed of strongly adsorbed gas molecules, behave like solid surfaces, and that the surface heterogeneity between them results in a pinning effect.

A Fourier method for estimating potential energy and lateral forces from frequency-modulation lateral force microscopy data

One mode of atomic force microscopy (AFM) is frequency-modulation AFM, in which the tip is driven to oscillate at its resonance frequency which changes as the tip interacts with the surface. Frequency-modulation lateral force microscopy (FM-LFM) is the variant of this technique in which the tip is oscillated along the surface. For an isolated adsorbate on a flat surface, the only signal in FM-LFM is caused by the short-range interaction with the adsorbate. Various deconvolution methods exist to convert the observed frequency shift into the more physically relevant parameters of force and energy. While these methods are often used for FM-AFM data, the high number of inflection points of FM-LFM data make standard deconvolution methods less reliable. In this article, we present a method based on Fourier decomposition of FM-LFM data and apply it to data taken of an isolated CO molecule on the Pt(111) surface. We probe the potential energy landscape past the potential energy minimum and show how over an adsorbate, the potential energy can be evaluated with a single FM-LFM image.

Multiply Modified Repeating DNA Templates for Production of Novel DNA-Based Nanomaterial.

Here, we report synthesis of long (thousands of base pairs), uniform double-stranded (ds) DNA comprising short (6-15 base pairs) tandem repeats. The synthesis method is based on self-assembly of short (6-15 bases) half-complementary 5'-end phosphorylated single-stranded oligonucleotides into long ds polymer molecules and covalent association of the oligonucleotide fragments in the polymer by DNA ligase to yield complete non-nicked ds DNA. The method is very flexible in regard to the sequence of the oligonucleotides and their length. Human telomeric DNA comprising thousands of base pairs as well as methylated, mismatched, and fluorescent dye-modified uniform dsDNA molecules can be synthesized. We have demonstrated by high resolution frequency-modulation atomic force microscopy that the structure of DNA containing mismatches is strongly different from that of the non-mismatched one. The DNA molecules comprising groups capable of anchoring metal particles and other redox active elements along the whole length of the nucleic acid polymer should find use as wires or transistors in future nanoelectronic applications.

Variations in Atomic-Scale Step Edge Structures and Dynamics of Dissolving Calcite in Water Revealed by High-Speed Frequency Modulation Atomic Force Microscopy

Calcite dissolution plays critical roles in the global carbon cycle in the Earth, biomineralizations, and weathering of buildings. However, in spite of the importance, the atomistic events at the step edges during the dissolution have remained elusive because of the difficulties in their direct visualization. In this study, we used high-speed frequency modulation atomic force microscopy (FM-AFM) for visualizing various atomic-scale step edge structures and dynamics during the calcite dissolution in water. The obtained images reveal the coexistence of the steps with and without a transition region (TR); a Ca(OH)2 monolayer formed along the step edge as an intermediate state in the dissolution. The TRs are more frequently observed along the slowly dissolving acute steps than along the rapidly dissolving obtuse steps. This finding and our imaging of the TR formation process suggest that the free energy to form a TR is comparable to that for removing ions directly from the step edge and an increase in the loc...

Investigating ice surfaces formed near the freezing point in the vapor phase via atomic force microscopy

An atomic force microscope (AFM) using a qPlus sensor was developed to observe ice surfaces grown near the freezing point in the vapor phase. The AFM system was equipped with multi-environmental control mechanisms for the temperature, humidity, and pressure of the introduced gas and the substrate temperature. Topographic images of the basal face of the ice, grown from a supersaturated water vapor, were obtained near equilibrium conditions via frequency modulation AFM (FM-AFM). Surface morphologies corresponding to steps and terraces were successfully observed. Force-curve measurements were also performed on the ice surfaces using FM-AFM. The results can be explained by the quasi-liquid layer on the ice surface.

Analytical method for the measurement of the electrostatic force and the contact potential difference excluding the effect of the Casimir force with a conventional atomic force microscope

From the previous study by Inami and Sugimoto [Phys. Rev. Lett. 114, 246102 (2015)], it is known that a conventional frequency-modulation atomic force microscope (FM-AFM) system does not give an accurate contact potential difference (CPD) when it depends on the distance, and a novel method to measure an accurate CPD based on the energy dissipation was proposed. This method requires additional experimental setups to the conventional FM-AFM system to measure the energy dissipation. We propose the analytical method for the measurement of the distance dependence of the CPD with a conventional FM-AFM without additional setup which is based on evaluating the electrostatic force excluding the effect of the Casimir force and local charges.

Molecular-scale visualization and surface charge density measurement of Z-DNA in aqueous solution

The DNA in the left-handed conformation (Z-conformation) was first discovered by A. Rich, who revealed the crystalline structure of a DNA oligomer d(GC)3 by X-ray diffraction method. Later it was also found that DNA molecules change their conformations from typical right-handed form (B-DNA) to the left-handed form (Z-DNA) under specific conditions (B–Z transition). Furthermore, the detailed structures of the interface between B- and Z-DNAs, B-Z junction, was also determined with an atomic resolution. Recently it was found that some proteins have the Z-DNA binding domains, but the biological functions of Z-DNA are not well understood yet. Therefore the investigation of Z-DNA under physiological conditions is highly essential. In this study, we demonstrated the high-resolution real-space imaging of DNA molecules having the Z- and B-form conformations by frequency-modulation atomic force microscopy (FM-AFM), that has made a great progress in recent years, in an aqueous solution. The major and minor grooves of both DNA conformations were clearly visualized. Furthermore, the surface charge density was measured by three-dimensional (3D) force mapping method. We found that Z-form region was less negatively charged than the B-form region.

In-situ characterization of O-terminated Cu tips for high-resolution atomic force microscopy

Functionalizing a metal tip with a single CO molecule (CO tip) leads to an unprecedented spatial resolution of small organic molecules by frequency-modulation atomic force microscopy (FM-AFM) at low temperatures. O-terminated Cu tips (CuOx tips) show comparable imaging capabilities as CO tips but exhibit a much stiffer apex. So far, to verify tip functionalization with oxygen (i.e., CuOx tips), scanning tunneling microscopy and AFM images, together with force spectroscopy curves of copper oxide domains, have been compared with calculated data for different tip models. Here, we apply the carbon-monoxide front atom identification (COFI) method and additional force spectroscopy to characterize CuOx tips in-situ on a Cu(110) surface. In COFI, a single CO molecule adsorbed on a Cu surface is imaged to atomically resolve the tip apex. Based on our findings, we suggest accompanying tip fingerprinting with COFI and force spectroscopy to identify the atomic and chemical compositions of the apex of CuOx tips for high-resolution AFM experiments.

Atomic-Level Viscosity Distribution in the Hydration Layer.

The viscosity of solvation structures is crucial for the development of energy-efficient biofunctional and electrochemical devices. Elucidating their subnanoscale distributions can cause the formation of a sustainable energy society. Here, we visualize the site-specific three-dimensional damping distribution on a CaCO_{3} surface composed of binary ion species using ultra-low-noise frequency modulation atomic force microscopy. With the support from molecular dynamics simulation, we found a strikingly large damping at the calcium sites, which demonstrates the capability of this methodology to visualize atomic-scale viscosity in the hydration layers. Our finding will expedite the evolutions of various functional devices.

Correlative force and tip-enhanced Raman microscopy

Tip-enhanced Raman scattering (TERS) microscopy attracts increasing attention for visualization and characterization of strain distribution on crystalline samples at a nanoscale due to nano-sized fields localized at a metal tip. However, as the metal tip approaches close to a sample surface, a force acts between the tip and sample, which can induce unwanted perturbation on the local strain of the sample. Analysis and evaluation of intrinsic strains on samples with a high reliability demands a technique to correlate TERS spectra with the tip-sample force. Here, we present a TERS microscope based on a frequency-modulation atomic force microscope (FM-AFM) using a quartz tuning fork (QTF) as a force sensor. By continuously monitoring a shift in the resonance frequency of the QTF during TERS, the tip-sample force can be directly measured in both attractive and repulsive force regions, which is not possible by other AFMs. TERS spectra of single-walled carbon nanotubes (CNTs) were measured simultaneously while changing the tip-sample distance and hence the tip-sample force acting on the CNTs. We found that TERS occurs at the tip-sample distance where the repulsive force dominantly works and mostly decays out in the attractive force region.

Putting force laws to the test

Force Microscopy In frequency-modulated atomic force microscopy, force is not measured directly. The resonant frequency amplitude and phase of the vibrating cantilever are converted into force through mathematical inversion algorithms. The resolution of this approach now extends to measuring the force between individual atoms, but Sader et al. show that the underlying interatomic forces can also vary rapidly. These conditions can make the inversion of the frequency shifts mathematically ill-posed and lead to unphysical results. They formulate a simple inflection point test of the changes in force with distance of the tip from the surface that ensures that the inversion algorithm problem will yield an accurate force measurement. Nat. Nanotechnol. 13 , 1088 (2018).