Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator

Dynamic atomic force microscopy (dAFM) continues to grow in popularity among scientists in many different fields, and research on new methods and operating modes continues to expand the resolution, capabilities, and types of samples that can be studied. But many promising increases in capability are accompanied by increases in complexity. Indeed, interpreting modern dAFM data can be challenging, especially on complicated material systems, or in liquid environments where the behavior is often contrary to what is known in air or vacuum environments. Mathematical simulations have proven to be an effective tool in providing physical insight into these non-intuitive systems. In this article we describe recent developments in the VEDA (virtual environment for dynamic AFM) simulator, which is a suite of freely available, open-source simulation tools that are delivered through the cloud computing cyber-infrastructure of nanoHUB (www.nanohub.org). Here we describe three major developments. First, simulations in liquid environments are improved by enhancements in the modeling of cantilever dynamics, excitation methods, and solvation shell forces. Second, VEDA is now able to simulate many new advanced modes of operation (bimodal, phase-modulation, frequency-modulation, etc.). Finally, nineteen different tip-sample models are available to simulate the surface physics of a wide variety different material systems including capillary, specific adhesion, van der Waals, electrostatic, viscoelasticity, and hydration forces. These features are demonstrated through example simulations and validated against experimental data, in order to provide insight into practical problems in dynamic AFM.     

Prediction of atomic force microscope probe dynamics through the receptance coupling method

The increased growth in the use of tip-based sensing, manipulations, and fabrication of devices in atomic force microscopy (AFM) necessitates the accurate prediction of the dynamic behavior of the AFM probe. The chip holder, to which the micro-sensing device is attached, and the rest of the AFM system can affect the overall dynamics of the probe. In order to consider these boundary effects, we propose a novel receptance coupling method to mathematically combine the dynamics of the AFM setup and probe, based on the equilibrium and compatibility conditions at the joint. Once the frequency response functions of displacement over force at the tool tip are obtained, the dynamic interaction forces between the tip and the sample in nanoscale can be determined by measuring the probe tip displacement.     

Correlation Between Probe Shape and Atomic Friction Peaks at Graphite Step Edges

Molecular dynamics simulation and atomic force microscopy are used to study the nature of friction between nanoscale tips and graphite step edges. Both techniques show that the width of the lateral force peak as the probe moves up a step is directly correlated with the size and shape of the tip. The origin of that relationship is explored and the similarities and differences between the measurements and simulations are discussed. The observations suggest that the relationship between lateral force peak width and tip geometry can be used as a real-time monitor for tip wear during atomic scale friction measurements.     

AFM变载荷刻划硅基底的分子动力学研究

基于改进的分子动力学模型,研究了原子力显微镜(AFM)探针在硅表面变载荷刻划的形变特性。利用结构辨认算法显示非晶层的形成,并建立切屑分布的定量评价指标。在此基础上考察刻划速度、针尖半径和探针锥角对刻划效果的影响。结果表明:(1)当刻划速度小于0.3 nm/ps或大于等于1.5 nm/ps时,基底表面的切屑较少,刻划速度对沟槽表面的影响不大;(2)当针尖半径小于等于1 nm时,探针会发生磨损,当针尖半径大于等于1.5 nm时,探针发生弹性形变,针尖半径为2~3.5 nm能达到最佳刻划效果;(3)较大的锥角有利于减少基底表面的切屑分布。     

Complex dynamics of carbon nanotube probe tips

Carbon nanotube (CNT) tips in tapping mode atomic force microscopy (AFM) enable very high-resolution imaging, measurements, and manipulation at the nanoscale. We present recent results based on experimental analysis that yield new insights into the dynamics of CNT probe tips in tapping mode AFM. Experimental measurements are presented of the frequency response and dynamic amplitude-distance data of a high-aspect-ratio multi-walled (MW) CNT tip. Higher harmonics of the microcantilever are measured in frequency ranges corresponding to attractive regime and the repulsive regime where the CNT buckles dynamically. Surface scanning is performed using a MWCNT tip on a SiO(2) grating to verify the imaging instabilities associated with MWCNT buckling when used with normal control schemes in the tapping mode. Lastly, the choice of optimal setpoints for tapping mode control using CNT tip are discussed using the experimental results.     

Molecular dynamics simulation of the contact process in AFM surface observations

In the present work, several molecular dynamics simulations have been performed to clarify dynamically the contact mechanism between the specimen surface and probe tip in surface observations by an atomic force microscope (SFM) or friction force microscope (FFM). In the simulation, a three‐dimensional model is proposed where the specimen and the probe are assumed to consist of monocrystalline copper and rigid diamond or a carbon atom, respectively. The effect of the cantilever stiffness of the AFM/FFM is also taken into consideration. The surface observation process is simulated on a well‐defined Cu{100} surface. From the simulation results it has been verified that the surface images and the two‐dimensional atomic‐scale stick‐slip phenomenon, just as is the case for real AFM/FFM surface observations, can be detected from the spring force acting on the cantilever. From the evaluation of the behaviour of specimen surface atoms, the importance of the specimen stiffness in deciding the cantilever properties can also be understood. The influence of the probe tip shape on the force images is also evaluated. From the results it can be verified that the behaviour of the specimen surface atoms as well as the solid surface images in AFM/FFM surface observations can be understood using the molecular dynamics simulation of the model presented.     

Controlling tip–sample interaction forces during a single tap for improved topography and mechanical property imaging of soft materials by AFM

We introduce a method that exploits the “active” nature of the force-sensing integrated readout and active tip (FIRAT), a recently introduced atomic force microscopy (AFM) probe, to control the interaction forces during individual tapping events in tapping mode (TM) AFM. In this method the probe tip is actively retracted if the tip–sample interaction force exceeds a user-specified force threshold during a single tap while the tip is still in contact with the surface. The active tip control (ATC) circuitry designed for this method makes it possible to control the repulsive forces and indentation into soft samples, limiting the repulsive forces during the scan while avoiding instability due to attractive forces. We demonstrate the accurate topographical imaging capability of this method on suitable samples that possess both soft and stiff features.     

Analysis of simulated scanning of atomic-scale silicon surface by atomic force microscopy

This study constructs a contact-mode atomic force microscopy (AFM) simulation measurement model with constant force mode to simulate and analyze the outline scanning measurement by AFM. The simulation method is that when the probe passes the surface of sample, the action force of the atom of sample received by the atom of the probe can be calculated by using Morse potential. Through calculation, the equivalent force on the cantilever of probe can be acquired. By using the deflection angle equation for the cantilever of probe developed and inferred by this study, the deflection angle of receiving action force can be calculated. On the measurement point, as the deflection angle reaches a fixed deflection angle, the scan height of this simulation model can be acquired. By scanning in the right order, the scan curve of the simulation model can be obtained. By using this simulation measurement model, this study simulates and analyzes the scanning of atomic-scale surface outline. Meanwhile, focusing on the tip radii of different probes, the concept of sensitivity analysis is employed to investigate the effects of the tip radius of probe on the atomic-scale surface outline. As a result, it is found from the simulation on the atomic-scale surface that within the simulation scope of this study, when the tip radius of probe is greater than 12 nm, the effects of single atom on the scan curve of AFM can be better decreased or eliminated.     

Simulation-aided design and fabrication of nanoprobes for scanning probe microscopy

We proposed and demonstrated a flexible and effective method to design and fabricate scanning probes for atomic force microscopy applications. Computer simulations were adopted to evaluate design specifications and desired performance of atomic force microscope (AFM) probes; the fabrication processes were guided by feedback from simulation results. Through design-simulation-fabrication iterations, tipless cantilevers and tapping mode probes were successfully made with errors as low as 2% in designed resonant frequencies. For tapping mode probes, the probe tip apex achieved a 10 nm radius of curvature without additional sharpening steps; tilt-compensated probes were also fabricated for better scanning performance. This method provides AFM users improved probe quality and practical guidelines for customized probes, which can support the development of novel scanning probe microscopy (SPM) applications.     

Effect of cantilevers' dimensions on phase contrast in multifrequency atomic force microscopy

During the past years, different theoretical and experimental works are done to enhance the observables (mostly higher eigenmode's phase contrast) in multifrequency atomic force microscopy methods. In this study, the geometry of rectangular cantilevers is studied and an optimum dimension that can provide maximum phase contrast for a given set of samples is found. The analysis is done both numerically and experimentally. A sensitivity analysis is provided to demonstrate which dimension (length, width, thickness, tip‐radius, and cantilever and sample angle) of the cantilever has a higher effect on the results. The effects of geometrical dimensions are categorized into to: (a) effect on dynamics of the cantilever (b) effects on cantilever's specifications (i.e., spring constant and quality factor). Length and width of the cantilever dominates the static behavior of the cantilever. While thickness (for lower values), tip radius, and approach angle mostly affect the dynamic behavior of the cantilever. Theoretically, it is found as the length increases the phase contrast increase. This relationship is opposite for width. It was also observed that the effect of thickness for a specific range on the phase contrast depends on the 1st eigenmode amplitude setpoint. This study shows for having higher contrast, lower tip‐radius is needed. The optimum angle between cantilever and sample to enhance bimodal atomic force microscopy imaging is also found. Based on the commercially available cantilevers, the optimum cantilever dimension is provided. Three different cantilevers with similar dimensions are experimentally tested and theoretical results are verified.     

A torsional resonance mode AFM for in-plane tip surface interactions

Changing the method of tip/sample interaction leads to contact, tapping and other dynamic imaging modes in atomic force microscopy (AFM) feedback controls. A common characteristic of these feedback controls is that the primary control signals are based on flexural deflection of the cantilever probes, statically or dynamically. We introduce a new AFM mode using the torsional resonance amplitude (or phase) to control the feedback loop and maintain the tip/surface relative position through lateral interaction. The torsional resonance mode (TRmode™) provides complementary information to tapping mode for surface imaging and studies. The nature of tip/surface interaction of the TRmode facilitates phase measurements to resolve the in-plane anisotropy of materials as well as measurements of dynamic friction at nanometer scale. TRmode can image surfaces interleaved with TappingMode™ with the same probe and in the same area. In this way we are able to probe samples dynamically in both vertical and lateral dimensions with high sensitivity to local mechanical and tribological properties. The benefit of TRmode has been proven in studies of water adsorption on HOPG surface steps. TR phase data yields approximately 20 times stronger contrast than tapping phase at step edges, revealing detailed structures that cannot be resolved in tapping mode imaging. The effect of sample rotation relative to the torsional oscillation axis of the cantilever on TR phase contrast has been observed. Tip wear studies of TRmode demonstrated that the interaction forces between tip and sample could be controlled for minimum tip damage by the feedback loop.     

An edge reversal method for precision measurement of cutting edge radius of single point diamond tools

A method, which is referred to as the edge reversal method, is proposed for precision measurement of the cutting edge radius of single point diamond tools. An indentation mark of the cutting edge which replicates the cutting edge geometry is firstly made on a soft metal substrate surface. The cutting edge of the diamond tool and its indentation mark, which is regarded as the reversal cutting edge, are then measured by utilizing an atomic force microscopy (AFM), respectively. The cutting edge radius can be accurately evaluated through removing the influence of the AFM probe tip radius, which is comparable to the cutting edge radius, based on the two measured data without characterization of the AFM probe tip radius. The results of measurement experiments and uncertainty analysis are presented to demonstrate the feasibility of the proposed method.     

Velocity dependent friction laws in contact mode atomic force microscopy

Friction forces in the tip–sample contact govern the dynamics of contact mode atomic force microscopy. In ambient conditions typical contact radii between tip and sample are in the order of a few nanometers. In order to account for the large interaction area the dynamics of contact mode atomic force microscope (AFM) is investigated under the assumption of a multi-asperity contact interface between tip and sample. Thus, the kinetic friction force between tip and sample is the product of the real contact area between both solids and the interfacial shear strength. The velocity strengthening of the lateral force is modeled assuming a logarithmic relationship between shear-strength and velocity. Numerical simulations of the system dynamics with this empirical model show the existence of two different regimes in contact mode AFM: steady sliding and stick–slip where the tip undergoes periodically stiction and kinetic friction. The state of the system depends on the scan velocity as well as on the velocity dependence of the interfacial friction force between tip and sample. Already small viscous damping contributions in the tip–sample contact are sufficient to suppress stick–slip oscillations.     

Non-optical tip–sample distance control method for scanning near-field optical microscopy using a piezoresistive micro cantilever

A piezoresistive micro cantilever is applied to monitor the displacement of an optical fibre probe and to control tip–sample distance. The piezoresistive cantilever was originally made for a self-sensitive atomic force microscopy (AFM) probe and has dimensions of 400 µm length, 50 µm width and 5 µm thickness with a resistive strain sensor at the bottom of the cantilever. We attach the piezoresistive cantilever tip to the upper side of a vibrating bent optical fibre probe and monitor the resistance change amplitude of the strain sensor caused by the optical fibre displacement. By using this resistance change to control the tip–sample distance, the two-cantilever system successfully provides topographic and near-field optical images of standard samples in a scanning near-field optical microscopy (SNOM)/AFM system. A resonant characteristic of the two-cantilever system is also simulated using a mechanical model, and the results of simulation correspond to the experimental results of resonance characteristics.     

Long polymeric tips of atomic force microscopy for large biological samples

We show a new atomic force microscopy technique for obtaining high‐resolution topographic images of large bio‐samples. To obtain high‐resolution topographic images for the samples, we fabricated a long polymeric tip with a small protrusion using two‐photon adsorbed photo‐polymerization techniques. The obtained tip length was over 50 µm, and the tip was used directly to visualize COS‐1 and 293 cells. Compared with commercial tips, the long tip made it easier to obtain topographic images of the large cells. In the magnified topographic images, the sub‐100‐nm resolution was confirmed with the long tips. This long probe tip is expected to broaden large sample‐related studies and applications in the future.     

Analysis of dynamic cantilever behavior in tapping mode atomic force microscopy

Tapping mode atomic force microscopy (AFM) provides phase images in addition to height and amplitude images. Although the behavior of tapping mode AFM has been investigated using mathematical modeling, comprehensive understanding of the behavior of tapping mode AFM still poses a significant challenge to the AFM community, involving issues such as the correct interpretation of the phase images. In this paper, the cantilever's dynamic behavior in tapping mode AFM is studied through a three dimensional finite element method. The cantilever's dynamic displacement responses are firstly obtained via simulation under different tip‐sample separations, and for different tip‐sample interaction forces, such as elastic force, adhesion force, viscosity force, and the van der Waals force, which correspond to the cantilever's action upon various different representative computer‐generated test samples. Simulated results show that the dynamic cantilever displacement response can be divided into three zones: a free vibration zone, a transition zone, and a contact vibration zone. Phase trajectory, phase shift, transition time, pseudo stable amplitude, and frequency changes are then analyzed from the dynamic displacement responses that are obtained. Finally, experiments are carried out on a real AFM system to support the findings of the simulations. Microsc. Res. Tech. 78:935–946, 2015. © 2015 Wiley Periodicals, Inc.     

Tip-to-sample distance dependence of an electrostatic force in KFM measurements

In most scanning probe methods like an atomic force microscopy, a cantilever is mechanically vibrated in order to obtain topographies. Therefore, a tip-to-sample distance periodically changes during the scanning. Since the electrostatic force, which is a long-range force, is used for potential feedback in Kelvin probe force microscopy (KFM), such mechanical vibration leads to the fluctuation of the electrostatic force between the tip and the sample. In this study, firstly, we performed two-dimensional simulations of the electric fields between surfaces of the tip and the sample and evaluated the tip-to-sample distance dependence of the electrostatic force. Secondly, we experimentally confirmed the existence of the fluctuation of the electrostatic force and the tip-to-sample distance dependence of the electrostatic force was evaluated. Both the simulations and the experiments on the tip-to-sample distance dependence showed the importance of considering the tip sidewall effect in the KFM potential determination.     

Microfabrication of a combined AFM-SNOM sensor

The objective of this work is to fabricate a scanning probe sensor that combines the well-established method for atomic force microscopy, employing a micro-machined Si cantilever and integrated tip, with a probe for the optical near field. A photosensitive pn-junction is integrated into the tip for that purpose and an Al coating is applied to the tip. It comprises an aperture of 50-70 nm in diameter at the apex of the tip in order to spatially limit the interaction of the tip to the optical near field of the sample. Characterization of the tip and first results of simultaneously recorded force and photon images are presented.     

Coaxial arrangement of a scanning probe and an X-ray microscope as a novel tool for nanoscience

We report on the design and first tests of a novel instrument aimed at combining the benefits of scanning force microscopy with those of X-ray spectroscopy. For this we built an instrument combining a scanning transmission X-ray microscope with a beam-deflection atomic force microscope in a coaxial geometry. This allows to combine X-ray absorption spectroscopy and high resolution topography in-situ. When replacing the conventional scanning probe tip by a coaxially shielded tip the instrument will allow detection of the photoelectrons produced by resonant X-ray absorption. This could yield spectroscopic information with a spatial resolution approaching the values achievable with atomic force microscopy.     

Combined low-temperature scanning tunneling/atomic force microscope for atomic resolution imaging and site-specific force spectroscopy

We present the design and first results of a low-temperature, ultrahigh vacuum scanning probe microscope enabling atomic resolution imaging in both scanning tunneling microscopy (STM) and noncontact atomic force microscopy (NC-AFM) modes. A tuning-fork-based sensor provides flexibility in selecting probe tip materials, which can be either metallic or nonmetallic. When choosing a conducting tip and sample, simultaneous STM/NC-AFM data acquisition is possible. Noticeable characteristics that distinguish this setup from similar systems providing simultaneous STM/NC-AFM capabilities are its combination of relative compactness (on-top bath cryostat needs no pit), in situ exchange of tip and sample at low temperatures, short turnaround times, modest helium consumption, and unrestricted access from dedicated flanges. The latter permits not only the optical surveillance of the tip during approach but also the direct deposition of molecules or atoms on either tip or sample while they remain cold. Atomic corrugations as low as 1 pm could successfully be resolved. In addition, lateral drifts rates of below 15 pm/h allow long-term data acquisition series and the recording of site-specific spectroscopy maps. Results obtained on Cu(111) and graphite illustrate the microscope's performance.