Defining the parameters of a cantilever tip AFM by reference structure

A method of measurement and control of atomic force microscope (AFM) probe parameters is offered. The AFM real cantilever parameters are defined.     

Study on effects of tip geometry on AFM nanoscratching tests

To investigate effects of tip geometry on AFM nanoscratching process, an experimental calibration method measuring three-dimensional (3D) scratching forces based on the cantilever deflection is presented. On the surface of single crystal copper and silicon, nanoscratching tests are carried out using a pyramidal diamond tip. Effects of tip geometry (including the hemisphere of the tip and three sides of the pyramid) on scratching forces, friction coefficient and specific energy are studied. Results show that the scratching depth of about 10–15 nm is a transition point in scratching tests for the diamond tip used in this paper. Below this value, the hemisphere is dominant, whereas at the scratching depth of larger than this value, three sides of the tip play the key role in scratching tests. Friction coefficients are different at different tip orientations influenced by the contact area between the tip and the sample and attack angle at the scratching depth of greater than 10–15 nm. Specific energy is not sensitive to tip geometry because it reveals the energy required for removal of materials.     

Influence of the tip mass and position on the AFM cantilever dynamics: Coupling between bending,torsion and flexural modes

The effects of the geometrical asymmetric related to tip position as a concentrated mass, on the sensitivity of all three vibration modes, lateral excitation (LE), torsional resonance (TR) and vertical excitation (VE), of an atomic force microscopy (AFM) microcantilever have been analyzed. The effects of the tip mass and its position are studied to report the novel results to estimating the vibration behavior of AFM such as resonance frequency and amplitude of the microcantilever. In this way, to achieve more accurate results, the coupled motion in all three modes is considered. In particular, it is investigated that performing the coupled motion in analysis of AFM microcantilever is almost necessary. It is shown that the tip mass and its position have significant effects on vibrational responses. The results show that considering the tip mass decreases the resonance frequencies particularly on high-order modes. However, dislocating of tip position has an inverse effect that causes an increase in the resonance frequencies. In addition, it has been shown that the amplitude of the AFM microcantilever is affected by the influences of tip and its position. These effects are caused by the interaction between flexural and torsional motion due to the moment of inertia of the tip mass.     

Dynamic response of rotating flexible cantilever pipe conveying fluid with tip mass

In this study the vibration system is consisted of a rotating cantilever pipe conveying fluid and a tip mass. The equation of motion is derived by using the Lagrange's equation. Also, the equation of motion is derived applying a modeling method that employs hybrid deformation variables. The influences of the rotating angular velocity and the velocity of fluid flow on the dynamic behavior of a cantilever pipe are studied by the numerical method. The effects of a tip mass on the dynamic behavior of a rotating cantilever pipe are also studied. The influences of a tip mass, the velocity of fluid, the angular velocity of a cantilever pipe and the coupling of these factors on the dynamic behavior of a cantilever pipe are analytically clarified. The natural frequencies of a cantilever pipe conveying fluid are proportional to the angular velocity of the pipe and a tip mass in both axial direction and lateral direction.     

Interlaboratory round robin on cantilever calibration for AFM force spectroscopy

Single-molecule force spectroscopy studies performed by Atomic Force Microscopes (AFMs) strongly rely on accurately determined cantilever spring constants. Hence, to calibrate cantilevers, a reliable calibration protocol is essential. Although the thermal noise method and the direct Sader method are frequently used for cantilever calibration, there is no consensus on the optimal calibration of soft and V-shaped cantilevers, especially those used in force spectroscopy. Therefore, in this study we aimed at establishing a commonly accepted approach to accurately calibrate compliant and V-shaped cantilevers. In a round robin experiment involving eight different laboratories we compared the thermal noise and the Sader method on ten commercial and custom-built AFMs. We found that spring constants of both rectangular and V-shaped cantilevers can accurately be determined with both methods, although the Sader method proved to be superior. Furthermore, we observed that simultaneous application of both methods on an AFM proved an accurate consistency check of the instrument and thus provides optimal and highly reproducible calibration. To illustrate the importance of optimal calibration, we show that for biological force spectroscopy studies, an erroneously calibrated cantilever can significantly affect the derived (bio)physical parameters. Taken together, our findings demonstrated that with the pre-established protocol described reliable spring constants can be obtained for different types of cantilevers.     

Analysis of the effect of mechanical properties of liquid and geometrical parameters of cantilever on the frequency response function of AFM

The dynamic behavior of atomic force microscopy (AFM) cantilevers in liquid is completely different from its behavior in air due to the applied hydrodynamic force. Exciting cantilever with frequencies close to resonance frequency and primary position alignment are two critical issues that should be considered in deriving frequency response function (FRF). In this paper, the hydrodynamic force has been modeled with string of spheres and the effect of the damping and the added mass on the model has been analyzed. Afterward, this force is applied to the dynamic equation so that the dynamic behavior of AFM cantilevers is studied in liquids by analyzing the effect of some important parameters such as added mass, internal, and fluid damping. By simulations of the dynamic equations for a silicon cantilever, FRF is determined in both air and liquid. In addition, the effects of two significant parameters of liquid mechanical properties (liquid viscosity and density) and geometrical parameters of cantilever on FRF are studied. The results for string of spheres model are compared with the other hydrodynamic model and the experimental data. When length/width ratio decreases, it is found that string of spheres model has a better agreement than the other hydrodynamic model with experimental data.     

On the dynamics of tapered vibro-impacting cantilever with tip mass

This paper explores nonlinear dynamic behavior of vibro-impacting tapered cantilever with tip mass with regard to frequency response analysis. A typical frequency response curve of vibro-impacting beams displays well-known resonance frequency shift along with a hysteric jump and drop phenomena. We did a comprehensive parametric analysis capturing the effects of taper, tip-mass, stop location, and gap on the non-smooth frequency response. Analysis is presented in a non-dimensional form useful for other similar cases. Simulation results are further validated with corresponding experimental results for a few cases. Illustrative comparison of simulation results for varying parameters brings out several interesting aspects of variation in the nonlinear behavior.     

The effect of fluid properties and geometrical parameters of cantilever on the frequency response of atomic force microscopy

Nowadays, the atomic force microscopy plays an indispensable role in imaging and manipulation of biological samples. To observe some specific behaviors and biological processes, fast and accurate imaging techniques are required, and one way to speed up the imaging process is to use short cantilevers. For short beams, the Timoshenko model seems to be more accurate compared to other models such as the Euler–Bernoulli. By using the Timoshenko beam model, the effects of rotational inertia and shear deformation are taken into consideration. In this paper, the frequency response of a rectangular atomic force microscope (AFM) in liquid environment has been analyzed by using the Timoshenko beam model. Afterward, since the dynamic response of AFM is influenced by the applied medium, the effects of physical and mechanical properties (e.g., fluid density and viscosity) on the frequency response of the system have been investigated. The frequency responses of the AFM cantilever immersed in various liquids have been compared with one another. And eventually, to study the influence of geometry on the dynamic behavior of AFM, the effect of the cantilever's geometrical parameters (e.g., cantilever length, width and thickness) on the frequency response of the system has been studied.     

Phase detection of electrostatic force by AFM with a conductive tip

Electrostatic force measurements were performed by the Kelvin probe force microscopy, which consists of the atomic force microscopy and a conductive tip. Sample surface potential was evaluated through the electrostatic force, which works between the sample and the tip when we apply an AC bias at a frequency f(s) with a DC offset. If the DC offset voltage is equal to the surface potential difference between the sample and the tip, the amplitude of the f(s) component in the electrostatic force becomes zero, and the phase of the f(s) component jumps 180 degrees there. We found that the complementary use of the amplitude and phase signals improved the accuracy of the determination of the surface potential. We measured both the work functions of some metals and the surface Fermi levels of an InAs layers on (1 0 0) and (1 1 0) GaAs substrates based on the phase detection method of the electrostatic force.     

Combined quantitative ultrasonic and time-resolved interaction force AFM imaging

The authors describe a method where quantitative ultrasonic atomic force microscopy (UAFM) is achieved during time-resolved interaction force (TRIF) imaging in intermittent contact mode. The method uses a calibration procedure for quantitative UAFM. It improves elasticity measurements of stiff regions of surfaces while retaining the capabilities of the TRIF mode for topography, adhesion, dissipation, and elasticity measurements on soft regions of sample surfaces. This combination is especially advantageous when measuring and imaging samples with broad stiffness range in a nondestructive manner. The experiments utilize an active AFM probe with high bandwidth and the UAFM calibration is performed by measuring the magnitude of the time-resolved UAFM signal at a judiciously chosen frequency for different contact stiffness values during individual taps. Improved sensitivity to stiff surface elasticity is demonstrated on a special sample. The results show that combining UAFM with TRIF provides 2.5 GPa (5%) standard deviation on the silicon surface reduced Young's modulus, representing 5× improvement over using only TRIF mode imaging.     

An experimental study of the contact mode AFM scanning capability of polyimide cantilever probes

This paper presents a preliminary exploration of high-speed contact mode performed with a polyimide probe. The probe is batch micromachined by a lithographic manufacturing process. It offers a spring constant of <0.1N/m, a resonance frequency of about 50k Hz, and a tip diameter of 50-100 nm. The probe is particularly suitable for scanning soft specimens such as biological and polymeric samples. Topographical contact mode imaging at high scanning rates of 48 Hz (1.47 mm/s) has been demonstrated, detecting features <100 nm over a 15 microm scan, yielding >7 bit resolution at 48 Hz. Scanning rates of 16 Hz (0.5mm/s) have been demonstrated for lateral force imaging with spatial resolution of 100 nm over a 15 microm scan, which translates into >7 bit resolution at 16 Hz. These results suggest that the probe can be used in high throughput applications.     

Step response measurement of AFM cantilever for analysis of frequency-resolved viscoelasticity

Extension of AFM-based viscoelasticity measurement into a frequency-resolved analysis is attempted. A cantilever immersed into and interacting with distilled water was employed for the trial system. Using a home-built wideband magnetic excitation AFM, a step force with a transient time less than 1 μs is applied to the AFM cantilever and its deflection is measured. The 1st and 2nd mode resonance ringing of the cantilever was suppressed using quality-factor-control technique, so that the measurement system becomes equivalent to driving a resonance-free virtual cantilever within the bandwidth limited by the surviving 3rd mode resonance. From the obtained response of the cantilever deflection, a frequency-dependent complex compliance of the cantilever-water system was derived in a frequency range of 1–100 kHz. Effect of water confining between the tip and a mica substrate is discussed.     

Influence of tip mass on dynamic behavior of cracked cantilever pipe conveying fluid with moving mass

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange’s equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.     

Experimental and theoretical studies of frequency response function of dagger-shaped atomic force microscope cantilever in different immersion environments

In this study, the amplitude of frequency response functions of vertical and rotational displacements and resonant frequency of a dagger-shaped atomic force microscope cantilever have been investigated. To increase the accuracy of theoretical model, all necessary details for cantilever and sample surface have been taken into account. In this paper, carbon tetrachloride (CCL₄), methanol, acetone, water and air have been considered as the environments. In the most cases, presence and absence of tip–sample interaction force have studied. For a sample cantilever immersed in air, both of the Euler–Bernoulli and Timoshenko beam theories have been compared. The results indicate that the tip–sample interaction force raises the resonant frequency. Increasing the liquid viscosity leads to a decrease in the resonant frequency and the amplitude of frequency response functions of vertical and rotational displacements. Increasing the rectangular and tapered parts lengths, decreases the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements. By increasing the cantilever thickness the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements increases. Theoretical model for air and water has been compared with experimental work. Results show good agreement.     

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.     

Analysis of photopolymerized acrylic films by AFM in pulsed force mode

This paper highlights the potential of atomic force microscopy in the pulsed force mode to investigate the photopatterning of acrylic‐based films. The pulsed force mode is a nonresonant mode designed to allow approach curves to be recorded along the scanning path. It thereby provides the topography of the sample and a direct and simple local characterization of adhesion and stiffness. This mode can be used either for imaging or for locally probing the mechanical properties of a surface. In particular, a correlation between stiffness and conversion of the monomer was established. The close examination of the pulsed force mode signal brought accurate information on the photoinduced modification of the film. Polymer films with submicron photopatterning generated by interferometric illumination were analyzed by pulsed force mode. It was established that the gradient of mechanical properties throughout the films was strongly dependant on the irradiation conditions.     

Kinetostatic model of spring constant ratios for an AFM cantilever with end extended mass

In previous work we showed that the kinetostatic method is very effective in computing the increase in value of the spring constants of an AFM free (with or without added mass) and supported rectangular cantilever for higher mode oscillations relative to their values for natural vibration. We have considered in all previous cases that added mass is a concentrated one. However, the additional mass may be an extended one particularly in the case of a V-shaped cantilever. In this article we consider the influence of the constituent beam’s (leg’s) mutual skew and the altered position of the nodal points in the case when the attached extended triangular (trapezoid) mass of the V-shaped cantilever has a significant moment of rotational inertia and a center of this mass gravity located beyond the constituent beam end. We show that considering these effects in using the kinetostatic model yields results for the ratios of the spring constants at higher modes of oscillation and their values at the first frequency natural vibration for a V-shaped cantilever which are in good agreement with the thermomechanical noise amplitudes obtained by other researchers. This should prove helpful for the proper calibration of V-shaped cantilevers whose application with higher modes oscillation provides increased measurement sensitivity.     

Study of the sensitivity and resonant frequency of the torsional modes of an AFM cantilever with a sidewall probe based on a nonlocal elasticity theory

A relationship based on a nonlocal elasticity theory is developed to investigate the torsional sensitivity and resonant frequency of an atomic force microscope (AFM) with assembled cantilever probe (ACP). This ACP comprises a horizontal cantilever and a vertical extension, and a tip located at the free end of the extension, which makes the AFM capable of topography at sidewalls of microstructures. First, the governing differential equations of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of nonlocal elasticity theory and Hamilton's principle. Afterward, a closed‐form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. These analysis accounts for a better representation of the torsional behavior of an AFM with sidewall probe where the small‐scale effect are significant. The results of the proposed model are compared with those of classical beam theory. The results show that the sensitivities and resonant frequencies of ACP predicted by the nonlocal elasticity theory are smaller than those obtained by the classical beam theory. Microsc. Res. Tech. 78:408–415, 2015. © 2015 Wiley Periodicals, Inc.     

Mapping of lateral vibration of the tip in atomic force microscopy at the torsional resonance of the cantilever

Lateral vibration of the tip in atomic force microscopy was mapped at the torsional resonance of the cantilever by attaching a shear piezo element at the base of the cantilever or under the sample. Fixed frequency excitation and self-excitation of torsional motion were implemented. The lateral vibration utilized as measured by an optical lever was in the order of 10 pm to 3 nm, and its frequency approximately 450 kHz for a contact-mode silicon nitride cantilever. The amplitude and phase of the torsional motion of the cantilever was measured by a lock-in-amplifier or a rectifier and plotted in x and y as the sample was raster scanned. The imaging technique gave contrast between graphite terraces, self-assembled monolayer domains, silicon and silicon dioxide, graphite and mica. Changing contrast was observed as silicon islands oxidized in atmosphere, showing that the imaging technique can detect change in lateral tip mobility due to changes occurring near the surface. Torsional self-excitation showed nanometric features of self-assembled monolayer islands due to different lateral dissipation. Dependence of torsional resonance frequency on excitation amplitude, and contrast change due to driving frequency around resonance were observed.