Atomic Force Microscopy Microcantilevers Research Articles

A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces

Precise and accurate representation of an Atomic Force Microscopy (AFM) system is essential in studying the effects of boundary interaction forces present between the probe's tip and the sample. In this paper, a comprehensive analytical model for the AFM system utilizing a distributed-parameters based approach is proposed. More specifically, we consider two important attributes of these systems; namely the rotary inertia and shear deformation when compared with the Euler-Bernoulli beam theory. Moreover, a comprehensive nonlinear interaction force is assumed between probe's and sample in order to reveal the response of the system more realistically. This nanoscale interaction force is based on a general form consisting of both attractive and repulsive components as well as a function of the tip-sample distance and the microcantilever's base and sample oscillations. Mechanical properties of the sample could interact with the nanomechanical coupling field between the probe' tip and sample and be implemented in studying the composition information of the sample and the ultra-small features inside it. Therefore, by modulating the dynamics of the AFM system such as the driving amplitude of the microcantilever the procedure for the subsurface imaging is described. The presented approach here could be implemented for designing the AFM probes by examining the tip-sample interaction forces dominant by the van der Waals forces. Several numerical case studies are presented and the force-distance diagram reveals that the proposed nonlinear nanomechanical force along with the distributed-parameters model for the microcantilever is able to fulfill the mechanics of the Lennard-Jones potential.

Mechanical and tribological characterization of a thermally actuated MEMS cantilever

The temperature effect on the mechanical and tribological behaviors of a microelectromechanical systems cantilever is experimentally investigated using an atomic force microscope. A nonlinear variation of the bending stiffness of microcantilevers as a function of temperature is determined. The variation of the adhesion force between the tip of atomic force microscope (AFM) probe (Si3N4) and the microcantilever fabricated in gold is monitored at different temperatures. Using the lateral mode operation of atomic force microscope, the influence of temperature on friction coefficient between the tip of AFM probe and microcantilever is presented. Finite element analysis is used to estimate the thermal field distribution in microcantilever and the axial expansion.

$Q$ Control of an Atomic Force Microscope Microcantilever: A Sensorless Approach

The scan rate and image resolution of the atomic force microscope (AFM) operating in tapping-mode may be im proved by modifying the quality (Q) factor of the AFM micro cantilever according to the sample type and imaging environment. Piezoelectric shunt control is a new method of controlling the Q factor of a piezoelectric self-actuating AFM microcantilever. The mechanical damping of the microcantilever is controlled by an electrical impedance placed in series with the tip oscillation circuit. A synthetic impedance was designed to allow easy modification of the control parameters which may vary with environmental conditions. The proposed techniques are experimentally demonstrated to reduce the Q factor of an AFM microcantilever from 297.6 to 35.5. AFM images obtained using this method show significant improvement in both scan rate and image quality.

Frequency response of atomic force microscopy microcantilevers oscillating in a viscous liquid: A comparison of various methods

Operating an Atomic Force Microscopy (AFM) with the cantilever and sample immersed in a liquid has many advantages, including the elimination of capillary forces and reduction of van der Waals forces in the study of liquid–solid interactions. Accurately identifying the maximum of the amplitude–frequency curves at which resonances occur is a challenging issue. The frequency response of a cantilever beam in a viscous liquid near a surface depends on the hydrodynamic loadings. First, in this paper, there is a comparison of predicted resonant frequencies from five different theoretical models, with measurements for the case of an ambient liquid of infinite extent. The precision of each method is indicated. Then, the motion of microcantilevers of variable widths close to a solid surface is simulated. When the cantilever tip approaches the sample surface gradually, the effect of squeezed film damping causes the resonance frequencies to shift toward lower values at lower amplitudes, and subsequently as the tip-sample separation becomes smaller, the resonance peaks seem to vanish completely. The results demonstrate that any changes in the geometrical dimensions of the cantilever and in the fluid properties may influence the accuracy of the model. Furthermore, due to the considerable effect of tip-sample separation on the resonance, some models are restricted to be applicable only in the circumstances of free liquid.

Nonlinear dynamics of tapping-mode atomic force microscopy in liquid

One problem in imaging is due to coexistence of double stable responses which can reduce the precision of the images. Our target is comparing coexistence of double responses in liquid with responses obtained in air. Contact forces have some differences in liquid in comparison to air in magnitude and in the formulation. Hydrodynamic forces are also applied on the cantilever. This may change the nonlinear dynamics of tapping-mode Atomic Force Microscopy (AFM) in liquid in comparison to air. In this paper, we have simulated a tapping-mode AFM (TMAFM) cantilever in liquid environment and explored the existence of multi responses in amplitude and phase diagrams. For modeling we have used a continuous beam model with its first mode and forward-time simulation method for the solution of its hybrid dynamics. Frequency response results of the simulation show a good agreement with experiments. The results for studying the nonlinear dynamics of an AFM microcantilever show that while there are two stable responses in air, in liquid just one response exists. Amplitude diagrams show that there is not any shift from low amplitude to high amplitude and both diagrams of sweeping up and down of the driving frequency coincide on each other. Average force diagrams show that in liquid there is not any repulsive regime and the magnitude of attractive force is small too. Sensitivity analysis for studying the effect of the free amplitude shows that in common setpoints double responses do not occur in liquid. Frequency response results show that just in driving frequencies larger than the resonance frequency of the microcantilever in liquid double responses can occur.

Fabrication and analysis of cylindrical resin AFM microcantilevers

In this paper a new method of fabricating cylindrical resin microcantilevers using the Direct Digital Manufacturing (DDM) technique of Micro-stereolithography (MSL) is described. The method is rapid and commercially viable, allowing the fabrication of atomic force microscope (AFM) cantilevers which exhibit much larger spring constants than those currently commercial available. This allows for experimentation in a force regime orders of magnitude higher than currently possible using the AFM. This makes these cantilevers ideally suited for AFM-based depth sensing indentation. Due to their geometry, the assumptions used in the standard Euler-Bernoulli beam theory usually used to analyse AFM cantilevers may no longer be valid. Therefore approximate analytical solutions based on Timoshenko beam theory have been derived for the stiffness and resonant frequency of these cantilevers. Prototypes of the cantilevers have been fabricated and tested. Results show good agreement between experiment and theory.

J111023 非線形フィードバックによるFM-AFM用マイクロカンチレバープローブの振幅制御([J11102]マイクロナノ理工学:nmからmmまでの表面制御とその応用(2))

This study aims at improving the precision of measurements with a frequency modulation (FM) mode atomic force microscope (AFM). While an observation with the FM-AFM is carried out, a vibrating microcantilever probe scans over the sample surface. The measurement accuracy depends on how exactly a change in the eigen-frequency of the microcantilever is obtained. The amplitude suppression enables not only to make the oscillation frequency agree exactly with the eigen-frequency, but also to realize a non-contact observation for easily-deformable or easily-damageable specimens. However, it is difficult to cope with both keeping the microcantilever vibrating firmly and making the amplitude of its vibration as small as possible. To overcome this difficulty, a nonlinear feedback is applied to control the amplitude of the microcantilever probe used in the AFM. As a result, it is achieved that the AFM microcantilever can oscillate with a considerably reduced amplitude in the steady state. The key to the success of this nonlinear feedback control method is that the cantilever vibration can be categorized into the van der Pol-type self-excited oscillation. A prototype AFM was built to demonstrate experimentally the advantage of this amplitude control method. To date, the vibration amplitude less than one nanometer has been achieved in the steady state.

Observation Of Real-Time Thin Film Evolution Using Microcantilever Sensors

ABSTRACTAdsorption and desorption kinetics of thin film formation on metal surfaces has been directly monitored in real-time by optically measuring the deflection of activated atomic force microscope microcantilevers. Microcantilever deflection is caused by stress generated during the formation of an adsorbate layer on one side of the microcantilever. In this work, rapid adsorption of carboxylic acid in hydrocarbon solvent onto a gold surface was directly observed as a compressive stress developed on the microcantilever substrate. Upon exposure to alkylthiol, acid desorbed and was displaced by alkylthiol; this process was continuously monitored in real-time. Experiments suggest that some film organization and intermolecular interaction are required before substantial surface stress can be detected.

Anodization of aluminium coated atomic force microscopy microcantilevers for conversion of the coating into nanoporous alumina

We have performed anodization in 0.3M aqueous oxalic acid of the thin aluminium coating of commercial atomic force microscopy microcantilevers for contact mode. Since similar micromechanical devices are widely used in modern chemical sensors and biosensors, having an inert nanoporous surface on their top would allow for effective functionalization by physisorption of sensitive molecules or nanoparticles. However, the useful mechanical properties of the cantilever have to be preserved first. We demonstrate that by potentiostatic anodization at 40V stopped after 15s successful formation of nanoporous alumina is obtained without significant changes in either shape, resonance properties, or spring constant of the cantilevers.

Mode-selective noncontact excitation of microcantilevers and microcantilever arrays in air using the ultrasound radiation force

We demonstrate the use of focused ultrasound waves to excite eigenmodes of microfabricated structures such as atomic force microscopy microcantilevers and coupled microcantilever arrays, among the smallest objects that have been excited in air using ultrasound radiation force. The method is based on the radiation force produced by a double-sideband suppressed carrier ultrasound waveform, centered at 500 kHz. The difference frequency between the sidebands, ranging from 10 to 200 kHz, excited resonances of these structures. Frequency response curves and deflection shapes were consistent with conventional base excitation, demonstrating the feasibility of noncontact excitation for a variety of microscale devices.

New control methodology of microcantilevers in atomic force microscopy

We apply an external feedback control technique to vibrating microcantilevers in atomic force microscopy. Here we have no difficulty in getting information on periodic orbits required for application of the external feedback control unlike controlling chaos since stable orbits are used as reference ones. This approach enables us not only to control vibrations of the cantilevers but also to measure the sample surfaces (surface topographies) simultaneously. The efficiency and validity of our approach is demonstrated by numerical simulations and a theoretical analysis with the assistance of numerical computations.

Measurement of fluid properties using an acoustically excited atomic force microscope micro-cantilever

In this study, we develop a technique that can be used for extracting the properties of high viscosity Newtonian liquids at the microliter scale using an atomic force microscope. We obtained the responses of two different cantilevers in solutions of glycerin and water using thermal and acoustic frequency sweep excitations. The thermal excitation method cannot be used for liquids with viscosity substantially higher than 1 mPa s because of the existence of a noise floor which obscures the cantilever response. The acoustic frequency sweep excitation can overcome this limitation. The fluid properties were extracted by combining a theoretical model with the experimentally obtained results for the frequency sweep excitation. By using the cantilever phase response, errors of less than 14% in viscosity and density were achieved. This error can be explained by a local increase in fluid temperature of 3 °C due to the laser energy.

Spatio-temporal dynamics of microcantilevers tapping on samples observed under an atomic force microscope integrated with a scanning laser Doppler vibrometer: applications to proper orthogonal decomposition and model reduction

As the use of microsystems has become more widespread, the need for reduced order models that accurately and efficiently predict their dynamic behavior has also grown. Proper orthogonal decomposition (POD) has proven to be a beneficial model-reduction tool in structural dynamics; however, its use in the development of reduced order models of microsystems from experimental data has not received much attention. In this paper, we combine a scanning laser vibrometer with a fully functional atomic force microscope (AFM) to measure the vibration field of AFM microcantilevers tapping on stiff and soft samples. Both stiff and soft AFM microcantilevers with internal resonance are studied. This represents a wide class of vibrating microsystems with spatially confined nonlinearity at the sharp probe tip arising from short and long range surface forces. We apply POD to the measured vibration field of AFM cantilevers and show that a small number of experimentally extracted proper orthogonal modes (POMs) can accurately represent the nonlinear microcantilever dynamics under a variety of conditions. Moreover only one or two sets of POMs are needed to represent the dynamics under a wide range of operating conditions including in the attractive and repulsive regimes of oscillation.

Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory

In this paper, the resonant frequency and sensitivity of atomic force microscope (AFM) microcantilevers are studied using the modified couple stress theory. The classical continuum mechanics is incapable of interpreting micro-structure-dependent size effects when the size of structures is in micron- and sub-micron scales. However, this dependency can be well treated by using non-classical continuum theories. The modified couple stress theory is a non-classic continuum theory which employs additional material parameters besides those appearing in classical continuum theory to treat the size-dependent behavior. In this work, writing differential equations of motion of AFM cantilevers together with appropriate boundary conditions based on the couple stress theory, the analytical expressions are derived for the natural frequency and sensitivity. According to the numerical results, when the ratio of beam thickness to the material length scale parameter is less than 10, the difference between the classical based and the couple stress based results of resonance frequencies and sensitivities is considerable. The results show the significant importance of the size effects in behavior of AFM microcantilevers.

Ultrasensitive detection of Vibrio cholerae O1 using microcantilever-based biosensor with dynamic force microscopy

This work presents the first demonstration of a cantilever based cholerae sensor. Dynamic force microscopy within atomic force microscope (AFM) is applied to measure the cantilever's resonance frequency shift due to mass of cell bound on microcantilever surface. The Vibrio cholerae O1, a food and waterborne pathogen that caused cholera disease in human, is a target bacterium cell of interest. Commercial gold-coated AFM microcantilevers are immobilized with monoclonal antibody (anti- V. cholerae O1) by self-assembled monolayer method. V. cholerae O1 detection experiment is then conducted in concentrations ranging from 1 × 10 3 to 1 × 10 7 CFU/ml. The microcantilever-based sensor has a detection limit of ∼1 × 10 3 CFU/ml and a mass sensitivity, Δ m/Δ F, of ∼146.5 pg/Hz, which is at least two orders of magnitude lower than other reported techniques and sufficient for V. cholerae detection in food products without pre-enrichment steps. In addition, V. cholerae O1 antigen–antibody binding on microcanilever is confirmed by scanning electron microscopy. The results demonstrate that the new biosensor is promising for high sensitivity, uncomplicated and rapid detection of V. cholerae O1.

Linear and nonlinear approaches towards amplitude modulation atomic force microscopy

Frequency response behavior of microcantilever is analytically and experimentally investigated in amplitude modulation Atomic Force Microscopy (AFM). AFM microcantilever probe is modeled as a continuous beam, and tip-sample interaction force is considered to include both attractive and repulsive force regimes. The developed model is compared with the linear lumped-parameters model that has been extensively used in the literature so far. Experimental measurements are also provided for the frequency response of a typical microcantilever-sample system to demonstrate the advantages of the developed model over the linear formulation. The results indicate that the nonlinear continuous model is more accurate, particularly in the estimation of the saturated amplitude value and frequency zone in which the tip-sample contact happens.

적합직교분해법을 이용한 AFM 마이크로캔틸레버의 진동해석

The proper orthogonal decomposition(POD) is used to the vibration analysis of microcantilever in tapping mode atomic force microscopy(AFM). The proper orthogonal modes (POM) are extracted from vibrating signals of microcantilever when it resonates and taps the sample. We present recent ideas based on POD and detailed experiments that yield new perspectives into the microscale structures such as the tapping cantilever. The linearized modeling technique based on POD is very useful to show the principal characteristics of the complex dynamic responses of the AFM microcantilever.

Analysis and control of micro-cantilever in dynamic mode AFM

The dynamic behavior of micro-cantilever-sample system in atomic force microscopy (AFM) in tapping operational mode is studied. Micro-cantilever is modeled by single-mode approximation and subjected to sinusoidal force input. The interaction between tip and sample is modeled by Lennard–Jones potential. Using this dynamic model, the phase portrait of the system is obtained for a range of cantilever-sample distance, and the effect of cantilever parameters on predictability of the system is discussed. Then the nonlinear behavior of the cantilever-sample system is controlled by a robust sliding-mode controller. System output is designed to track the sinusoidal stimulation of the cantilever base under sample surface perturbation during scanning process. Results of SMC are simulated in MATLAB and compared to a stability that has been proved by PID controller which shows better controller effort and less cantilever tip position accuracy.

Photoacoustic detection of gases using microcantilevers

We describe a new technique for measuring the infrared absorption spectra of gases using atomic force microscope microcantilevers. This photoacoustic system is demonstrated for a dilute acetylene/helium mixture by recording the acetylene ν1+ν3 infrared overtone transitions using a wavelength modulated tunable diode laser as the infrared light source. The technique presents significant advantages over existing methods in terms of size, simplicity, speed and insensitivity to ambient vibrations. The maximum achievable signal-to-noise for resonant and non-resonant photoacoustic excitation of the microcantilever is examined and is found to be limited by the microcantilever’s Brownian noise.

Nonlinear vibrations of microcantilevers subjected to tip-sample interactions: Theory and experiment

Improvement of microcantilever-based sensors and actuators chiefly depends on their modeling accuracy. Atomic force microscopy (AFM) is the most widespread application of microcantilever beam as a sensor, which is usually influenced by the tip-sample interaction force. Along this line of reasoning, vibration of AFM microcantilever probe is analyzed in this paper, along with analytical and experimental investigation of the influence of the sample interaction force on the microcantilever vibration. Nonlinear integropartial equation of microcantilever vibration subject to the tip-sample interaction is then derived and multiple time scales method is utilized to estimate the tip amplitude while it is vibrating near the sample. A set of experiments is performed using a commercial AFM for both resonance and nonresonance modes, and the results are compared with the theoretical results. Hysteresis, instability and amplitude drop can be identified in the experimental curves inside the particle attraction domain. They are likely related to the interaction force between the tip and sample as well as the ever-present water layer during the experiments. A fair agreement is observed between the theoretical simulations and experimental findings, which obviously demonstrates the effectiveness and applicability of the developed model.