Atomic Force Microscopy Microcantilevers Research Articles

Enhancing the optical lever sensitivity of microcantilevers for dynamic atomic force microscopy via integrated low frequency paddles

A method is presented to enhance the optical lever sensitivity in dynamic atomic force microscopy (AFM) by nearly an order of magnitude over a wide frequency bandwidth. This is achieved by fabricating or releasing a paddle with a soft hinge close to the free end of the AFM microcantilever such that the paddle resonance frequency is well below the fundamental resonance frequency of the microcantilever. We show a significant increase in signal to noise ratio when cantilever motion is observed at the paddle for AFM systems that are not limited by thermal noise. Also, any effects due to the excitation of the second eigenmode were decoupled by locating the paddle at the node of the second eigenmode. We use these probes for higher harmonic imaging in amplitude modulated AFM (AM–AFM) on a standard polymer blend made of polystyrene and low density polyethylene. We demonstrate significantly improved contrast in higher harmonic images when observing cantilever motion at the paddle. Thus this microcantilever design can improve significantly conventional cantilever performance for dynamic AFM and is compatible with low-cost, high yield microfabrication processes.

Real-Time Reconstruction of Multimode Tip Motion of Microcantilevers in Dynamic Atomic Force Microscopy

A modal projection filtering method is proposed for the dynamic atomic force microscopy (AFM) to accurately reconstruct the multimode tip motion of the AFM microcantilever from the single measurement signal of the optical lever method in real time. The optical lever method is inherently a slope detection method, wherein each individual dynamic mode pertinent to the slope detection principle of the measurement system has its own distinct measurement sensitivity because of the unique dynamic mode shape per a mode. The proposed modal projection filtering method uses the experimentally identified multimode dynamic model of the AFM microcantilever along with the calibrated measurement sensitivities of individual dynamic modes to design the modal projection filters to extract the responses of individual dynamic modes from the single measurement signal. The tip motion of the AFM microcantilever is then accurately reconstructed by using a linear superposition of the extracted responses of multiple dynamic modes. The designed modal projection filters were implemented in a field programmable gate array for real-time computation with an update rate of 1 MHz. Computer simulations and experimental investigations were performed to validate the principle of and to demonstrate the performance of the proposed method.

Analysis of hysteresis effect on the vibration motion of a bimodal non-uniform micro-cantilever using MCS theory

Nowadays, to enhance the performance of atomic force microscopy (AFM) micro-cantilevers (MCs) during imaging, reduce costs and increase the surface topography precision, advanced MCs equipped with piezoelectric layers are utilized. Using the modified couple stress (MCS) theory not only makes the modeling more exhaustive, but also increases the accuracy of prediction of the vibration behavior of the system. In this paper, Hamilton’s principle by consideration of the MCS theory has been used to extract the equations. In addition, to discretize the equations, differential quadrature method has been adopted. Analysis of the hysteresis effect on the vibration behavior of the AFM MC is of significant importance. Thus, to model the hysteresis effect, Bouc–Wen method, which is solved simultaneously with the vibration equations of non-uniform Timoshenko beam, has been utilized. Furthermore, a bimodal excitation of the MC has been considered. The results reveal that the hysteresis effect appears as a phase difference in the time response. Finally, the effect of the geometric parameters on the vibration frequency of the system which is excited by combination of the first two vibration modes of the non-uniform piezoelectric MC has been examined. The results indicate the considerable effect of the MC length in comparison with other geometric parameters such as the MC width and thickness.

Dynamic mulitmode analysis of non-linear piezoelectric microcantilever probe in bistable region of tapping mode atomic force microscopy

Atomic Force Microscopy (AFM) uses a scanning process performed by a microcantilever probe to create a three dimensional image of a nano-scale physical surface. The dynamics of the AFM microcantilever motion and tip–sample force is needed to generate accurate images. In this paper, the non-linear dynamics of a piezoelectric microcantilever probe in tapping AFM will be investigated. The equations of motion are derived for a non-linear contact force, the analytical expressions for natural frequencies and mode shapes are obtained, and the method of multiple scales is used to find the analytical frequency response of the microcantilever. Results show that the non-linear excitation force creates a shift in the frequency response curve during contact mode. This frequency shift is an important consideration in the modeling of AFM dynamics for generation of accurate images as well as for accurate readings when using the AFM microcantilever for other applications. The frequency shift also leads to a bistable region, in which a high and a low amplitude solution coexist. The response of the microcantilever at a single input frequency and voltage are analyzed for both high and low amplitude solutions with the main difference being that the high amplitude solution makes contact with the sample while the low amplitude solution does not. This contact results in higher harmonics of the microcantilever being excited. The response in the bistable region is compared to the response in the monostable region. Additionally, a convergence analysis is used to determine the number of modes necessary to describe the motion of the microcantilever in tapping mode. It is determined that one mode is insufficient, two modes are sufficient for most applications, and five modes is the most that would be necessary for applications that require very precise readings.

Split quartz tuning fork sensors for enhanced sensitivity force detection

Quartz tuning forks (TFs) are often employed in dynamic-mode atomic force microscopy (AFM) as piezoelectric force sensors, to replace the usual AFM microcantilevers, especially in ultra-high vacuum or cryogenic environments. A sharp tip is attached to one of the fork prongs, to obtain atomic scale AFM resolution. We devise a novel TF design by splitting the electrodes of its two prongs, which are produced at the factory as connected to each other, in order to address each of them separately. In such way, the motion of the probe tip can be unambiguously measured, irrespective of the motion of the other prong, which conversely influences its measurement in standard TFs. Furthermore, attachment of the probe tip dramatically spoils the oscillator Q-factor, as it unbalances the two prongs of the TF, with consequent dissipation of energy through the fork holder, due to the motion of the center of mass (CM) of the system. The possibility to independently drive the two prongs of the split TF gives the opportunity to rebalance them just by electrical means, thereby restoring the original Q-factor, by stopping the CM motion. By modeling the split TF as a three-mass, four-spring system, its behavior can be accurately described. Our model is used to explore alternative operation modes with enhanced sensitivity to applied forces.

Aerodynamic damping of sidewall bounded oscillating cantilevers

As a result of their simplicity, low power consumption, and relative ease of implementation, oscillating cantilevers have been investigated for use in multiple applications. However, the in situ operation in many cases, requires oscillating near one or more solid walls. When the separation distance between the vibrating cantilever and the solid wall becomes small, damping from the surrounding fluid is increased, which in turn can increase the power required to maintain certain operational performance characteristics (e.g., vibration amplitude). This increase in damping is a well-studied phenomenon for certain configurations (e.g., microcantilevers in Atomic Force Microscopy, or AFM), but is largely unexplored for a cantilever sweeping across a solid wall, which has direct impact for many macro-based applications including electronics cooling and propulsion. In this paper, we experimentally investigate the aerodynamic damping as a function of the gap between two sidewalls parallel to the oscillating motion of the cantilever. Multiple voltage and frequency inputs are considered in addition to the magnitude of the wall to cantilever gap. Experiments performed across a range of operating conditions reveal that decreasing the distance between the walls and the oscillating cantilever can increase the aerodynamic damping as much as 5 times that of the isolated (i.e., without sidewalls) operation. The resonance frequency is also shown to decrease when the gap spacing is extremely small, suggesting the added mass of the fluid is also sensitive to this variable. However, this change is much smaller (~0.5%) compared to the change typically observed in damping. The findings in the paper help to quantify the overall effect of solid enclosure walls on the performance of an oscillating cantilever, which will better enable the designer to achieve the maximum operational effectiveness. The experimental findings also suggest viscous damping with sidewalls could be predicted from first principles in a similar manner to well accepted analytical models of a cantilever vibrating above a solid surface.

Resonant frequency and sensitivity of a caliper formed with assembled cantilever probes based on the modified strain gradient theory.

The resonant frequency and sensitivity of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) is analyzed utilizing strain gradient theory, and then the governing equation and boundary conditions are derived by a combination of the basic equations of strain gradient theory and Hamilton's principle. The resonant frequency and sensitivity of the proposed AFM microcantilever are then obtained numerically. The proposed ACP includes a horizontal cantilever, two vertical extensions, and two tips located at the free ends of the extensions that form a caliper. As one of the extensions is located between the clamped and free ends of the AFM microcantilever, the cantilever is modeled as two beams. The results of the current model are compared with those evaluated by both modified couple stress and classical beam theories. The difference in results evaluated by the strain gradient theory and those predicted by the couple stress and classical beam theories is significant, especially when the microcantilever thickness is approximately the same as the material length-scale parameters. The results also indicate that at the low values of contact stiffness, scanning in the higher cantilever modes decrease the accuracy of the proposed AFM ACP.

Modulated–demodulated control: Q control of an AFM microcantilever

We outline the application of modulated–demodulated control to the quality (Q) factor control of an atomic force microscope microcantilever. We review the modulated–demodulated control technique, emphasize its linear time invariant nature and develop state space representations of the controller for design and analysis. The modulated–demodulated controller can be configured as both positive position feedback (PPF) and resonant controllers, which are effective in the control of negative imaginary systems. Negative imaginary systems theory has important application in the control of collocated mechanical systems and we briefly summarize the key relevant results. A high-frequency, tunable modulated–demodulated controller, designed specifically for MHz operation, was developed for experimental validation. The modulated–demodulated controller enables the use of a low-bandwidth baseband controller in the configuration of a high-bandwidth controller, thus simplifying the implementation of high-bandwidth controllers. We outline the controller characterization and demonstrate closed-loop control of a Bruker DMASP microcantilever. We also present AFM images highlighting the improvements in scan speed and image quality achieved as a result of Q control. Modulated–demodulated control appears well suited to the control of high-frequency resonant dynamics. In addition to high-speed atomic force microscopy, we believe this control technique may find applications in high-frequency microelectromechanical systems (MEMS).

Study of the sensitivity and resonant frequency of the flexural modes of an atomic force microscopy microcantilever modeled by strain gradient elasticity theory

In this study, the resonant frequency and sensitivity of an atomic force microscopy microcantilever are analyzed utilizing the strain gradient theory, and then the governing equation and boundary conditions are derived by a combination of the basic equations of the modified strain gradient theory and the Hamilton principle. Afterward, the resonant frequency and sensitivity of the proposed atomic force microscopy microcantilever are obtained numerically. The results of the current model are compared to those evaluated by both modified couple stress and classic beam theories. Results show that utilizing the strain gradient theory in the analysis of atomic force microscopy microcantilever dynamic behavior is necessary especially when the contact stiffness is high and the thickness of the microcantilever approaches the internal material length scale parameter.

Atomic force microscope microcantilevers used as sensors for monitoring humidity

A microcantilever sensor is presented. Functionalization of the cantilever with a polyaniline (PANI) sensitive layer and its use as a humidity sensor were investigated. Polyaniline was produced by interfacial synthesis and the sensitive layer was deposited on the microcantilever surface by the spin-coating method. The microcantilever deflection at various levels of relative humidity (RH) was read by means of the optical lever of an atomic force microscope (AFM Veeco Dimension V). A range of RH from 20% to 70% was introduced into the AFM chamber by mixing streams of dry and wet nitrogen. The sensitivity and reversibility of the sensors were assessed at various RH and temperatures (10, 20 and 30°C). A large deflection was observed in the coated microcantilever sensors, with faster response time at 10°C and better sensitivity and reversibility at 30°C. These results demonstrate that the spin-coated microcantilever can be used as a sensor to detect relative humidity at various different temperatures.

Functionalized AFM probes for force spectroscopy: eigenmode shapes and stiffness calibration through thermal noise measurements

The functionalization of an atomic force microscope (AFM) cantilever with a colloidal bead is a widely used technique when the geometry between the probe and the sample must be controlled, particularly in force spectroscopy. But some questions remain: how does a bead glued at the end of a cantilever influence its mechanical response? And more importantly for quantitative measurements, can we still determine the stiffness of the AFM probe with traditional techniques? In this paper, the influence of the colloidal mass loading on the eigenmode shape and resonant frequency is investigated by measuring the thermal noise on rectangular AFM microcantilevers with and without beads attached at their extremities. The experiments are performed with a home-made ultra-sensitive AFM, based on differential interferometry. The focused beam from the interferometer probes the cantilever at different positions and the spatial shapes of the modes are determined up to the fifth resonance, without external excitation. The results clearly demonstrate that the first eigenmode is almost unchanged by mass loading. However the oscillation behavior of higher resonances presents a marked difference: with a particle glued at its extremity, the nodes of the modes are displaced towards the free end of the cantilever. These results are compared to an analytical model taking into account the mass and inertial moment of the load in an Euler–Bernoulli framework, where the normalization of the eigenmodes is explicitly worked out in order to allow a quantitative prediction of the thermal noise amplitude of each mode. A good agreement between the experimental results and the analytical model is demonstrated, allowing a clean calibration of the probe stiffness.

Sensorless enhancement of an atomic force microscope micro-cantilever quality factor using piezoelectric shunt control

The image quality and resolution of the Atomic Force Microscope (AFM) operating in tapping mode is dependent on the quality (Q) factor of the sensing micro-cantilever. Increasing the cantilever Q factor improves image resolution and reduces the risk of sample and cantilever damage. Active piezoelectric shunt control is introduced in this work as a new technique for modifying the Q factor of a piezoelectric self-actuating AFM micro-cantilever. An active impedance is placed in series with the tip oscillation voltage source to modify the mechanical dynamics of the cantilever. The benefit of using this control technique is that it removes the optical displacement sensor from the Q control feedback loop to reduce measurement noise in the loop and allows for a reduction in instrument size.

Nonlinear dynamics and bifurcations in external feedback control of microcantilevers in atomic force microscopy

We study nonlinear dynamics and bifurcations in external feedback control of vibrating microcantilevers in atomic force microscopy. The efficiency and validity of the control methodology for microcantilevers was demonstrated and abundant nonlinear phenomena were observed in a previous numerical study. Using the averaging method and center manifold theory, we analyze a degenerate bifurcation of codimension two to explain a key feature of the previous numerical results. Numerical examples are also given, in which theoretical results are compared with numerical computations for bifurcations and unstable manifolds.

Modulated-Demodulated Q Control of an Atomic Force Microscope Microcantilever

We outline the application of the modulated-demodulated control technique to the quality (Q) factor control of an atomic force microscope microcantilever. The modulated-demodulated controller developed can be modeled as a linear time invariant controller, which resembles a positive position feedback (PPF) controller. We utilize negative imaginary theory to concisely summarize the requirements for robust stability of the closed loop system. The Q controller is verified experimentally on a microcantilever. Modulated-demodulated control appears to be well suited to the control of high frequency dynamics, simplifying the bandwidth requirements of the baseband controller. Due to the controller parameterization, the tuning process is extremely simple. We believe modulated-demodulated control could find applications in high speed atomic force microscopy (AFM) and microelectromechanical systems (MEMS).

Nonlinear dynamics of atomic force microscope microcantilevers in liquid environments - a review

Surface forces at the liquid-solid interface play a fundamental role in a wide range of scientific disciplines including electrochemistry, energy storage, wetting, catalysis, environmental science, biochemistry, biophysics, and physical biology. Dynamic Atomic Force Microscopy (dAFM) is being increasingly used to quantify and map these forces with nanometer resolution. In dynamic AFM surface forces are sensed from the changes they cause in the nonlinear dynamics of the oscillating AFM cantilever. However, the dynamics of the AFM cantilever at liquid-solid interface differs significantly compared to air or vacuum environments due to both the low Q-factor of the cantilever in liquids as well as the unique nature of intermolecular forces at solid-liquid interface. In this article we review the state-of-art of understanding of nonlinear dynamics of AFM microcantilevers in liquid environments and outline the many open areas of research both in mathematical modeling and in experiments that remain to be explored.

A New Approach to Active Q Control of an Atomic Force Microscope Micro-cantilever Operating in Tapping Mode

When imaging in tapping mode, scan speed and image quality may be improved by modification of the Atomic Force Microscope (AFM) micro-cantilever quality (Q) factor. The most commonly applied method of Q control uses velocity feedback with an estimate of the cantilever tip velocity obtained by phase shifting the displacement signal. System performance may be degraded and stability can not be guaranteed using this control technique as the control action affects unmodeled cantilever dynamics. In this paper a resonant controller is presented as a new method of controlling the cantilever Q factor which guarantees closed loop stability in the presence of unmodeled cantilever dynamics. AFM images are presented to demonstrate the effectiveness of this control technique.

A Dynamic Model of the Jump-To Phenomenon During AFM Analysis

The measurement of the physical properties of surfaces on the nanoscale is a long-standing problem, and the atomic force microscope (AFM) has enabled the investigation of surface energies and mechanical properties over a range of length scales. The ability to measure these properties for softer materials presents a challenge when interpreting data obtained from such measurements, in particular because of the dynamics of the compliant AFM microcantilever. This work attempts to better understand the interaction between an AFM tip and samples of varying elastic modulus, in the presence of attractive van der Waals forces. A theoretical model is presented in which the dynamics of the approach of an atomic force microscope cantilever tip toward a surface, prior to and during the van der Waals-induced jump-to phenomenon, are included. The cantilever mechanics incorporates the motion of the air through which the cantilever moves, the acceleration, inertia, and torque of the cantilever, and the squeezing of the fluid between the cantilever tip and the surface, leading to elastohydrodynamic lubrication and deformation of the substrate. Simulations of the cantilever approach are compared to measurements performed using an atomic force microscope, and the effect of cantilever drive velocity is investigated. Cantilevers presenting (1) spherical colloid probe tips and (2) pyramidal tips are employed, and substrates exhibiting Young's moduli of 3 MPa, 500 MPa, and 75 GPa are measured. The analysis presented could be extended to enhance understanding of dynamic phenomena in micro/nanoelectromechanical systems such as resonators and microrheometers, particularly those which contain soft materials and also where surface interactions are important.

Nonlinear dynamics of the atomic force microscope at the liquid-solid interface

The measurement of intermolecular forces at the liquid-solid interface is key to many studies of electrochemistry, wetting, catalysis, biochemistry, and mechanobiology. The atomic force microscope (AFM) is unique in its ability to measure and map these forces with nanometer resolution using the oscillating sharp tip of an AFM cantilever. These surface forces are only measured by observing the changes they induce in the dynamics of the resonant AFM probe. However, AFM cantilever dynamics at this interface can be significantly different when compared to air/vacuum environments due to the nature of nanoscale forces at the interface and the low-quality factors in liquids. In this work, we study the nonlinear dynamics of magnetically excited AFM microcantilevers on graphite and mica immersed in deionized water, high-concentration buffers, and methanol. By combining theory and experiments, a wealth of nonlinear dynamical phenomena such as superharmonic resonance, hysteretic jumps, and multimodal interactions are demonstrated and their dependence on hydration/solvation forces is clarified. These results are expected to aid ongoing efforts to link liquid-solid interface properties to cantilever dynamics and lead to accurate interpretation of data from experiments.

Nonlinear dynamics of tapping mode atomic force microscopy in the bistable phase

Nonlinear dynamics of amplitude modulation atomic force microscopy (AFM) is studied employing a reduced-order model based on a differential quadrature method (DQM). The AFM microcantilever is assumed to be operating in the dynamic contact or tapping mode while the microcantilever tip being initially located in the bistable region. We have found that the DQM is capable of precise prediction of the static bifurcation diagram and natural frequencies of the microcantilever. We have used the DQM to discretize the partial-differential equation governing the microcantilever motion and a finite difference method (FDM) to calculate limit-cycle responses of the AFM tip. It is shown that a combination of the DQM and FDM applied, respectively, to discretize the spatial and temporal derivatives provides an efficient, accurate procedure to address the complicated dynamic behavior exhibited by the AFM probe. The procedure was, therefore, utilized to study the response of the microcantilever to a base harmonic excitation through several numerical examples. We found that the dynamics of the AFM probe in the bistable region is totally different from those in the monostable region.

Study of the tip mass and interaction force effects on the frequency response and mode shapes of the AFM cantilever

The vibrational characteristics of an atomic force microscope (AFM) cantilever beam play a key role in dynamic mode of the atomic force microscope. As the oscillating AFM cantilever tip approaches the sample, the tip–sample interaction force influences the cantilever dynamics. In this paper, we present a detailed theoretical analysis of the frequency response and mode shape behavior of a cantilever beam in the dynamic mode subject to changes in the tip mass and the interaction regime between the AFM cantilever system and the sample. We consider a distributed parameter model for AFM and use Euler–Bernoulli method to derive an expression for AFM characteristics equation contains tip mass and interaction force terms. We study the frequency response of AFM cantilever under variations of interaction force between AFM tip and sample. Also, we investigate the effect of tip mass on the frequency response and also the quality factor and spring constant of each eigenmodes of AFM micro-cantilever. In addition, the mode shape analysis of AFM cantilever under variations of tip mass and interaction force is investigated. This will incorporate the presentation of explicit analytical expressions and numerical analysis. The results show that by considering the tip mass, the resonance frequencies of the cantilever are decreased. Also, the tip mass has a significant effect on the mode shape of the higher eigenmodes of the AFM cantilever. Moreover, tip mass affects the quality factor and spring constant of each modes.