Atomic Force Microscopy Microcantilevers Research Articles

Investigation on the Impact of Excitation Amplitude on AFM-TM Microcantilever Beam System's Dynamic Characteristics and Implementation of an Equivalent Circuit.

Alterations in the dynamical properties of an atomic force microscope microcantilever beam system in tapping mode can appreciably impact its measurement precision. Understanding the influence mechanism of dynamic parameter changes on the system's motion characteristics is vital to improve the accuracy of the atomic force microscope in tapping mode (AFM-TM). In this study, we categorize the mathematical model of the AFM-TM microcantilever beam system into systems 1 and 2 based on actual working conditions. Then, we analyze the alterations in the dynamic properties of both systems due to external excitation variations using bifurcation diagrams, phase trajectories, Lyapunov indices, and attraction domains. The numerical simulation results show that when the dimensionless external excitation g < 0.183, the motion state of system 2 is period 1. When g < 0.9, the motion state of system 1 is period 1 motion. Finally, we develop the equivalent circuit model of the AFM-TM microcantilever beam and perform related software simulations, along with practical circuit experiments. Our experimental results indicate that the constructed equivalent circuit can effectively analyze the dynamic characteristics of the AFM-TM microcantilever beam system in the presence of complex external environmental factors. It is observed that the practical circuit simulation attenuates high-frequency signals, resulting in a 31.4% reduction in excitation amplitude compared to numerical simulation results. This provides an essential theoretical foundation for selecting external excitation parameters for AFM-TM cantilever beams and offers a novel method for analyzing the dynamics of micro- and nanomechanical systems, as well as other nonlinear systems.

Analytical solution for size-dependent nonlinear behavior of AFM microcantilever with assembled probe in liquid environments

Using modified strain gradient theory, this study aims to examine the size-dependent nonlinear behavior of atomic force microscopy (AFM) with an assembled cantilever probe (ACP) in various liquid environments. The largest contribution of this theory lies in its consideration of the material length scale parameter (MLSP) to analyze the effect of size on physical characteristics. When studying ACP in liquids, the hydrodynamic force creates a different behavior compared to an ACP beam enclosed in air. In this study, Hamilton’s principle is used to derive the nonlinear partial differential equation (PDE) of motion and associated boundary conditions (BCs) of the ACP in liquid environments. To achieve this, a combination of Euler-Bernoulli’s theory and strain gradient concepts are employed. As the next step, a reduced order model of the system is developed using the Galerkin method. To assess the nonlinear frequency response of the ACP in various liquid environments, perturbation technique, including the method of multiple scales (MMS), is applied to the developed reduced order model. The study also calculates resonance frequencies, phase planes, stability, and the potential function of the system analytically. The results of this study indicate that the system becomes nonlinear as the ratio of beam thickness to MLSP decreases. Several factors, including the ratio of beam thickness to MLSP as well as the viscous damping coefficient, can influence the jump phenomenon. Furthermore, the results of the phase and amplitude of the ACP in liquid environments demonstrate that an increase in the (h/l) ratio results in a decrease in response amplitude and a leftward shift in the phase of the response diagram. This phenomenon is indicative of a softening behavior exhibited by the system. Lastly, the paper examines the validity and accuracy of the MMS solution by comparing it to a numerical solution.

GPL-Reinforced composite piezoelectric microcantilever dynamics in atomic force microscope

Currently, Atomic Force Microscope (AFM) is utilized as an efficient tool for nanoscale measurements and nanomanipulation of particles. The central part of AFM is considered to be the microcantilever (MC) used in the device. AFM MC is generally made from silicon. Since functionally graded graphene-nanoplatelet-reinforced composite (GPLRC) materials are highly popular in industry and academic research, the present study aims to be the first attempt to investigate the possibility of utilizing these materials in AFM MC. Also, it seeks to compare the nonlinear vibrational behavior of the MC made from this type of material with that of the silicon MC and also to investigate the vibrational behavior of the GPLRC MC in interaction with the sample surface. To do so, the GPLRC MC vibrated with the piezoelectric layer on its top is utilized. In order to increase the sensitivity of the MC to the interaction force between the surface and the probe tip, the tip of the MC is considered narrower. The differential equation of the vibrational motion of the MC near the surface of the sample is derived by considering the Lennord-Jones model according to the Euler-Bernoulli theory and applying the Lagrange method. In order to solve the nonlinear differential equation of motion with partial derivatives in terms of the time and the position of each point on the MC, Galerkin variable-separation method and multiple time scale (MTS) method are applied. The results of the dynamic modeling near the surface of the sample indicate that the MC made of GPLRC is more sensitive to the nonlinearity of the interaction force as compared to the common silicon MC.

A control method for acoustic radiation force of ultrahigh frequency ultrasound based on variable frequency pulse width modulation

Ultrahigh frequency ultrasound (&amp;gt;60 MHz) has emerged as a crucial actuating mechanism for non-contact manipulation, owing to its unique acoustic field properties. The acoustic field traps microparticles mainly via the gradient force of acoustic radiation force (ARF) on the transverse plane, which is up to hundreds of nanonewtons. In theory, directly using ARF can strengthen the manipulation force. Currently, the direct implementation of ARF is restricted to a specific frequency and magnitude range, which lacks a comprehensive and versatile control method. Additionally, it lacks an ARF calibration method that accommodates a wide magnitude and frequency range. We propose a variable frequency pulse width modulation-based control method for ARF, which uses an atomic force microscope microcantilever as a mechanical sensor to calibrate the magnitude and frequency. The precise control of ARF emitted by an 85 MHz transducer was achieved with a resolution of hundreds of piconewtons, magnitude range spanning from nanonewtons to micronewtons, and frequency range of 1 kHz to hundreds of kilohertz. This control method breakthrough holds great promise for expanding the application of ultrahigh frequency ultrasound in noncontact manipulation.

Low frequency photothermal excitation of AFM microcantilevers

Photothermal excitation at frequencies below the mechanical resonance of the atomic force microscopy (AFM) microcantilever can be utilized in force modulation microscopy, fast force displacement curve acquisition, and tip-based mass spectroscopy. To understand the microcantilever bending response in these modes, accurate models of the thermoelastic response of the AFM microcantilever are needed. We study the sub-resonance photothermal vibrational response of coated and uncoated AFM microcantilevers as a function of laser modulation frequency and spot location. The sub-resonance microcantilever response shows distinct thermoelastic regimes. Below the microcantilever's thermal roll-off frequency, the vibration amplitude is mostly constant. Past this frequency, the vibration amplitude decreases with increasing frequency. At modulation frequencies below the thermal roll-off frequency, the most efficient photothermal laser spot to excite harmonic motion is near the free end of both coated and uncoated microcantilevers. For the tested coated microcantilevers, the most efficient photothermal laser location migrates from near the free end of the microcantilever to near the fixed end as modulation frequency increases. For the tested uncoated microcantilever, the most efficient photothermal laser location remains unchanged at the tested frequencies. To predict the bending response of the coated microcantilever, a bilayer bending model is implemented. At low frequencies, this model underpredicts the bending response compared to experiments by up to 90%. This may be due to neglecting microcantilever bending contributed by a through-thickness temperature gradient. Our results illustrate different aspects of the frequency-dependent photothermal laser spot optimization that can guide users to maximizing microcantilever response to a given input power.

High resolution atomic force microscopy with an active piezoelectric microcantilever.

Active microcantilevers with on-chip sensing and actuation provide significant advantages in tapping mode Atomic Force Microscopy (AFM). Collocated transduction allows for effective manipulation of cantilever dynamics through feedback control, enabling higher scan rates. However, the adjacency of the sensing and actuation electrodes is known to result in a high level of feedthrough, leading to a low imaging resolution. Readout circuit noise further deteriorates the imaging precision. Here, we investigate the noise sources that affect AFM microcantilevers with collocated aluminum nitride (AlN) actuator-sensor pairs. We reported these cantilevers in earlier work and demonstrated that they display a very low level of feedthrough between the actuation and sensing electrodes. We present a high signal-to-noise ratio (SNR) sensing method that enables us to demonstrate high-resolution AFM on a calibration grating with nm-step silicon carbide (SiC) terraces. Measuring the Lorentzian response of the cantilever's Brownian motion with the on-chip active sensor at resonance enables us to calibrate the dynamic stiffness at the first fundamental resonance mode, without utilizing an optical sensor.

Nanoscale cutting using self-excited microcantilever

The application of self-excitation is proposed to improve the efficiency of the nanoscale cutting procedure based on use of a microcantilever in atomic force microscopy. The microcantilever shape is redesigned so that it can be used to produce vibration amplitudes with sufficient magnitudes to enable the excitation force applied by an actuator to be transferred efficiently to the tip of the microcantilever for the cutting process. A diamond abrasive that is set on the tip is also fabricated using a focused ion beam technique to improve the cutting effect. The natural frequency of the microcantilever is modulated based on the pressing load. Under conventional external excitation conditions, to maintain the microcantilever in its resonant state, it is necessary to vary the excitation frequency in accordance with the modulation. In this study, rather than using external excitation, the self-excitation cutting method is proposed to overcome this difficulty. The self-excited oscillation is produced by appropriate setting of the phase difference between the deflection signal of the microcantilever and the feedback signal for the actuator. In addition, it is demonstrated experimentally that the change in the phase difference enables us to control the amplitude of the self-excitation. As a result, control of the cutting depth is achieved via changes in the phase difference.

Exploring nanowire regrowth for the integration of bottom-up grown silicon nanowires into AFM scanning probes

Bottom-up grown single-crystalline silicon nanowires (SiNWs) are highly intriguing to build nanoscale probes, for instance for atomic force microscopy (AFM), due to their mechanical robustness and high aspect ratio geometry. Several strategies to build such nanowire-equipped probes were explored but their fabrication is still elaborate, time-consuming and relies partly on single-crystalline substrates. Here, we explore a new strategy to fabricate AFM probes that are equipped with single-SiNW scanning tips. The conceptual evaluation begins with a discussion on the overall design and softness of such probes based on finite-element-method simulations. For the experimental realization, SiNWs were grown by the well-established gold-catalyzed vapor–liquid–solid method employing gaseous monosilane. As-grown SiNWs were subsequently transferred onto flexible membranes and even freestanding AFM microcantilever beams via mechanical nanowire contact printing. Elongation of the deposited nanowires by so-called regrowth was triggered by reusing the original gold catalyst to yield the prospective AFM scanning tip. SiNW-equipped scanning probes were created in this manner and were successfully employed for topography imaging. Although a multitude of challenges remains, the created probes showed an overall convincing performance and a superior durability.

Multilayered non‐uniform atomic force microscope piezoelectric microcantilever control and vibration analysis considering different excitation based on the modified couple stress theory

Atomic force microscope (AFM) is one of the most powerful tools for surface scanning, force measurement, and nano-manipulation. To improve its performance, vibration and control of AFM micro-cantilever (MC) should be studied. Hysteresis, as an undesired phenomenon affecting vibration amplitude and phase, is also another important issue to be examined. In this paper, vibration analysis and control of a ZnO non-uniform multi-layered piezoelectric MC has been investigated in non-contact mode. A modified couple stress theory has been used to obtain the strain energy for modeling the MC. In order to control the amplitude, a sliding mode controller (SMC) has been utilized on AFM, due to its application in uncertain and nonlinear systems. For applying the control signal, two methods of piezo and base actuation are studied. The results are compared with proportional integral derivative (PID) control method and it is demonstrated that SMC method reduces the control input close to the surface and increases the accuracy near the surface. In addition to MC control, hysteresis amplitude and phase differences are investigated by applying the Prandtl-Ishlinskii model. Also, surface topography is studied with hysteresis. The simulations show backward phase difference and an increase in amplitude, accordingly.

Truncated Nonlinear Interferometry for Quantum-Enhanced Atomic Force Microscopy.

Nonlinear interferometers that replace beam splitters in Mach-Zehnder interferometers with nonlinear amplifiers for quantum-enhanced phase measurements have drawn increasing interest in recent years, but practical quantum sensors based on nonlinear interferometry remain an outstanding challenge. Here, we demonstrate the first practical application of nonlinear interferometry by measuring the displacement of an atomic force microscope microcantilever with quantum noise reduction of up to 3dB below the standard quantum limit, corresponding to a quantum-enhanced measurement of beam displacement of 1.7 fm/sqrt[Hz]. Further, we minimize photon backaction noise while taking advantage of quantum noise reduction by transducing the cantilever displacement signal with a weak squeezed state while using dual homodyne detection with a higher power local oscillator. This approach may enable quantum-enhanced broadband, high-speed scanning probe microscopy.

Measurement of thin film magnetostriction using field-dependent atomic force microscopy

Measurement of thin film magnetostriction is a challenging task, as magnetostrictive material deformations in parts per million, in conjunction with materials at small dimensions, require high precision, often with dedicated set-ups, for reproducible results. We have developed a novel approach employing a commercial atomic force microscope (AFM) with attached electromagnets. Magnetostriction measurements are demonstrated on 50–500 nm thick Fe81Al19 films sputter deposited directly on high aspect ratio commercial AFM micro-cantilevers. A magnetostrictive deflection of the cantilever bimorph translates into a deflection force acting in a contact mode measurement, which is interpreted and recorded as a change in height. For determination of the magnetostriction coefficient λs, we have developed a modified version of the equation for the magnetostrictive deflection of a cantilever bimorph by Guerrero and Wetherhold, taking into account long-range attractive forces acting during contact mode AFM measurements in air. The sub-atomic precision of the AFM, combined with the widespread availability of all components and the simple set-up, makes the measurement of magnetostriction on films of just a few tens of nanometers thickness easily accessible.

Investigation of the axial load effect on the vibration and topography of the AFM oblique four-layered piezoelectric micro-cantilever

In this paper, the vibration behavior of atomic force microscopy (AFM) micro-cantilever (MC) with a piezoelectric layer in the non-contact mode considering the axial load in the air medium was studied. In the dynamic modes of AFM nano-robot, parameters such as amplitude, frequency and motion phase are used as feedback factors in the control system in order to extract sample surface information and the nanoparticle voltage. Consequently, to extract these parameters, the vibration analysis of the MCs of this nano-robot is essential. Additionally, because of the wide-spread applications of oblique MCs, applying the axial and transverse forces into the model is absolutely necessary. In order to simulate the AFM four-layered piezoelectric MC with the axial displacement, Timoshenko beam theory as well as modified couple stress theory has been used. Considering the axial displacement in the modeling not only leads to more degrees of freedom, but also has increased the amount of calculations. To extract the equations of the system, energy method has been used, and then, the FEM was applied to discrete the equations. To verify the accuracy of the results, the frequency and time responses of FEM have been compared with the results of the 3D mode simulation obtained by COMSOL software and experimental results. The comparison of results indicates that modifying the modeling by considering the axial displacement has increased the accuracy of the frequency and time responses. The error percentage of the first frequency response is 0.42% and the error percentage of the time response is 0.0053%. Furthermore, to examine the effect of MC geometry on its vibrational behavior, frequency and time responses of three common geometries of AFM MCs have been extracted. The results illustrate the improvement of modeling in all three geometries. Then, the sample surface topography of MCs at the first and second excitation frequencies in contact with rectangular roughnesses demonstrated the decline of time delay at the second excitation frequency. The results of the topography simulation in the air environment show that the roughness’s trend is better at the second mode than at the first mode. Finally, the effect of MC angle on the topography of the rectangular MC surfaces in contact with the rectangular roughness in 2D and 3D modes was examined in the presence and the absence of axial load. The results show that in the presence of the axial displacement in modeling, by increasing of MC angle, the topography quality increases drastically.

Free and forced vibrations of atomic force microscope piezoelectric cantilevers considering tip-sample nonlinear interactions

Abstract The aim of this article is to investigate the vibrational behavior of rectangular and V-shaped atomic force microscopy (AFM) microcantilevers with an extended piezoelectric layer using the finite element method (FEM). Firstly, the results of 3D FEM simulation are compared to the experimental and analytical ones to assess the accuracy of the method. Then, the free and forced vibrations of rectangular and V-shape piezoelectric microcantilevers in the absence and presence of nonlinear interactions between the microcantilever tip and the surface sample are studied. A nonlinear spring is used in the finite element modeling to simulate the nonlinear attraction-repulsion interactions between the tip and the sample. The amplitude of the AFM microcantilever is considered to be comparably small, hence the geometric nonlinearity of the microcantilever is insignificant. In the free vibration part, the resonance frequencies and mode shapes are obtained. In the forced vibration cases, an AC voltage with the resonance frequencies obtained in the free vibration analysis is applied to the piezoelectric layer to operate the microcantilever. The resonance amplitude of the tip of AFM microcantilever is derived accordingly. All simulations are performed for two cases; the first one is a fixed microcantilever at the end and free to move and rotate, and the second one is a microcantilever whose rotational degree of freedom and lateral displacement is tied up with applying a symmetric constraint. So, an important study parameter in this work is the effect of torsional modes on the vibrational behavior of AFM piezoelectric microcantilevers.

Vibration Analysis and Control of AFM Microcantilever Based on the MCS Theory Using the FSMC Control in the Air

This study is aimed to find out the relation between the vibration motion and control of an atomic force microscope (AFM) piezoelectric microcantilever for free and forced vibrations in the air environment. In fact, the MC is the most important part of AFM, performing the most vital operations. Hence, the dynamic analysis and control of the MC are mandatory to obtain optimal performance. Enhancing the optimization of this system increases the sampling rate as well as the accuracy and resolution of the obtained images. MCs with a piezoelectric layer possess a higher speed and accuracy compared to conventional MCs which are simpler and less expensive. Also, in the MC vibration modeling, the Timoshenko beam model based on the modified couple stress theory is used. Next, using the Hamilton’s principle, the MC motion equations are derived by considering the geometric discontinuities as a result of the piezoelectric layer and two electrode layers. These equations are solved by using the finite element method. The MC frequency and time responses at different distances from the sample surface are obtained and compared with experimental results. In addition, the sample surface topography in the non-contact mode when the MC passes through different roughnesses in the first and second vibration modes has been investigated. Moreover, the fuzzy-sliding mode control (FSMC), which is a robust control method, is employed due to uncertainties when modeling the system. The results are compared with those of the sliding mode control (SMC) and PID control methods. For the cases of far from the surface and close to it, the MC is actuated by the piezoelectric layer and piezo-stack base, respectively. The proposed FSMC control can properly reduce chattering in the SMC to improve the results.

Higher modes and higher harmonics in the non-contact atomic force microscopy

The present paper proposes a new mathematical approach to study the role of higher harmonics and higher mode shapes in the dynamics of an atomic force microscope microcantilever. The basic principle of the present method, called the direct harmonic balance, is similar to the well-known method of harmonic balance, but the key difference is that this method does not require discretizing the partial differential equation, governing the probe dynamics. In contrast to the traditional harmonic balance, the direct harmonic balance method, introduced here, attacks the partial differential equation directly, leading to a more efficient solution procedure. The accuracy of this method is demonstrated using a perturbation method. The direct harmonic balance method is then employed to investigate the nonlinear oscillations of the atomic force microscope probe in the non-contact mode. The significance of higher mode shapes and higher harmonics is illustrated through several frequency-response curves, presented for various cases. It is found out that while higher modes are more sensitive to the amplitude of excitation, they have a smaller frequency shift. It is also found out that the second harmonic exhibits high sensitivity to the initial tip/sample separation distance. In addition, it is shown that reducing the tip/sample initial distance results in a considerable growth in the magnitude of the second harmonic, which can be used as a reliable signal to explore topography of the sample.

The limit of mass determination with an AFM cantilever-based system

The application of an atomic force microscope (AFM) based microcantilever system for the determination of mass of gold nanoparticles (AuNPs) has been demonstrated. In this system, standard AFM microcantilevers for measurements in vacuum have been employed. The limit of mass determination with our AFM-based system has been determined to be of the order of 10-10 g. The prospects of employing AFM cantilever-based sensors for highly sensitive protein detection in proteomic studies and in diagnostics have been discussed.

Effect of three types of piezoelectric cantilever on the topography quality in the vicinity of rough surface in a fluid ambient

• Advanced mathematical modeling for different types of piezoelectric micro cantilever. • Utilizing modified couple stress theory. • Advanced liquid modeling. • Predicting the piezoelectric non uniform micro cantilever vibration behavior in fluid. • Tapping and non-contact topography in liquid. The use of higher vibration modes and different geometries of the atomic force microscopy (AFM) piezoelectric micro cantilever (MC) is affected by the surface topography quality in a liquid medium. Therefore, utilizing an appropriate MC geometry and vibration mode is of a great importance. This paper analyzes the effect of different types of AFM MCs on the surface topography quality in the noncontact and tapping modes in a liquid medium. The modified couple stress theory (MCS) in a liquid based on the Timoshenko beam theory is used in order to enhance the accuracy of MC dynamic modeling. In addition, the differential quadrature (DQ) method has been used to discrete the equations. Identification of environmental forces helps to measure the accurate MC vibration amplitude. Investigating the effect of geometric and force parameters on the MC vibration behavior leads to understanding the system to design it properly in a liquid medium. Based on the advanced dynamic modeling, the best MC geometry for the specific surface roughness has been determined in the liquid for the surface topography. Also, due to oscillating the MC near the sample surface, the effect of interaction forces between the sample surface and the MC, including van der Waals, contact and squeeze forces is analyzed in a liquid medium in addition to the hydrodynamic forces. Furthermore, due to the reduction of the MC amplitude caused by the squeeze force; the MC is angled in proportion to the horizontal surface.

Experimental and theoretical analysis of the DMASP cantilever vibration behavior based on the MCS theory in moist environment

A micro cantilever (MC) and a probe are two main components of the atomic force microscope (AFM). The dimensions of these components are in micro scales while their oscillation amplitude is on a nanometer scale. The present study intended to not only increase the accuracy of the simulation with regard to geometric discontinuities based on the Timoshenko beam model using the modified couple stress (MCS) theory but also increase the accuracy of the prediction of a system behavior by considering the hysteresis effect into the system vibration equations based on Bouc–Wen model. Since, the classical theory disregarded the molecular structure of matter and neglected the microstructure size dependency, which raise its physical breakdowns in micro and nanoscale applications. Therefore, some micro continuum theories are developed to account for the microstructure effects by introducing additional material constants to the conventional ones. Due to the lack of the experimental results for this kind of MCs, this paper is focused on the both experimental and simulation results by utilizing the DMASP MC. The roughness of the surfaces affects the MC vibration behavior in the air medium. Therefore, surface roughness affecting van der Waals force has been considered in the air medium. Furthermore, the simulation results are compared with experimental results in the air medium with different moisture content during the surface topography. Due to the results, the best surface topography is achieved in the third vibration mode. Since the piezoelectric MC can tolerate the limited voltage, for this AFM MC type, the best surface topography is achieved in the third mode. Hence, this paper highly recommends using the third vibration mode during the surface topography. Finally, based on the EFAST method the most effective parameters on the AFM MC performance are the piezoelectric layer length, thickness and the probe length.

Peptide engineered microcantilevers for selective chemical force microscopy and monitoring of nanoparticle capture.

Engineered peptides capable of binding to silica have been used to provide contrast in chemical force microscopy and tested for their capacity to selectively capture silica nanoparticles (NPs). Gold coated atomic force microscopy (AFM) microcantilevers with integrated tips and colloidal probes were functionalized with engineered peptides through a thiol group of a terminal cysteine which was linked via a glycine trimer to a 12-mer binding sequence. The functionalized probes demonstrated a significantly increased binding force on silicon oxide areas of a gold-patterned silicon wafer, whereas plain gold probes, and those functionalized with a random permutation of the silica binding peptide motif or an all-histidine sequence displayed similar adhesion forces to gold and silicon oxide. As the functionalized probes also allowed contact mode imaging subsequently to the adhesion mapping, also the associated friction contrast was measured and found to be similar to the adhesion contrast. Furthermore, the adsorption of silica NPs onto planar gold surfaces functionalized in the same manner was observed to be selective. Notably, the surface coverage with silica NPs was found to decrease with increasing pH, implying the importance of electrostatic interactions between the peptide and the NPs. Finally, the adsorption of silica NPs was monitored via the decrease in fundamental resonance frequency of an AFM microcantilever functionalized with silica binding peptides.

Effectiveness of Modal Decomposition for Tapping Atomic Force Microscopy Microcantilevers in Liquid Environment.

The modal decomposition of tapping mode atomic force microscopy microcantilevers in liquid environments was studied experimentally. Microcantilevers with different lengths and stiffnesses and two sample surfaces with different elastic moduli were used in the experiment. The response modes of the microcantilevers were extracted as proper orthogonal modes through proper orthogonal decomposition. Smooth orthogonal decomposition was used to estimate the resonance frequency directly. The effects of the tapping setpoint and the elastic modulus of the sample under test were examined in terms of their multi-mode responses with proper orthogonal modes, proper orthogonal values, smooth orthogonal modes and smooth orthogonal values. Regardless of the stiffness of the microcantilever under test, the first mode was dominant in tapping mode atomic force microscopy under normal operating conditions. However, at lower tapping setpoints, the flexible microcantilever showed modal distortion and noise near the tip when tapping on a hard sample. The stiff microcantilever had a higher mode effect on a soft sample at lower tapping setpoints. Modal decomposition for tapping mode atomic force microscopy can thus be used to estimate the characteristics of samples in liquid environments.