Atomic Force Acoustic Microscopy Research Articles

Analytical model of the nonlinear dynamics of cantilever tip-sample surface interactions for various acoustic atomic force microscopies

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Resonance frequency analysis for surface-coupled atomic force microscopy cantilever in ambient and liquid environments

Shifts in the resonance frequencies of surface-coupled atomic force microscope (AFM) probes are used as the basis for the detection mechanisms in a number of scanning probe microscopy techniques including atomic force acoustic microscopy (AFAM), force modulation microscopy, and resonance enhanced piezoresponse force microscopy (PFM). Here, we analyze resonance characteristics for AFM cantilever coupled to surface in liquid environment, and derive approximate expressions for resonant frequencies as a function of vertical and lateral spring constant of the tip-surface junction. This analysis provides a simplified framework for the interpretation of AFAM and PFM data in ambient, liquid, and vacuum environments.

Quantitative Evaluation of Elastic Properties of Nano-Crystalline Nickel Using Atomic Force Acoustic Microscopy

Atomic force acoustic microscopy (AFAM) is a near-field technique, where the vibration behavior of a micro-fabricated elastic cantilever beam in contact with a sample surface is sensitive to its local elastic properties. The resolution of this technique is given by the contact radius a c of the atomic force microscope sensor-tip on the sample surface. Taking into account only the Hertzian forces, a c depends on the static load applied by the cantilever, on the elastic constants of the tip and the sample and on the geometry of the contacting bodies. The shape of the sensor tip used in atomic force acoustic microscopy is between a sphere and a flat punch. Hence a c extends from just below 10nm to a few tens of nanometers. In this review, we give an overview of the AFAM technique, present data on the indentation moduli of nanocrystalline nickel, and discuss some of the error sources in quantitative AFAM. The AFAM indentation moduli measured are comparable to the values obtained by nanoindentation and lower than the indentation moduli calculated from ultrasonic velocity measurements. There seems to be a decrease of the indentation modulus with decreasing grain size for grain sizes below 30nm. The data are discussed taking into account X-ray diffraction and electron back-scattering data revealing some texture and macro-strain due to internal stresses in the samples investigated.

Tuning Nanoscopic Water Layers on Hydrophobic and Hydrophilic Surfaces with Laser Light

The evolutional function of ordered interfacial water near solid surfaces was postulated by Szent-Györgyi: "Life actually, may have started with building these water structures." Here we report their tunability with laser light on both hydrophobic and hydrophilic surfaces. On the former, the light caused their depletion--on the latter, an increase in fluidity--as measured by atomic force acoustic microscopy. Interfacial water layers play a key role in cellular recognition. Their tunability promises to revolutionize various fields in biomedical engineering and life sciences.

Simulation of contact stiffness of a hemispherical island inclusion

Numerical analysis is carried out for constructing a model simulating the contact stiffness of a solitary hemispherical island inclusion in an infinitely extended substrate. The contact stiffness is measured using atomic force acoustic microscopy with tips having a constant contact radius. Finite element analysis using the isotropic model of the materials is employed for this purpose. The model can be used for studying nanocomposite materials.

Effect of nonstoichiometric defects on antiparallel domain formation in LiNbO3

The structures of inverted nanodomains in LiNbO3 crystals were investigated using atomic force microscopy (AFM) combined with piezoresponse force microscopy and atomic force acoustic microscopy. The acoustic and AFM topographic images reflected in domain structures with polarization orientation revealed that unexpected antiparallel domains randomly exist in inverted nanodomains in congruent LiNbO3 but not in near-stoichiometric one. The Gibbs free energy change ΔG associating with the internal field Eint in congruent LiNbO3 was discussed. We propose that nonstoichiometric defects, which caused Eint during polarization reversal, play a key role in formation of antiparallel domains in congruent LiNbO3 crystals.

Atomic force acoustic microscopy characterization of nanostructured selenium–tin thin films

Nanostructured tin selenide based ultrathin films have been deposited on fused quartz substrates by thermal evaporation. The morphological and structural properties of the obtained polycrystalline SnSe films have been routinely characterized using atomic force microscopy (AFM), high-resolution transmission electron microscopy (HRTEM), and small-area electron diffraction (SAED). The atomic force acoustic microscopy (AFAM) technique has been used in order to perform a preliminary characterization of the local elastic properties of a film surface. The reported results represent our first attempt to explore the capability of the AFAM technique to discriminate between different phases in such nanostructured compounds.

Nonlinear contact resonance spectroscopy in atomic force microscopy

There are several techniques which combine atomic force microscopy with ultrasonics. In atomic force acoustic microscopy the cantilever is forced to ultrasonic vibrations while the tip is in contact with a sample surface. The various physical forces acting between the tip and the surface depend nonlinearly on the distance. Therefore linear approximations are restricted to tip–sample displacements covering small parts of the interaction force curve. This situation is realized for example at high static loads and small amplitudes of the cantilever and the sample surface vibrations. The nonlinearity of the forces becomes noticeable by generation of higher harmonics in the spectrum of the cantilever vibration. A frequency dependent transfer function can be derived from the model of the cantilever as a beam with constant cross-section using the differential equation for flexural vibrations. By multiplying the transfer function with experimental spectra the nonlinear contact and adhesion forces were calculated as a function of time. In situ measurements of the cantilever and the sample vibrations by a calibrated heterodyne Mach–Zehnder interferometer are presented. This allowed us to reconstruct the tip–sample interaction forces as a function of tip–sample distance.

AFM and Acoustics: Fast, Quantitative Nanomechanical Mapping

Combining atomic force microscopy and ultrasonic methods allows near-field detection of acoustic signals and thereby otherwise inaccessible nanoscale mechanical characterization. The two predominant variations, ultrasonic force microscopy and atomic force acoustic microscopy, are reviewed in detail. Applications of each to ceramics, polymers, metals, biological materials, and even subsurface structures are discussed, with a particular emphasis on image contrast mechanisms, data analysis, and experimental challenges. Finally, recent advances of these concepts into high-speed surface property mapping are presented, demonstrating 100-fold enhancements in full-frame imaging speeds.

Characterization of epoxy/single-walled carbon nanotubes composite samples via atomic force acoustic microscopy

Atomic force acoustic microscopy technique has been used to characterize structural and mechanical properties of a nanocomposite sample, obtained by incorporating single-walled carbon nanotubes (SWCNTs) into epoxy resin. The aim of the reported preliminary characterization is to investigate the reliability of such a technique as a tool for the qualitative evaluation of the homogeneity of the dispersion of SWCNTs into the epoxy matrix, as well as for the quantitative mapping of local elastic properties of sample surface.

SPM Characterization of Pulsed Laser Deposited Nanocrystalline CrN Hard Coatings

Nanocrystalline CrN coatings, widely required for surface engineering application covering wear and corrosion resistance, need to be investigated for atomic scale morphology, surface roughness, local stiffness, phase uniformity, and homogeneity. Evolution of these properties as a function of thickness need to be studied. In this paper, we have attempted to address these issues through use of a multimode scanning probe microscope (SPM) equipped to carry out Atomic Force Microscopy (AFM) and Atomic Force Acoustic microscopy (AFAM) of Chromium nitride films (100-500 nm thick) on Si prepared under high vacuum by pulsed Laser Ablation using Nd-YAG Q-switched laser. Prior to SPM analysis, the coatings were annealed in N2 atmosphere at 700 degrees C for 30 minutes for improving crystallanity and coating substrate adhesion. The GIXRD patterns of these annealed specimens showed formation of nanocrystalline CrN. Also signature of amorphous phases was seen. The grain size was estimated to be less than 30 nm. Contact mode AFM imaging revealed a roughness value less than 50 nm. Local stiffness values were calculated from AFM force-distance curves. Imaging of frictional force and surface flaws are being investigated by Frictional Force Microscopy (FFM), resonance spectroscopy, and AFAM, respectively. The contrast in AFAM images is seen due to variation in surface elasticity in reference and CrN samples. Stiffness constant and elastic modulus were calculated for both the samples and compared.

Imaging distribution of local stiffness over surfaces using atomic force acoustic microscopy

We report a systematic study to determine local elastic properties of surfaces using atomic force acoustic microscopy(AFAM). AFAM is a combination of atomic force microscopy (AFM) and acoustic waves. We describe the technique and principle of AFAM in detail and interpret the obtained images using simple arguments. We have used (1) polished commercial piezoelectric PZT, Pb(Zr,Ti)O3 ceramic, (2) thin film of PZT deposited by the sol–gel technique and (3) thin film of Au deposited on a Si(0 0 1) substrate to elucidate the capability of the AFAM technique to image the distribution of local stiffness over the sample surface. We have also used a complementary technique such as force–distance measurements using the AFM mode to support the interpretation of the AFAM images. We have determined semi-quantitatively the change in the local stiffness over the sample surface using both the force–distance measurement and the change in the contact resonance peak frequency at various regions. We have also shown that the AFAM technique can be used to get a better surface image contrast where contact mode AFM shows poor contrast.

Vibrational dynamics of concentrated-mass cantilevers in atomic force acoustic microscopy: Presence of modes with selective enhancement of vertical or lateral tip motion

Concentrated-mass (CM) cantilevers previously proposed by the author have features significantly effective for atomic force acoustic microscopy (AFAM), in which sample stiffness can be detected at nano scale by a vibrating tip. CM cantilevers improve the sensitivity of the detection and simplify the dynamics then lead to success in evaluations of the elastic modulus. The present study proposed a new type of CM cantilevers based on analyses of the vibrational dynamics taking account of previously ignored factors including the lateral contact stiffness and the inertia moment of a particle attached as a CM. A rod-like particle was attached on a tip in the new type to enhance the inertia moment in addition to the translational inertia. The first two modes behaved like one-freedom models, namely translational (vertical) and rotational (lateral) motions of the attached mass and the tip. Experiments on a sapphire wafer verified that the vertical and lateral stiffness can be simultaneously evaluated without mutual interference.

Finite-Element Simulation of Cantilever Vibrations in Atomic Force Acoustic Microscopy

Atomic Force Acoustic Microscopy has been proven to be a powerful technique for materials characterization with nanoscale lateral resolution. This technique allows one to obtain images of elastic properties of materials. By means of spectroscopic measurements of the tip-sample contact-resonance frequencies, it is possible to obtain quantitative values of the mechanical stiffness of the sample surface. For quantitative analysis a reliable relation between the spectroscopic data and the contact stiffness is required based on a correct geometrical model of the cantilever vibrations. This model must be precise enough for predicting the resonance frequencies of the tip-sample interaction when excited over a wide range of frequencies. Analytical models have served as a good reference for understanding the vibrational behavior of the AFM cantilever. They have certain limits, however, for reproducing the tip-sample contact-resonances due to the cantilever geometries used. For obtaining the local elastic modulus of samples, it is necessary to know the tip-sample contact area which is usually obtained by a calibration procedure with a reference sample. In this work we show that finiteelement modeling may be used to replace the analytical inversion procedure for AFAM data. First, the three first bending modes of cantilever resonances were used for finding the geometrical dimension of the cantilever employed. Then the normal and in-plane stiffness of the sample were obtained for each measurement on the surface to be measured. A calibration was needed to obtain the tip position of the cantilever by making measurements on a sample with known surface elasticity, here crystalline silicon. The method developed in this work was applied to AFAM measurements on silicon, zerodur, and strontium titanate.

Influence of the cantilever holder on the vibrations of AFM cantilevers

Dynamic techniques exploiting the vibration of atomic force microscope (AFM) cantileversare often superior to quasi-static operation, in particular with respect to the signal-to-noiseratio. Tapping mode, magnetic force microscopy or torsional resonance (TR)-mode forexample exploit the resonance amplification of bending or torsional modes of the cantilever.In atomic force acoustic microscopy (AFAM) and related techniques aiming to measureelasticity or adhesion quantitatively on a nanometre scale, the cantilever vibrates while thetip is in contact with a sample surface. The higher vibration modes are included in theevaluation. Well-defined resonance maxima of the cantilever are a prerequisite for allresonance techniques. To allow their handling, microscaled commercial cantilevers arefabricated in one piece with a holder of millimetre dimensions providing the base towhich the cantilever beam is suspended. Here, we examine experimentally andtheoretically how the cantilever holder influences the vibration of the cantilevers.

Atomic force microscopy cantilever simulation by finite element methods for quantitative atomic force acoustic microscopy measurements

Measurements of vibrational spectra of atomic force microscopy (AFM) microprobes in contact with a sample allow a good correlation between resonance frequencies shifts and the effective elastic modulus of the tip-sample system. In this work we use finite element methods for modeling the AFM microprobe vibration considering actual features of the cantilever geometry. This allowed us to predict the behavior of the cantilevers in contact with any sample for a wide range of effective tip-sample stiffness. Experimental spectra for glass and chromium were well reproduced for the numerical model, and stiffness values were obtained. We present a method to correlate the experimental resonance spectrum to the effective stiffness using realistic geometry of the cantilever to numerically model the vibration of the cantilever in contact with a sample surface. Thus, supported in a reliable finite element method (FEM) model, atomic force acoustic microscopy can be a quantitative technique for elastic-modulus measurements. Considering the possibility of tip-apex wear during atomic force acoustic microscopy measurements, it is necessary to perform a calibration procedure to obtain the tip-sample contact areas before and after each measurement.

Nanoscale Electromechanical and Mechanical Imaging of Butterfly Wings by Scanning Probe Microscopy

Structure of a Vanessa virginiensis butterfly wing has been studied on length scales from 50 m to 10 nm using a combination of scanning probe microscopy (SPM) techniques. Local variations in mechanical properties detected by Ultrasonic Force Microscopy and Atomic Force Acoustic Microscopy demonstrate imaging with the spatial resolution of about 10 nm, which exceeds the resolution of conventional SPM topographic imaging. The butterfly wings are shown to exhibit a piezoelectric behavior, which is attributed to the presence of chitin fibers with a characteristic piezoelectric constant of the order of 1 pm/V. It is suggested that orientation of chitin can be determined in real space on the nanometer level by measuring the vector piezoelectric response of the sample, thus providing a novel structural characterization tool for biological systems.

Local indentation modulus characterization via two contact resonance frequencies atomic force acoustic microscopy

Atomic force acoustic microscopy is a dynamical AFM-based technique developed for non-destructive characterization of elastic properties of materials at micrometrical and sub-micrometrical scale. A standard AFM apparatus is equipped with a piezoelectric transducer exciting longitudinal oscillations at ultrasonic frequencies in the sample under investigation. Tip–sample contact stiffness is obtained through the values of the measured resonance frequencies of the cantilever contacting the sample surface, thus allowing one to obtain the value of the sample indentation modulus. The paper describes a generalization of the technique: while performing topography, the first and the second contact resonance frequencies are acquired at each point of the scanned area. Data are then properly processed and acoustic images are obtained as a bi-dimensional pattern of the indentation modulus over the imaged samples area. The technique is illustrated in two different kinds of sample: a metallographic (1 1 0) GaAs sample, prepared by incorporating GaAs single crystals into an epoxy matrix, and a diamond-like carbon film, deposited on a Mo substrate by laser ablation from a glassy carbon target.

Technique for rapid in vitro single-cell elastography

Statistically meaningful assays require scanning a large number of cells in a short time. Here we present a technique for rapid in vitro single-cell elastography. The technique is based on atomic force acoustic microscopy but (1) requires only a few minutes of scan time, (2) can be used on live cells briefly removed from most of the nutrient fluid, (3) does negligible harm or damage to the cell, (4) provides semiquantitative information on the distribution of modulus across the cell and (5) yields data with 1- to 10-nm resolution. We describe the new technique in detail, apply it to baby hamster kidney cells, verify the results and calibrate the images with atomic force microscope force-distance measurements. The technique enables rapid assessment of physical/biochemical signals on the cell modulus and contributes to current understanding of cell mechanics.

Quantitative measurements of indentation moduli by atomic force acoustic microscopy using a dual reference method

Atomic force acoustic microscopy (AFAM) was used to quantitatively determine material indentation moduli by measuring local mechanical responses. A dual reference method has been shown to be capable of extracting the modulus of a material within 3% of the calculated expected value without any assumptions of the probe’s mechanical properties. The use of this developed method also allows for the calculation of the maximum precision in the quantitative determination of the indentation modulus of materials using AFAM. A parallel analysis of the single and dual reference AFAM techniques isolates the inaccuracy induced by the assumption that the indentation modulus of the atomic force microscopy probe used is the same as bulk silicon.