Analyses of vibration responses on nanoscale processing in a liquid using tapping-mode atomic force microscopy

An analytical solution of the vibration responses of biological specimens using atomic force microscopy (AFM), which often requires operation in a liquid, is developed. In this study, the modal superposition method is employed to analyze the vibration responses of AFM cantilevers in tapping mode (TM) operated in a liquid and in air. The hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The tip–sample interaction forces were transformed into axial, distributed transversal, and bending loading, and then applied to the end region of the AFM through the tip holder. The effects of transverse stress and bending stress were adopted to solve the dynamic model. With this model, a number of simulations were carried out to investigate the relationship between the transient responses of the cantilever in a liquid and the parameters considered in nanoscale processing. The simulations show that the vibration of AFM cantilevers in a liquid has dramatically different dynamic characteristics from these of that in air. The liquid reduces the magnitude of the transversal response and reduces the cantilever resonances. Moreover, the magnitudes of response become larger with increasing intermolecular distances and smaller with decreasing tip length. The cantilever vibration amplitudes significantly depend on the damping constant and the mass proportionality constant.     

Determination of the mass of polymer films using an AFM cantilever

There are no established methods that have a sensitivity during the determination of an adsorbed polymer film mass that is not worse than 1 ng that do not require additional calibration and the usage of reference measures. A highly sensitive method for measuring an adsorbed polymer is proposed in this work. The added mass was determined by the change of the resonance frequency of a cantilever used in atomic-force microscopy (AFM) as a probe. A modification of the cantilever surface is proposed that allows one to avoid the affect of the adsorbed polymer on the cantilever force constant. The mass of poly(diallyldimethylammonium) (PDDA) chloride adsorbed on the cantilever surface was obtained with a sensitivity of 0/01 ng using an AFM cantilever.     

Dynamics of microcantilever integrated with geometric nonlinearity for stable and broadband nonlinear atomic force microscopy

We explore the use of a nonlinear cantilever system integrating geometric nonlinearity for AFM imaging, in contrast from the traditional linear cantilever system. The intrinsically nonlinear AFM cantilever system exhibits broadband resonance over a bandwidth several times of its linear resonant frequency and possesses an intrinsic stability that virtually eliminates the instability induced by the tip–sample interactions involved in a linear AFM system, thus the artifact of image contrast reversal. The ability to realize broadband operation may extend the application of AFM to spectral analysis of tip–sample interactions across a broad frequency range at the nanoscale.     

Frequency shifts of cantilever in AFM

The frequency shift and frequency shift image of cantilever in AFM have been studied by numerical integration of the equation of motion of cantilever for silicon tip with rutile TiO₂(0 0 1) surface in UHV conditions and by the Hamaker summation method for the tip-surface interaction forces. The effects of the excitation frequency at the cantilever base and the equilibrium position of the tip on the frequency shift have been calculated and the results showed the same phenomena as those measured, e.g., the frequency shift increased dramatically or rapidly before the contact point and was then almost level off after the contact point. The effects of scanning speed and the initial closest distance of tip to the contact point have been calculated at different excitation frequencies at the cantilever base and the results showed that proper frequency shift image could be obtained either by noncontact mode at the excitation frequency slightly less than the resonance frequency of free cantilever, or by tapping mode at the excitation frequency a few times smaller than the resonance frequency of free cantilever.     

Evaluation of the contact resonance frequencies in atomic force microscopy as a method for surface characterisation (invited)

The combination of ultrasound with atomic force microscopy (AFM) opens the high lateral resolution of scanning probe techniques in the nanometer range to ultrasonics. One possible method is to observe the resonance frequencies of the AFM sensors under different tip-sample interaction conditions. AFM sensors can be regarded as small flexible beams. Their lowest flexural and torsional resonance frequencies are usually found to be in a range between several kHz and several MHz depending on their exact geometrical shape. When the sensor tip is in a repulsive elastic contact with a sample surface, the local indentation modulus can be determined by the contact resonance technique. Contact resonances in the ultrasonic frequency range can also be used to improve the image contrast in other dynamic techniques as, for example, in the so-called piezo-mode. Here, an alternating electric field is applied between a conducting cantilever and a piezoelectric sample. Via the inverse piezoelectric effect, the sample surface is set into vibration. This excitation is localised around the contact area formed by the sensor tip and the sample surface. We show applications of the contact resonance technique to piezoelectric ceramics.     

AFM detection of the mechanical resonances of coiled carbon nanotubes

We introduce a method for atomic force microscopy (AFM)-based detection of mechanical resonances in helix-shaped multi-walled carbon nanotubes. After deposition on an oxidized silicon substrate, the three-dimensional structure of suspended nanotubes, which bridges an artificially created step on the surface, can be visualized using AFM operating in the non-contact mode. The suspended coiled nanotubes are resonantly excited, in situ, at the fundamental frequency by an ultrasonic transducer connected to the substrate. When the AFM tip is positioned above the coiled nanotube, the cantilever is unable to follow the fast nanotube oscillations. Nevertheless, an oscillation amplitude-dependent signal is generated due to the non-linear force-to-distance dependence. Measurement of the mechanical resonances of the helix-shaped carbon nanotubes can be used to quantitatively determine their elastic properties. Assuming that a coiled nanotube can be modeled as a suspended helix-shaped uniformly thin elastic beam, the obtained resonance frequency is consistent with a Young's modulus of 0.17ǂ.05 TPa.     

Interferometric profiling of microcantilevers in liquid

Silicon micro cantilevers are used as highly sensitive transducers for a wide range of physical, chemical and biochemical stimuli. Vibrating the cantilevers at higher-order resonant modes can achieve extra sensitivity, but the difficulty lies in determining exactly which modes are excited in the cantilever. This problem is exacerbated for cantilever sensors operating in liquid where the computational analysis of the resonance modes is very challenging. Using strobed interferometric microscopy, we are able to image the dynamic behavior of individual (100×500×1 μm³) cantilevers in an eight cantilever array over frequencies from 0–1 MHz. We show how some modifications to the interferometric microscope allow for the spatial visualization of 16 longitudinal modes of cantilevers working in liquid with nanometer-scale amplitudes. We also compare the shift in frequency response and reduction in quality factor for cantilevers resonating in liquid versus in air and simulations in vacuum. Because the resonant frequency spectrum is fairly complex and does not follow simple intuition, our work maps the actual behavior of cantilevers without having any specific knowledge of the sample and environment parameters and without the necessity of involved simulations and calculations.     

原子力显微镜探针悬臂几何结构变化对高次谐波信息增强的研究

轻敲模式原子力显微镜高次谐波信号包含待测样品表面纳米力学特性等方面的信息, 但是传统原子力显微镜的高次谐波信号非常微弱. 里兹法证明在探针悬臂的特定位置打孔可以实现探针的内共振从而增强高次谐波信号强度. 本文通过有限元仿真计算获得探针第一共振频、第二共振频及其比值随着孔的尺寸和位置变化的规律. 在实验上通过聚焦离子束在探针悬臂上打孔使其第二共振频约为第一共振频的6倍, 提高了第6次谐波信号的信噪比, 并在实验室研制的高次谐波成像实验装置上获得了6次谐波图像. 关键词： 轻敲模式原子力显微镜 探针悬臂几何结构 高次谐波 聚焦离子束加工     

Detection of single-electron charging in an individual InAs quantum dot by noncontact atomic-force microscopy

Single-electron charging in an individual InAs quantum dot was observed by electrostatic force measurements with an atomic-force microscope (AFM). The resonant frequency shift and the dissipated energy of an oscillating AFM cantilever were measured as a function of the tip-back electrode voltage, and the resulting spectra show distinct jumps when the tip was positioned above the dot. The observed jumps in the frequency shift, with corresponding peaks in dissipation, are attributed to a single-electron tunneling between the dot and the back electrode governed by the Coulomb blockade effect, and are consistent with a model based on the free energy of the system. The observed phenomenon may be regarded as the "force version" of the Coulomb blockade effect.     

Numerical study of the hydrodynamic drag force in atomic force microscopy measurements undertaken in fluids

When atomic force microscopy (AFM) is employed for in vivo study of immersed biological samples, the fluid medium presents additional complexities, not least of which is the hydrodynamic drag force due to viscous friction of the cantilever with the liquid. This force should be considered when interpreting experimental results and any calculated material properties. In this paper, a numerical model is presented to study the influence of the drag force on experimental data obtained from AFM measurements using computational fluid dynamics (CFD) simulation. The model provides quantification of the drag force in AFM measurements of soft specimens in fluids.The numerical predictions were compared with experimental data obtained using AFM with a V-shaped cantilever fitted with a pyramidal tip. Tip velocities ranging from 1.05 to 105 μm/s were employed in water, polyethylene glycol and glycerol with the platform approaching from a distance of 6000 nm. The model was also compared with an existing analytical model. Good agreement was observed between numerical results, experiments and analytical predictions. Accurate predictions were obtained without the need for extrapolation of experimental data. In addition, the model can be employed over the range of tip geometries and velocities typically utilized in AFM measurements.     

Thermal effects on mass detection sensitivity of carbon nanotube resonators in nonlinear oscillation regime

A mass sensor using a nano-resonator has high detection sensitivity, and mass sensitivity is higher with smaller resonators. Therefore, carbon nanotubes (CNTs) are the ultimate materials for these applications and have been actively studied. In particular, CNT-based nanomechanical devices may experience high temperatures that lead to thermal expansion and residual stress in devices, which affects the device reliability. In this letter, to demonstrate the influence of the temperature change (i.e., thermal effect) on the mass detection sensitivity of CNT-based mass sensor, dynamic analysis is carried out for a CNT resonator with thermal effects in both linear and nonlinear oscillation regimes. Based on the continuum mechanics model, the analytical solution method with an assumed deflection eigenmode is applied to solve the nonlinear differential equation which involves the von Karman nonlinear strain–displacement relation and the additional axial force associated with thermal effects. A thermal effect on the fundamental resonance behavior and resonance frequency shift due to adsorbed mas, i.e., mass detection sensitivity, is examined in high-temperature environment. Results indicate a valid improvement of fundamental resonance frequency by using nonlinear oscillation in a thermal environment. In both linear and nonlinear oscillation regimes, the mass detection sensitivity becomes worse due to the increasing of temperature in a high-temperature environment. The thermal effect on the detection sensitivity is less effective in the nonlinear oscillation regime. It is concluded that a temperature change of a mass sensor with a CNT-based resonator can be utilized to enhance the detection sensitivity depending on the CNT length, linear/nonlinear oscillation behaviors, and the thermal environment.     

Validity and Accuracy of Resonance Shift Prediction Formulas for Microcantilevers: A Review and Comparative Study

This article provides a review of methods of predicting mass-induced resonance shifts in microcantilevers. It combines a review of factors that influence resonance frequency shifts, such as material properties, size effects, and support compliance with a comparative study of accuracy of predicting resonance shifts due to mass adsorption. The applicability and accuracy of widely used formulas to correlate mass addition with resonance shift are assessed through comprehensive comparison with experimental measurements and numerical methods. The methods include both distributed parameter and lumped parameter formulations. The applications include distributed added masses, tip masses, and added mass at arbitrary locations along a cantilever span.     

新型AFM探针的制备及应用

采用熔拉 -腐蚀复合方法 ,将普通单模石英光纤制成直锥形光纤探针。利用自制工具将探针打弯 ,制成悬臂式光纤探针 ,在AFM上取得了较理想的测试结果。将自制光纤探针和商用硅材料探针获得的两种扫描图像进行了对比 ,分析了悬臂式光纤探针的特点     

Force probing of protein crystals: An atomic force microscopy study

The atomic force microscope (AFM) was used for measuring force-distance curves on horse spleen ferritin crystals in liquid environment. In the region of the approach curve which corresponds to tip-surface contact, discrete jumps were recorded, as predicted by molecular dynamics simulations in the case of low tip-sample interaction. The observed jumps can be related to the removal of individual molecules from the surface by the AFM tip. A simple steric model, which takes into account tip and ferritin molecule size, can explain the displacements observed with excellent agreement. The elemental force jump resulting from the approach curves is a direct measure of the force required to remove a single molecule from the crystal face. We discuss the conditions under which the cantilever potential energy difference along the elemental force step provides the energy of extraction of a single molecule. The estimate of the intermolecular binding energy turns out to be in good agreement with the value calculated independently from the surface free energy of ferritin crystals. Received 10 February 2000 and Received in final form 4 May 2000     

Nanoscale imaging of surface piezoresponse on GaN epitaxial layers

Surfaces of GaN films were investigated by atomic force microscopy (AFM) with implemented piezoelectric force microscopy technique. A model of PFM based on the surface depletion region in GaN films is discussed. The local piezoelectric effect of the low frequency regime was found to be in phase with the applied voltage on large domains, corresponding to a Ga-face of the GaN layer. Low piezoresponse is obtained within the inter-domain regions. The use of frequencies near a resonance frequency enhances very much the resolution of piezo-imaging, but only for very low scanning speed the piezo-imaging can follow the local piezoelectric effect. An inversion of the PFM image contrast is obtained for frequencies higher than the resonance frequencies. The effect of a chemical surface treatment on the topography and the piezoresponse of the GaN films was also investigated. Textured surfaces with very small domains were observed after the chemical treatment. For this kind of surfaces, piezo-induced torsion rather than bending of the AFM cantilever dominates the contrast of the PFM images. A small memory effect was observed, and explained by surface charging and confinement of the piezoelectric effect within the carrier depletion region at the GaN surface.     

A Thin Liquid Film and Its Effects in an Atomic Force Microscopy Measurement

Recently, it has been observed that a liquid film spreading on a sample surface will significantly distort atomic force microscopy （AFM） measurements. In order to elaborate on the effect, we establish an equation governing the deformation of liquid film under its interaction with the AFM tip and substrate. A key issue is the critical liquid bump height yoc, at which the liquid film jumps to contact the AFM tip. It is found that there are three distinct regimes in the variation of yoc with film thickness H, depending on Hamaker constants of tip, sample and liquid. Noticeably, there is a characteristic thickness H^＊ physically defining what a thin film is; namely, once the film thickness H is the same order as H^＊, the effect of film thickness should be taken into account. The value of H^＊ is dependent on Hamaker constants and liquid surface tension as well as tip radius.     

Tip cleaning and sharpening processes for noncontact atomic force microscope in ultrahigh vacuum

Tip cleaning and sharpening processes for noncontact atomic force microscope (AFM) operated in ultrahigh vacuum (UHV) were carried out and evaluated by a scanning Auger microscope (SAM) with a field emission electron gun and a noncontact AFM in UHV combined with a scanning tunneling microscope and a field emission microscope. The cantilever used in this study was piezoresistive, which can be heated by passing a current through the resistive legs of the cantilever. As a pretreatment, the tip was irradiated with ultraviolet light in oxygen to remove carbon contaminants. It was heated at about 750°C to form a clean oxide layer in oxygen of 5×10⁻⁵ Torr in an SAM chamber. The desorption of the layer can make a remained tip apex sharper by heating under electron beam irradiation. A thermally oxidized layer was also eliminated by HF etching to sharpen the tip apex. The procedures are useful to obtain a well-defined Si tip suitable for a noncontact AFM.     

Top-down approach to fiber-top cantilevers

Taking inspiration from conventional top-down micromachining techniques, we have fabricated a low mass gold fiber-top cantilever via align-and-shine photolithography. The cantilever is characterized by measuring its resonance frequency and mechanical quality factor. Our results show that the device grants mass sensitivity comparable to that reported for similar standard cantilevers. This proof-of-concept paves the way to series production of highly sensitive fiber-top devices for remote detection of biochemical substances.     

Nano-probe-assisted technology of indium-nano-dot formation for site-controlled InAs/GaAs quantum dots

We have successfully and reproducibly fabricated uniform indium (In) nano-dots at a selected point. Nano-dot formation was realized using an atomic force microscope (AFM) probe with a specially designed cantilever, which was equipped with a hollow pyramidal tip with a sub-micron size aperture on the apex and an In-reservoir tank within the stylus. The In nano-dots formed in this study can be directly converted to InAs quantum dots by subsequent irradiation of arsenic flux in the molecular beam epitaxy chamber, which is connected to the AFM chamber through an ultra-high-vacuum tunnel.     

Highly reproducible tip‐enhanced Raman scattering using an oxidized and metallized silicon cantilever tip as a tool for everyone

We have successfully improved the reproducibility of tip‐enhancement effect on metallized silicon cantilever tips for characterization of carbon nanotubes. Plasmon resonance tuning relative to an excitation wavelength is crucial for efficient tip‐enhancement, which is accomplished by thermal oxidization and subsequent metallization of commercial silicon tips. Because of the change of the refractive index of the tip from silicon to silicon dioxide, the plasmon resonance of the silver‐coated tip is blue‐shifted showing an enormous enhancement at 532 nm excitation. Highly reproducible tips exhibit an enhancement factor of >100 with a 100% yield. Because the tips are fabricated from commercially available silicon cantilever tips in a simple and robust way, our approach provides an important step of ‘tip‐enhanced Raman spectroscopy for everyone’. Copyright © 2012 John Wiley & Sons, Ltd.