Force gradient sensitive detection in lift-mode Kelvin probe force microscopy

We demonstrate frequency modulation Kelvin probe force microscopy operated in lift-mode under ambient conditions. Frequency modulation detection is sensitive to force gradients rather than forces as in the commonly used amplitude modulation technique. As a result there is less influence from electric fields originating from the tip's cone and cantilever, and the recorded surface potential does not suffer from the large lateral averaging observed in amplitude modulated Kelvin probe force microscopy. The frequency modulation technique further shows a reduced dependence on the lift-height and the frequency shift can be used to map the second order derivative of the tip-sample capacitance which gives high resolution material contrast of dielectric sample properties. The sequential nature of the lift-mode technique overcomes various problems of single-scan techniques, where crosstalk between the Kelvin probe and topography feedbacks often impair the correct interpretation of the recorded data in terms of quantitative electric surface potentials.     

Reduction of tip-sample contact using dielectrophoretic force scanning probe microscopy

Dielectrophoretic force microscopy is shown to allow for facile noncontact imaging of systems in aqueous media. Electrokinetic tip-sample forces were predicted from topography measurements of an interface and compared with experimental images. Correlation function and power spectral density analyses indicated that image feedback was maintained without mechanical contact using moderate potentials (e.g., approximately 18 nm off the surface for a 7-Vpp, 100-kHz waveform). The applied dielectrophoretic force and the corresponding increase in effective tip radius were predictably adjusted by changing the peak potential.     

Inverting amplitude and phase to reconstruct tip-sample interaction forces in tapping mode atomic force microscopy

Quantifying the tip-sample interaction forces in amplitude-modulated atomic force microscopy (AM-AFM) has been an elusive yet important goal in nanoscale imaging, manipulation and spectroscopy using the AFM. In this paper we present a general theory for the reconstruction of tip-sample interaction forces using integral equations for AM-AFM and Chebyshev polynomial expansions. This allows us to reconstruct the tip-sample interactions using standard amplitude and phase versus distance curves acquired in AM-AFM regardless of tip oscillation amplitude and in both the net attractive and repulsive regimes of oscillation. Systematic experiments are performed to reconstruct interaction forces on polymer samples to demonstrate the power of the theoretical approach.     

Mapping nanoscale elasticity and dissipation using dual frequency contact resonance AFM

We report on a technique that simultaneously quantifies the contact stiffness and dissipation of an AFM cantilever in contact with a surface, which can ultimately be used for quantitative nanomechanical characterization of surfaces. The method is based on measuring the contact resonance frequency using dual AC resonance tracking (DART), where the amplitude and phase of the cantilever response are monitored at two frequencies on either side of the contact resonance. By modelling the tip-sample contact as a driven damped harmonic oscillator, the four measured quantities (two amplitudes and two phases) allow the four model parameters, namely, drive amplitude, drive phase, resonance frequency and quality factor, to be calculated. These mechanical parameters can in turn be used to make quantitative statements about localized sample properties. We apply the method to study the electromechanical coupling coefficients in ferroelectric materials and the storage and loss moduli in viscoelastic materials.     

Mechanical manifestations of rare atomic jumps in dynamic force microscopy

The resonance frequency and the excitation amplitude of a silicon cantilever have been measured as a function of distance to a cleaved KBr(001) surface with a low-temperature scanning force microscope (SFM) in ultrahigh vacuum. We identify two regimes of tip-sample distances. Above a site-dependent critical tip-sample distance reproducible data with low noise and no interaction-induced energy dissipation are measured. In this regime reproducible SFM images can be recorded. At closer tip-sample distances, above two distinct atomic sites, the frequency values jump between two limiting curves on a timescale of tens of milliseconds. Furthermore, additional energy dissipation occurs wherever jumps are observed. We attribute both phenomena to rarely occurring changes in the tip apex configuration which are affected by short-range interactions with the sample. Their respective magnitudes are related to each other. A specific candidate two-level system is also proposed.     

Characterization of Probe Dynamic Behaviors in Critical Dimension Atomic Force Microscopy

This paper describes a detailed computational model of the interaction between an atomic force microscope probe tip and a sample surface. The model provides analyses of dynamic behaviors of the tip to estimate the probe deflections due to surface intermittent contact and the resulting dimensional biases and uncertainties. Probe tip and cantilever beam responses to intermittent contact between the probe tip and sample surface are computed using the finite element method. Intermittent contacts with a wall and a horizontal surface are computed and modeled, respectively. Using a 75 nm Critical Dimension (CD) tip as an example, the responses of the probe to interaction forces between the sample surface and the probe tip are shown in both time and frequency domains. In particular, interaction forces between the tip and both a vertical wall and a horizontal surface of a silicon sample are modeled using Lennard-Jones theory. The Snap-in and Snap-out of the probe tip in surface scanning are calculated and shown in the time domain. Based on the given tip-sample interaction force model, the calculation includes the compliance of the probe and dynamic forces generated by an excitation. Cantilever and probe tip deflections versus interaction forces in the time domain can be derived for both vertical contact with a plateau and horizontal contact with a side wall. Dynamic analysis using the finite element method and Lennard-Jones model provide a unique means to analyze the interaction of the probe and sample, including calculation of the deflection and the gap between the probe tip and the measured sample surface.     

Tapping-mode scanning force microscopy: Metallic tips and samples

The operation of a tapping-mode scanning force microscope using a metallic tip and metallic sample, with a bias voltage applied between the two, is modelled as a driven nonlinear oscillator, where metal-metal adhesion and electric forces are taken into account. The model, which applies to the case where the sample indentation by the tip is minimal, shows that one can obtain a good estimate of the tip-sample contact time from the tip-sample current.     

Effects of nonlinear forces on dynamic mode atomic force microscopy and spectroscopy

In this paper, we describe the effects of nonlinear tip-sample forces on dynamic mode atomic force microscopy and spectroscopy. The jumps and hysteresis observed in the vibration amplitude (A) versus tip-sample distance (h) curves have been traced to bistability in the resonance curve. A numerical analysis of the basic dynamic equation was used to explain the hysteresis in the experimental curve. It has been found that the location of the hysteresis in the A-h curve depends on the frequency of the forced oscillation relative to the natural frequency of the cantilever.     

Three-dimensional dynamic force spectroscopy measurements on KBr(001): atomic deformations at small tip-sample separations

Three-dimensional dynamic force spectroscopy measurements were carried out above KBr(001) at low temperature in order to investigate the distance dependence of the tip-sample interactions. In particular, the recorded 3D frequency shift data as well as the extracted interaction force and potential energy fields were analysed with respect to influences of tip and/or sample deformations. We found that a postprocessing correction of the observed deformations significantly modifies the magnitude of the extracted interaction forces and also the image contrast.     

原子力声显微镜成像及分析

超声检测技术与原子力显微技术相结合,构成原子力声显微镜(AFAM),能够实现样品内部纳米结构的测量,并分析如局域弹性模量、刚度等力学性能.本文在传统的原子力显微镜(AFM)的基础上初步构建了AFAM,利用AFM轻敲模式下的微悬臂梁振动激励信号来驱动样品背面的压电超声换能器,并利用轻敲模式控制系统中的锁相环检测经过样品后由探针收集的振动信号,形成振幅及相位图像.这种AFAM方法不需外接信号发生器、锁相放大器及相关控制电路,从而避免AFM内、外部的仪器及控制电路的不同步而引起的AFAM振幅/相位与形貌图像间的偏移.此外,还分析了形貌结构对AFAM振幅图像的影响,为进一步研究AFAM亚表面成像奠定了基础.     

Contrast inversion in electrostatic force microscopy imaging of trapped charges: tip-sample distance and dielectric constant dependence

We present a numerical and analytical study of the behavior of both electrostatic force and force gradient created by a charge trapped below the surface of a dielectric on an atomic force microscope tip as a function of the dielectric constant and tip-sample distance. As expected, the force decreases monotonously when the dielectric constant increases. However, a maximum in the dielectric constant dependence of the force gradient is found. This maximum occurs in the typical experimental parameters' range and depends on the tip-sample distance and the sample thickness. The analytical study permits us to understand the physical origin of this phenomenon and is in good agreement with the numerical simulation for small tip-sample distances. We also report a study exemplifying a possible contrast inversion in electrostatic force microscopy (EFM) signals while scanning, at different heights, two charges trapped in a sample having heterogeneous dielectric domains. In addition to this particular contrast inversion effect, this study can be considered as a way to gain insight into the mechanisms of EFM image formation as a function of the dielectric constant and tip-sample.     

Frequency modulated atomic force microscopy on MgO(001) thin films: interpretation of atomic image resolution and distance dependence of tip-sample interaction

Atomically resolved images on a MgO(001) thin film deposited on Ag(001) obtained in ultrahigh vacuum by frequency modulated atomic force microscopy at low temperature are presented and analysed. Images obtained in the attractive regime show a different type of contrast formation from those acquired in the repulsive regime. For the interpretation of the image contrast we have investigated the tip-sample interaction. Force and energy were recovered from frequency shift versus distance curves. The derived force curves have been compared to the force laws of long-range, short-range and contact forces. In the attractive regime close to the minimum of the force-distance curve elastic deformations have been confirmed. The recovered energy curve has been scaled to the universal Rydberg model, yielding a decay length of l = 0.3?nm and ΔE = 4.2?aJ (26?eV) for the maximum adhesion energy. A universal binding-energy-distance relation is confirmed for the MgO(001) thin film.     

Cantilever arrays with self-aligned nanotips of uniform height

Cantilever arrays are employed to increase the throughput of imaging and manipulation at the nanoscale. We present a fabrication process to construct cantilever arrays with nanotips that show a uniform tip-sample distance. Such uniformity is crucial, because in many applications the cantilevers do not feature individual tip-sample spacing control. Uniform cantilever arrays lead to very similar tip-sample interaction within an array, enable non-contact modes for arrays and give better control over the load force in contact modes. The developed process flow uses a single mask to define both tips and cantilevers. An additional mask is required for the back side etch. The tips are self-aligned in the convex corner at the free end of each cantilever. Although we use standard optical contact lithography, we show that the convex corner can be sharpened to a nanometre scale radius by an isotropic underetch step. The process is robust and wafer-scale. The resonance frequencies of the cantilevers within an array are shown to be highly uniform with a relative standard error of 0.26% or lower. The tip-sample distance within an array of up to ten cantilevers is measured to have a standard error around 10 nm. An imaging demonstration using the AFM shows that all cantilevers in the array have a sharp tip with a radius below 10 nm. The process flow for the cantilever arrays finds application in probe-based nanolithography, probe-based data storage, nanomanufacturing and parallel scanning probe microscopy.     

Understanding dissipative tip-molecule interactions with submolecular resolution on an organic adsorbate

Three-dimensional force spectroscopy measurements on 3,4,9,10-perylene-tetra-carboxylic dianhydride adsorbed on Ag(111) are combined with first-principles calculations to characterize the dissipative tip-molecule interactions with submolecular resolution. The experiments reveal systematic differences between the energy dissipation at the end groups and the center of the molecules that change with the tip-sample distance. Guided by the strength of the experimental conservative forces, an Ag-contaminated Si tip is identified as the likely tip termination in the experiments. Based on this tip configuration, the energy dissipation in the tip-sample contact is determined from the approach and retraction force curves calculated as a function of distance for different molecule sites. These calculations provide an explanation for the experimental trends in terms of the competition between localized dissipation mechanisms involving the quite mobile oxygen atoms on the sides of the molecule, and global molecular deformations involving the more rigid perylene core. The results confirm that the observed dissipation can be explained in terms of adhesion hysteresis and show the power of combined experimental-theoretical spectroscopy studies in the characterization of the underlying microscopic mechanisms.     

Wide-band measurements of dc voltages using two-parametric amplitude adaptation

A method of analyzing the accuracy and speed of adaptive measuring instruments based on two-parametric iteration algorithms of amplitude adaptation in precision high-speed dc voltage measurements is discussed. The method makes it possible to estimate the real and maximum attainable accuracy of adaptive dc voltage measurements over a wide dynamic range. Translated from Izmeritel'naya Tekhnika, No. 5, pp. 49–51, May, 1996.     

基于原子力显微镜的碳纳米管焊接

在利用碳纳米管（CNT）制作纳米电子器件时,碳纳米管与金属电极的接触特性将决定器件性能.为此本文提出了一种利用原子力显微镜（AFM）进行碳纳米管焊接的新方法.仿真研究了探针电场的强度与分布,解释了焊接中电场产生的机理,进一步分析了偏压、探针-样品距离与探针悬臂梁偏转位移之间的关系;并通过这些优选的相关实验参数进行了焊接实验验证.实验结果表明,碳纳米管与电极间的接触电阻由2.86×106Ω减小至7.14×105Ω,并可实现碳纳米管在电极上的良好固定.     

A method to quantitatively measure the elastic modulus of materials in nanometer scale using atomic force microscopy

A method is proposed for quantitatively measuring the elastic modulus of materials using atomic force microscopy (AFM) nanoindentation. In this method, the cantilever deformation and the tip-sample interaction during the early loading portion are treated as two springs in series, and based on Sneddon's elastic contact solution, a new cantilever-tip property α is proposed which, together with the cantilever sensitivity A, can be measured from AFM tests on two reference materials with known elastic moduli. The measured α and A values specific to the tip and machine used can then be employed to accurately measure the elastic modulus of a third sample, assuming that the tip does not get significantly plastically deformed during the calibration procedure. AFM nanoindentation tests were performed on polypropylene (PP), fused quartz and acrylic samples to verify the validity of the proposed method. The cantilever-tip property and the cantilever sensitivity measured on PP and fused quartz were 0.514?GPa and 51.99?nm?nA(-1), respectively. Using these measured quantities, the elastic modulus of acrylic was measured to be 3.24?GPa, which agrees well with the value measured using conventional depth-sensing indentation in a commercial nanoindenter.     

A resolution study for electrostatic force microscopy on bimetallic samples using the boundary element method

Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements. To study EFM measurements on bimetallic samples with surface potential inhomogeneities as a special case, we have simulated such measurements using the boundary element method and calculated the force component and force gradient component that would be measured by amplitude modulation (AM) EFM and frequency modulation (FM) EFM, respectively. Such analyses have been performed for inhomogeneities of various shapes and sizes, for different tip-sample separations and tip geometries, for different applied voltages, and for different media (e.g., vacuum or water) in which the experiment is performed. For a sample with a surface potential discontinuity, the FM-EFM resolution expression agrees with the literature; however, the simulation for AM-EFM suggests the existence of an optimal tip radius of curvature in terms of resolution. On the other hand, for samples with strip-?and disk-shaped surface potential inhomogeneities, we have obtained quantitative expressions for the detectability size requirements as a function of experimental conditions for both AM-?and FM-EFMs, which suggest that a larger tip radius of curvature is moderately favored for detecting the presence of such inhomogeneities.     

Force microscopy experiments with ultrasensitive cantilevers

Force microscopy experiments with the pendulum geometry are performed with attonewton sensitivity (Rugar et al 2004 Nature 43 329). Single-crystalline cantilevers with sub-millinewton spring constants were annealed under ultrahigh-vacuum conditions. It is found that annealing with temperatures below 500?°C can improve the quality factor by an order of magnitude. The high force sensitivity of these ultrasoft cantilevers is used to characterize small magnetic and superconductive particles, which are mounted on the end of the cantilever. Their magnetic properties are analysed in magnetic fields as a function of temperature. The transition of a superconducting sample mounted on a cantilever is measured by the detection of frequency shifts. An increase of dissipation is observed below the critical temperature. The magnetic moment of ferromagnetic particles is determined by real time frequency detection with a phase-locked loop (PLL) as a function of the magnetic field. The dissipation between the probing tip and the sample is another important ingredient for ultrasensitive force measurements. It is found that dissipation increases at separations of 30?nm. The origins of this type of dissipation are poorly understood. However, it is predicted theoretically that adsorbates can increase this dissipation channel (Volokitin and Persson 2005 Phys.?Rev.?Lett. 94 086104). First experiments are performed under ultrahigh vacuum to investigate this type of dissipation. Long-range dissipation is closely related to long-range forces. The distance dependence of the contact potential is found to be an important aspect.     

Effects of frequencies of AC modulation voltage on piezoelectric-induced images using atomic force microscopy

Lead zirconate titanate (PZT) thin film is prepared by sol-gel method on Pt/Ti electrode/SiO₂/Si wafer. Local poling is performed on the PZT film using an atomic force microscope (AFM). The topography and piezoelectric-induced (PEI) images on the polarized PZT film are recorded using AFM at piezo-responsive mode, operated with an AC voltage at varying frequencies. The best PEI image was obtained at the frequency around 300 kHz. It is explained that the change of piezoelectric vibrations and input noise signals with the frequency of AC modulation voltage affects the intensity of PEI images.