Multi-modal analysis on the intermittent contact dynamics of atomic force microscope

A multi-modal analysis on the intermittent contact between an atomic force microscope (AFM) with a soft sample is presented. The intermittent contact induces the participation of the higher modes into the motion and various subharmonic motions are shown. The AFM tip mass enhances the coupling of different modes. The AFM tip mass is modeled by the Dirac delta function and the coupling effects are analyzed via the Galerkin method. The necessity of applying multi-modal analysis to the intermittent contact problem is demonstrated. Unlike the impact oscillator model which assumes the impact/contact time is infinitesimal, the contact time can be a significant fractional portion in each cycle, especially for the soft sample case and thus results in different dynamic behavior from that of an impact oscillator.     

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     

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.     

Contact dynamics of tapping mode atomic force microscopy

A comprehensive model on the dynamics of a tilted tapping mode atomic force microscopy (AFM) is presented, which includes the multimodal analysis, mode coupling mechanisms, adhesion, contact and friction forces induced by the tilting angle. A displacement criterion of contact/impact is proposed to eliminate the assumptions of the previous models such as infinite stiffness of sample or zero impact velocity, which makes the model presented here suitable for more general AFM application scenario, especially for the soft sample case. The AFM tip mass, tip–sample damping, contact forces and intermittent contact can all induce the higher modes participation into the system motion. One degree of freedom or one mode study on the AFM contact dynamics of tapping mode is shown to be inaccurate. The Hertz and Derjaguin–Muller–Toporov models are used for the comparison study of the non-adhesive and adhesive contacts. The intermittent contact and the contact forces are the two major sources of the system nonlinearity. The rich dynamic responses of the system and its sensitivity to the initial conditions are demonstrated by presenting various subharmonic and nonperiodic motions.     

Local surface cleaning and cluster assembly using contact mode atomic force microscopy

Conventional contact mode atomic force microscopy (AFM) has been used for local surface cleaning and cluster alignment. By using the AFM tip to sweep and push in contact mode, we have demonstrated that Cu clusters, prepared by vacuum evaporation onto Dow Cyclotene 3022 polymer and subsequent exposure to atmosphere, can easily be moved by the AFM tip, and assembled at the outer edge of the scanned region to form a line of clusters. We have found that the force applied by the tip plays an important role in the ease of cluster motion. Cyclotene surface treatment that enhances cluster adhesion hinders this ability, and may be used as a method of nanofabrication.     

Fabrication of nanostructures on Si(1 0 0) and GaAs(1 0 0) by local anodic oxidation

Atomic force microscopes have become useful tools not only for observing surface morphology and nanostructure topography but also for fabrication of various nanostructures itself. In this paper, the application of AFM for fabrication of nanostructures by local anodic oxidation (LAO) of Si(1 0 0) and GaAs(1 0 0) surfaces is presented. A special attention is paid to finding relations between the size of oxide nanolines (height and half-width) and operational parameters as tip-sample voltage and tip writing speed. It was demonstrated that the formation of silicon oxide lines obeys the Cabrera-Mott theory, i.e. the height of the lines grow, linearly with tip-sample voltage and is inversely proportional to logarithm of tip writing speed. As for GaAs substrates, the oxide line height grows linearly with tip-sample voltage as well but LAO exhibits a certain deviation from this theory. It is shown that the selective chemical etching of Si or GaAs ultrathin films processed by LAO makes it possible to use these films as nanolithographic masks for further nanotechnologies, e.g. fabrication of metallic nanostructures by ion-beam bombardment. The ability to control LAO and tip motion can be utilized in fabrication of complex nanostructures finding their applications in nanoelectronic devices, nanophotonics and other high-tech areas.     

隧道声显微镜的几种模式及理论研究

讨论了隧道声显微镜(TAM)的三种工作模式,即相互作用力-隧道间距模式、改进的STM测量模式和AFM测量模式,研究了它们的工作机理。建立了一个探针-样品相互作用的模型,理论分析了相互作用力与隧道间距的关系,计算结果与实验结果一致,该结果对于研制TAM实验系统和探针制备等具有指导意义.     

Linear and nonlinear approaches towards amplitude modulation atomic force microscopy

Frequency response behavior of microcantilever is analytically and experimentally investigated in amplitude modulation Atomic Force Microscopy (AFM). AFM microcantilever probe is modeled as a continuous beam, and tip-sample interaction force is considered to include both attractive and repulsive force regimes. The developed model is compared with the linear lumped-parameters model that has been extensively used in the literature so far. Experimental measurements are also provided for the frequency response of a typical microcantilever-sample system to demonstrate the advantages of the developed model over the linear formulation. The results indicate that the nonlinear continuous model is more accurate, particularly in the estimation of the saturated amplitude value and frequency zone in which the tip-sample contact happens.     

Study on topographic images of Sn/Si(1 1 1)-(√3 × √3)R30° surface by non-contact AFM

Various contrast of topographic images depending on a state of a tip apex on Sn/Si(1 1 1)-(√3 × √3)R30° surface was investigated using a low temperature non-contact AFM. With the type A tip, the image of the ring-type Sn, composed of six Sn atoms surrounding substitutional Si defect, was observed when the frequency shift (∣Δf∣) was small (the tip-sample distance, Z_tip-sample, was long), while the ring-type Sn was not observed and all the Sn atoms have the same contrast when ∣Δf∣ was large (Z_tip-sample was short). On the other hand, with the type B tip, modified from the type A tip by the tip-sample contact, the image of the ring-type Sn atoms was not observed regardless of variation of Δf. It is the first experimental result on the low temperature NC-AFM observation in the Sn/Si(1 1 1) system, which depends on short-range chemical bonding force or electrostatic force acting between the tip and the sample surface. In addition, the substitutional Si defects on the surface were seen as a dim spot or were not seen, also depending on the tip state.     

Theoretical Study on the Capillary Force between an Atomic Force Microscope Tip and a Nanoparticle

Considering that capillary force is one of the most important forces between nanoparticles and atomic force microscope （AFM） tips in ambient atmosphere, we develop an analytic approach on the capillary force between an AFM tip and a nanoparticle. The results show that the capillary forces are considerably affected by the geometry of the AFM tip, the humidity of the environment, the vertical distance between the AFM tip and the nanoparticle, as well as the contact angles of the meniscus with an AFM tip and a nanoparticle. It is found that the sharper the AFM tip, the smaller the capillary force. The analyses and results are expected to be helpful for the quantitative imaging and manipulating of nanoparticles by AFMs.     

原子力显微镜在轻敲模式下的动力学模型

基于Hamaker假设、Lennard-Jones势能定律及经典弹性理论建立了一种新型的球体与平面黏着接触的弹性模型，该模型显示黏着力在原子力显微镜(AFM)针尖趋近和撤离样品表面，即加载和卸载的两个过程中存在黏着滞后现象，表明了AFM在轻敲工作模式中存在能量耗散.同时，根据所建的黏着接触弹性模型，建立了AFM在轻敲工作模式下的动力学模型，研究了AFM在轻敲工作模式下的振动幅度、相位差及耗散功率随针尖与样品表面间距的变化规律，仿真结果与现有的实验结果相一致.     

Force dependence of transition rates in atomic friction

The lateral forces during stick-slip motion of an atomic force microscope cantilever on highly oriented pyrolytic graphite are measured and analyzed. We identify the regimes where thermally activated interstitial hopping of the cantilever tip proceeds according to a single-step reaction scheme and extract the corresponding force-dependent transition rates directly from the experimental data. We find that such a single-step reaction scenario is valid only at relatively high velocities, while at slower pulling speeds, a more complicated hopping mechanism must be at work. We suggest formation of multiple bonds of the tip-sample contact as a possible candidate for this mechanism.     

Effect of tip mass on frequency response and sensitivity of AFM cantilever in liquid

The effect of tip mass on the frequency response and sensitivity of atomic force microscope (AFM) cantilever in the liquid environment is investigated. For this purpose, using Euler–Bernoulli beam theory and considering tip mass and hydrodynamic functions in a liquid environment, an expression for the resonance frequencies of AFM cantilever in liquid is derived. Then, based on this expression, the effect of the surface contact stiffness on the flexural mode of a rectangular AFM cantilever in fluid is investigated and compared with the case where the AFM cantilever operates in the air. The results show that in contrast with an air environment, the tip mass has no significant impact on the resonance frequency and sensitivity of the AFM cantilever in the liquid. Hence, analysis of AFM behaviour in liquid environment by neglecting the tip mass is logical.     

Study on the nano machining process with a vibrating AFM tip on the polymer surface

The polymer has been proved to be nano machined by a vibrating tip in tapping mode of Atomic Force Microscope (AFM). The force between the tip and the surface is an important factor which determines success of the machining process. Controlling this force with high accuracy is the foundation of nanomachining in AFM tapping mode. To achieve a deeper understanding on this process, the tip is modeled as a driving oscillator with damping. Factors affecting the nano machining process are studied. The Hertz elastic contact theory is used to calculate the maximum contact pressure applied by the tip which is employed as a criterion to judge the deformation state of the sample. The simulation results show that: The driven amplitude can be used as a main parameter of controlling the machined depth. Sharper tips and harder cantilevers should be used for successful nanomachining with the vibrating tip. Under the same conditions, a larger tip radius will not only result in the machining error, but also lead to failure of the nanomachining process. The higher driving frequency will lead to a larger tapping force. However it cannot be used as a parameter to control the machined depth because of its narrow variation range. But it is a main error source for the nanomachining process in AFM tapping mode. Moreover, a larger Young's modulus polymer sample will induce a smaller machined depth, a larger maximum contact pressure and a bigger tapping force.     

Nanotack test: adhesive behavior of single latex particles

We present an investigation of the adhesive properties of latex films with nanometric thickness through force spectroscopy using an atomic force microscope (AFM). The AFM tip can be used to indent and excite mechanically one single latex particle, and provides an adhesion test which resembles macroscopic probe tack test, but at nanometric scales. We show that this AFM nanotack test can be analyzed quantitatively, normalizing the total rupture energy by the contact area formed during the indentation step. This contact area depends upon the mechanical properties and environment of the latex particle.     

Electrical performance of gallium nitride nanocolumns

The electrical characterization of gallium nitride (GaN) nanocolumns with a length up to 1 μm and a diameter of about 30–80 nm grown on doped silicon is a challenge for nano analytics. To determine the conductivity of these nanocolumns, I–V characteristics were recorded by atomic force microscopy (AFM). To measure the conductivity of a single nanocolumn, a conductive AFM tip was placed at the top of the nanocolumn. The measured current/voltage characteristic of a single nanocolumn shows the typical performance of a Schottky contact, which is caused by the contact between the metallic AFM tip and the semiconductor material of the nanocolumn. The height of the Schottky barrier is dependent on the work function of the AFM tip metal used. The linear part of the curve was used to calculate the differential resistance, which was found to be about 13 Ω cm and slightly dependent on the diameter.     

Dynamics of high quality factor force microscope microcantilevers operated in contact mode

In AFM system with contact mode operation, the surface structure is determined by measuring the variation of the microcantilever tip deflection as the tip scans across the sample. Therefore, the dynamic characteristics of the microcantilever, including the stability, rapidity and accuracy performances, are extremely important parameters in determining the performance of AFM. In this paper, we obtain the analytical expressions of the deflection, overshoot, and adjustment time of the cantilever by using the Laplace transform theorem. The influence of the intrinsic parameters on the system dynamics is discussed in detail, which provides theoretical guidance for selecting samples in the experiments. Moreover, we propose a new control method based on the velocity feedback control in order to enhance the dynamic features of the system. The results indicate that the new control method can effectively improve the dynamic characteristics of the microcantilever.     

Ultrasonic resonance regulated near-field scanning optical microscope and laser induced near-field optical-force interaction

We have developed a novel sample-tip regulation for a near-field optical microscope: an ultrasonic resonance regulation method. The regulation range is from 0 to 50 nm. It shows not only stability, simplicity in construction, but also versatility in vacuum, magnetic field, and low temperature environments. The main advantage of this technique is that it is a non-optical detecting scheme, which is very important for near-field spectroscopy. Such construction can also be used as a force microscope to study the topography of insulating samples. The laser light induced force interaction in the near-field range has been observed for the first time, showing that aided by laser radiation, the shear force between sample and tip can be changed depending on the type of sample. This can be interpreted as the light induced optical tip-sample interaction of light pressure effect. The van der Waals dispersion energy and the optical binding energy induced by laser beam between dielectric tip and samples play important role. The effect confirms a theoretical prediction. This new technique and phenomenon will add new aspects to near-field optics.     

Noncontact friction and force fluctuations between closely spaced bodies

Noncontact friction between a Au(111) surface and an ultrasensitive gold-coated cantilever was measured as a function of tip-sample spacing, temperature, and bias voltage using observations of cantilever damping and Brownian motion. The importance of the inhomogeneous contact potential is discussed and comparison is made to measurements over dielectric surfaces. Using the fluctuation-dissipation theorem, the force fluctuations are interpreted in terms of near-surface fluctuating electric fields interacting with static surface charge.     

Towards the fluorescence resonance energy transfer (FRET) scanning near-field optical microscopy: Investigation of nanolocal FRET processes and FRET probe microscope

The fluorescence resonance energy-transfer (FRET) process is investigated between donor dye molecules deposited on the sample surface and acceptor dye molecules deposited on the tips of scanning near-field and atomic force microscopes. The FRET process was observed only when the tip acquired contact with the sample and took place in regions of sizes of only a few tens of nanometers with only a few thousands (or even hundreds) of molecules involved. The dependence of the FRET intensity on the tip-sample acting force is recorded and interpreted. In relation to the obtained results, the construction of a previously proposed one-atom FRET SNOM is described.