Optimizing phase imaging via dynamic force curves

Tapping mode (TM, also called intermittent contact mode) atomic force microscopy (AFM) has been routinely used in many laboratories. However, consistent or deliberate control of measuring conditions and interpretation of results are often difficult. In this article, we demonstrate how measurement parameters (drive frequency, cantilever stiffness and oscillation amplitude) affect the tapping tip's state. This has been done by systematic dynamic force measurements performed on mica and polystyrene surfaces together with computer simulations. Our study shows the following results. (1) Weaker cantilevers, smaller amplitude and higher drive frequency (around the resonance) lead to an extension of the attractive region (greater phase lag) in amplitude–phase–distance curves and thus can help to achieve stable high-setpoint TM imaging with minimal tip–sample pressure. (2) Bistability of tapping tips often exists and may cause height artefacts if the setpoint falls in the bistable region. (3) Tapping tips with high vibrating energy (stiff cantilevers and large amplitude) driven at resonance are only slightly perturbed by tip–sample interactions and usually remain monostable during the sweep of the scanner position. This can help to achieve good phase contrast without significant artefacts when the setpoint falls in a continuous negative–positive phase shift transition region. (4) Low energy cantilevers (compliant cantilevers and small amplitude) usually result in large phase shift and can be used to acquire large phase contrast images. However, height artefacts will occur when the setpoint falls in the bistable region usually existing for such cantilevers. (5) Computer simulations are useful in understanding the bistability in dynamic force curves and determining either material properties or the optimal imaging parameters.     

Imitation of non-contact mode while scanning in the presence of an electric double layer?

Non-contact atomic force microscopy (NCAFM) minimizes the physical interaction between the AFM tip and the surface of interest. Several recent studies have reported observation of single atom defects using this technique. The repulsive force is presumably the primary interatomic force (cf. our paper on pseudo-non-contact mode in this issue) responsible for the reported atomic resolution in these studies. The combination of these factors, minimal tip–sample deformation and repulsive force interaction, are responsible for the observation of the single atom defects. In the present study, we show that similar resolution can be achieved utilizing the same two factors but which employs scanning in a surfactant. The method decreases the tip–sample interaction by eliminating the attractive forces between the tip and sample. The surfactant solution induces an electrical double-layer (EDL) on the surface of the tip and sample. This EDL creates additional repulsion that is distributed over a large area, and hence does not contribute noticeably to the image contrast during scanning. However, it does compensate for the high pressures normally experienced by the tip in the absence of surfactant. In addition, the presence of the EDL enhances tip stability during the image scan. This method has been tested on surfaces of such minerals as mica, chlorite, and anhydrite.     

A simplified but intuitive analytical model for intermittent-contact-mode force microscopy based on Hertzian mechanics

The forces acting on the substrate in intermittent-contact-mode (IC mode, tapping mode) atomic force microscopy are not accessible to a direct measurement. For an estimation of these forces, a simple analytical model is developed by considering only the shift of the cantilever resonance frequency caused by Hertzian (contact) forces. Based on the relationship between frequency shift and tip–sample force for large-amplitude frequency-modulation atomic force microscopy, amplitude and phase versus distance curves are calculated for the intermittent contact mode, and the forces on the substrate are calculated. The results show a qualitative agreement with numerical calculations, yielding typical maximal forces of 50–150 nN. When working above the unperturbed resonance, forces are found to be significantly larger than below the resonance.     

Influence of the sample-probe coupling on the resolution of transmitted near-field optical image

Numerical simulation of photon scanning tunneling microscopy is presented to study the near-field distribution in the vicinity a dielectric surface with one-dimensional sub-wavelength structures. Multiple scattering between the probe tip and the sample has been taken into account implicitly by matching electromagnetic boundary conditions at interfaces. The near-field intensity in transmission mode through two ridges on surface has been modeled in order to analyze the resolution of the system. The effects on the signal by the sample-tip coupling, the polarization of the incident light, and the angle of incidence are investigated. We find that the capability to recognize the feature will be improved when the tip–object interaction is strong.     

Relationship between the non linear dynamic behaviour of an oscillating tip–microlever system and the contrast at the atomic scale

In this paper, the dynamic behaviour of an oscillating tip–microlever system at the proximity of a surface is discussed. The attractive tip–surface interaction is simply described with a Van der Waals dispersive term and a sphere–plane geometry. We show that the non linear behaviour of the oscillator is able to explain the observed shifts of the resonance frequency as a function of the tip–surface distance without the need of introducing a particular short range force.     

The influence of tip–sample interaction on step fluctuations on Ag(111)

The fluctuations of the position of monatomic steps on Ag(111) are investigated by scanning tunneling microscopy (STM). We analyze the influence of tip–sample interaction by varying the gap impedance over more than two orders of magnitude. For tunneling tips providing a weak tip–sample interaction, we show that the step position autocorrelation function remains essentially unaltered. In this unperturbed case, the kinetics of step fluctuations are found to be dominated by one-dimensional mass transport. For larger variations of the tip–sample distance or for less favorable tip configurations, we observe a tip-induced increase of the step fluctuations. Our measurements suggest that this effect is caused rather by short-range forces than by the electric field in the tunneling gap.     

Simultaneous imaging of the In and As sublattice on InAs(110)-(1×1) with dynamic scanning force microscopy

Distance-dependent dynamic scanning force microscopy (SFM) measurements of InAs(110)-(1×1) acquired in ultrahigh vacuum at low temperatures are presented. On this surface, the atoms of the As sublattice are lifted by 80 pm with respect to the In sublattice and terminate the surface. Thus, since in most dynamic SFM images only protrusions with the periodicity of one sublattice are observed, these protrusions are correlated with the positions of the As atoms. However, under certain conditions, an additional contrast is visible which can be attributed to an interaction between the foremost tip atoms and the In atoms. Possible contrast mechanisms are discussed in terms of tip–sample distance and tip structure.     

Determination of tip–sample interaction forces from measured dynamic force spectroscopy curves

The forces between a sharp tip and a sample are characteristic for different sample materials. A new method for quantifying the elastic tip–sample interaction forces from measured frequency vs. distance curves is presented. The dynamic force–spectroscopy curves investigated were obtained by dynamic force microscopy under ultrahigh vacuum (UHV) conditions for large vibration amplitudes with commercial levers/tips. The full non-linear force–distance relationship is deduced via a numerical algorithm, where the equation of motion describing the oscillation of the tip is solved explicitly. The elastic force distance dependence can be determined by fitting the results of a computer simulation to experimental frequency vs. distance data. The obtained force–distance curves can be compared quantitatively with theoretical models.     

Theory for the effect of the tip–surface interaction potential on atomic resolution in forced vibration system of noncontact AFM

We present a perturbation theory which enables us to understand the physics of the cantilever-forced vibration in noncontact atomic-force microscopy (nc-AFM). Analytical expressions of the resonance curve and frequency shift are given. This theory is applied to the model system with a van der Waals tip–surface interaction potential. Based on this case study, it is elucidated how the resonance frequency shift is analytically described by an integral of the tip–surface interaction force. Then nc-AFM image of Si(111) 7×7 surface is calculated by the present theory. It is examined that this theory works as an algorithm for nc-AFM image simulator.     

剪切力模式近场扫描光学显微镜的恒幅反馈控制方法研究

剪切力模式近场扫描光学显微镜(Near-field Scanning Optical Microscopy,NSOM) 的音叉探针间距控制系统中,用相位反馈控制和检测剪切力,同时采用比例＋积分（PI）技术实现对音叉探针振幅的反馈控制,使探针振幅在扫描过程中保持为恒定值.用相位信号作为探针与样品间距控制信号,分别在无振幅反馈和有振幅反馈两种情况下,以不同速率扫描得到标准CD_RW光盘光栅的两组图像,并进行了比较分析.实验表明,恒振幅反馈电路的引入有助于提高探针系统的响应速度和灵敏度,改善所得图像的质量及分辨率.     

Contrast mechanism in non-contact SFM imaging of ionic surfaces

We analyse the mechanisms of contrast formation in NC-SFM imaging of ionic surfaces and calculate constant frequency shift scanlines of the perfect surfaces of NaCl and MgO. Non-contact SFM operation is modelled in a perturbed oscillator model using an atomistic simulation technique for force–field calculations. We demonstrate that the contrast in NC-SFM imaging of ionic surfaces is based on the interplay between the van der Waals interaction and the electrostatic interaction of the tip with the surface potential and the local surface polarisation induced by the tip. The results emphasise the importance of the tip-induced relaxation of the surface ions in the tip–surface interaction and image contrast.     

Exact solution of the frequency shift in dynamic force microscopy

The exact frequency shift of an AFM non-uniform probe with an elastically restrained root, subjected to van der Waals force, is derived. The original distributed system is considered and then its exact fundamental solutions and the general frequency equation are derived. Results are compared with those by the force gradient method and the perturbation method. The effects of several parameters on the sensitivity of measurement are investigated. Results show that the interpretation of frequency shift by using the force gradient method is unsatisfactory. The smaller the amplitude of oscillation and the tip–surface distance are, the larger the frequency shift. The design of a taper beam is recommended for increasing the sensitivity of measurement.     

Calculation of the frequency shift in dynamic force microscopy

A theoretical study of the quality and the range of validity of different numerical and analytical methods to calculate the frequency shift in dynamic force microscopy is presented. By comparison with exact results obtained by the numerical solution of the equation of motion, it is demonstrated that the commonly used interpretation of the frequency shift as a measure for the force gradient of the tip–sample interaction force is only valid for very small oscillation amplitudes and leads to misinterpretations in most practical cases. Perturbation theory, however, allows the derivation of useful analytic approximations.     

High-sensitivity piezoelectric tube sensor for shear-force detection in scanning near-field optical microscopy

An easy-to-implement non-optical shear-force detection setup for tip–sample distance regulation in scanning near-field optical microscopy is demonstrated. The detection method is based on attaching the near-field probe to a piezoelectric tube resulting in excellent mechanical contact between tip and detector. The main advantages of the method are good signal-to-background contrast and thus potential for high sensitivity. The method is demonstrated by obtaining approach curves of silicon surfaces. The suitability for optical experiments is further shown by measuring the near-field intensity distribution of the emission of a semiconductor laser.     

Adhesion hysteresis in dynamic atomic force microscopy

The effects of adhesion hysteresis in the dynamic‐dissipation curves measured in amplitude‐modulation atomic force microscopy are discussed. Hysteresis in the interaction forces is shown to modify the dynamics of the cantilever leading to different power dissipation curves in the repulsive and attractive regimes. Experimental results together with numerical simulations show that power dissipation, as measured in force microscopy, is not always proportional to the energy dissipated in the tip–sample interaction process. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ultrasonic radiation in dynamic force microscopy

In dynamic force microscopy the cantilever of an atomic force microscope is vibrated at ultrasonic frequencies in the range of several 10 kHz up to several MHz while scanning a sample surface. The amplitude and phase of the cantilever vibration as well as the shift of the cantilever resonance frequencies provide information about local sample surface properties. In several operation modes of dynamic force microscopy, for example force modulation microscopy, tapping mode or atomic force acoustic microscopy, the sensor tip is in contact with the sample at least during a fraction of its vibration cycle. The periodic indentation of the tip with the sample surface generates ultrasonic waves. In this paper, the ultrasonic radiation of a vibrating cantilever into a sample and its contribution to the damping of the cantilever vibration are calculated. The theoretical results are compared to experiments.     

Calculation of the optimal imaging parameters for frequency modulation atomic force microscopy

True atomic resolution of conductors and insulators is now routinely obtained in vacuum by frequency modulation atomic force microscopy. So far, the imaging parameters (i.e., eigenfrequency, stiffness and oscillation amplitude of the cantilever, frequency shift) which result in optimal spatial resolution for a given cantilever and sample have been found empirically. Here, we calculate the optimal set of parameters from first principles as a function of the tip–sample system. The result shows that the either the acquisition rate or the signal-to-noise ratio could be increased by up to two orders of magnitude by using stiffer cantilevers and smaller amplitudes than are in use today.     

Using the dissipation mode in high resolution atomic force microscopy

The possibility of using the dissipation mode in high-resolution atomic force microscopy is demonstrated. By the dissipation mode we mean the dynamic mode in which the cantilever oscillates at a resonance frequency and the oscillation amplitude serves as a signal of the feedback tracing a distance to the surface. The possibility of obtaining molecular resolution when scanning in air is shown. The procedure of choosing the optimum scanning parameters is considered.     

Determination of thermal effusivity of solids by a photoacoustic scanning technique

A new method is proposed to determine the thermal effusivity of solid samples using a one dimensional photoacoustic scanning technique. The method employs a sample configuration in which the backing for a good light absorber layer is changed from a reference sample to the unknown sample by scanning the absorber surface with an incident modulated light beam. From the measured phase difference or amplitude ratio one can determine the thermal effusivity of the unknown sample, knowing the effusivity of the reference sample. The Rosencwaig-Gersho theory of photoacoustic effect has been extended to the present experimental situation and expressions have been derived for photoacousitc phase difference and amplitude ratio as the backing is changed. Values calculated using these expressions are found to agree well with measured values for different sample combinations except in amplitude ratio values when the thermal effusivities of the samples differ very widely. The reason for this disagreement is discussed.     

Dissipation Energy in Tapping-Mode Atomic Force Microscopes Caused by Liquid Bridge

The dissipation of energy during the process of contact and separation between a tip and a sample is very important for understanding the phase images in the tapping mode of atomic force microscopes(AFMs). In this study, a method is presented to measure the dissipated energy between a tip and a sample. The experimental results are found to be in good agreement with the theoretical model, which indicates that the method is reliable.Also, this study confirms that liquid bridges are mainly produced by extrusion modes in the tapping mode of AFMs.