Quantification of the lateral detachment force for bacterial cells using atomic force microscope and centrifugation

To determine the lateral detachment force for individual bacterial cells, a quantitative method using the contact mode of an atomic force microscope (AFM) was developed in this study. Three key factors for the proposed method, i.e. scan size, scan rate and cantilever choice, were evaluated and optimized. The scan size of 40×40 μm² was optimal for capturing sufficient number of adhered cells in a microscopic field and provide adequate information for cell identification and detachment force measurement. The scan rate affected the measurement results significantly, and was optimized at 40 μm/s considering both force measurement accuracy and experimental efficiency. The hardness of applied cantilevers also influenced force determination. The proposed protocol for cantilever selection is to use those with the lowest spring constant first and then step up to a harder cantilever until all cells are detached. The lateral detachment force of Escherichia coli cells on polished stainless steel and a glass-slide coated with poly-l-lysine were measured as 0.763±0.167 and 0.639±0.136 nN, respectively. The results showed that the established method had good repeatability and sensitivity to various bacteria/substrata combinations. The detachment force quantified by AFM (0.639±0.136 nN) was comparable to that measured by the centrifugation method (1.12 nN).     

Characterization of MEMS piezoresistive pressure sensors using AFM

Atomic force microscope (AFM) is adapted to characterize an ultrasensitive piezoresistive pressure sensor based on microelectromechanical system (MEMS) technology. AFM is utilized in contact mode to exert force on several different micromachined diaphragm structures using a modified silicon cantilever with a particle attached to its end. The applied force is adjusted by changing the trigger voltage during each engage step of the probe-tip on the diaphragm surface. The contact force is determined from the force plots obtained for each trigger voltage in advanced force mode. Low force values in the range of 0.3–5 μN have been obtained with this method. This force induces strain on the bridge-arm of the diaphragm where the polysilicon resistor is located. The resultant change in the resistance produced due to varying force/pressure is measured using a delta mode current–voltage (I–V) measurement set-up. The contact mode AFM in conjunction with a nanovoltmeter enables the calibration of very sensitive force sensors down to 0.3 μN.     

Piezoelectric based resonant mass sensor using phase measurement

The paper presents design, development and testing of a resonant sensor to measure mass in the range of 0-12 g. The sensor is built using cantilever structure with piezoelectric excitation, sensing and microcontroller based closed loop electronics. The sensor measures the unknown mass by measuring the shift in resonance frequency of the cantilever beam. The shift in resonance frequency for a change in mass is detected by measuring the phase difference between the piezoelectric sensor output and actuator input using microcontroller. The proposed measurement system is simple and accuracy is found to be ±1.2% of full scale deflection.     

Resonance based DC current sensor

The paper presents design, development and testing of a resonant proximity DC current sensor to measure current in the range of 0-20 mA. The sensor is built using cantilever structure with piezoelectric excitation, sensing and closed loop electronics. The sensor measures the DC current by measuring the shift in resonance frequency of the cantilever beam. The proposed measurement system is novel, simple and accuracy is found to be 1.1% of full scale deflection.     

Characteristics of a dynamic atomic force microscopy based on a higher-order resonant silicon cantilever and experiments

In order to improve the sensitivity and scanning speed of the dynamic AFM, a surface scanning method using higher-order resonant cantilever is adopted and investigated based on the higher-order resonance characteristics of the silicon cantilever, and the theoretical analysis and experimental verification on the higher-order resonance characteristics of the corresponding dynamic AFM cantilever are given. In this method, the cantilever is excited to oscillate near to its higher-order resonant frequency which is several times higher than that of the fundamental mode. Then the characteristic changes a lot compared with the first-order resonant cantilever. Because of the changes of the quality factor, amplitude and the mode shape of the cantilever, the higher-order resonant AFM gets higher sensitivity and scanning speed. Based on the home-built tapping-mode AFM experiment system, the resolution and the response time of the first and second order resonance measured by experiment are respectively: 0.83 nm, 0.42 nm; 1265 μs, 573 μs. The higher-order resonance cantilever has higher sensitivity and the dynamic measurement performance of the cantilever is significantly improved from the experimental results. This can be a useful method to develop AFM with high speed and high sensitivity. Besides above, the surface profile of a grating sample and its three-dimensional topography are obtained by the higher-order resonant mode AFM.     

Accurate determination of spring constant of atomic force microscope cantilevers and comparison with other methods

We present calibration results of commercial AFM cantilevers using the KRISS nanoforce calibrator (NFC) that can determine traceably spring constants with an uncertainty better than 1%, along with the results obtained from other four calibration methods: the dimensional method, the cantilever-on-cantilever method, the Sader method, and the thermal noise method. Two types (contact and tapping mode) of beam-shaped AFM cantilevers with nominal spring constants of 0.9 N m⁻¹ and 42 N m⁻¹, respectively, were investigated in this study. Because of its small uncertainty, the NFC method was used to assess the uncertainties of other four methods through comparisons between values obtained from other methods and those from the NFC method for the same cantilever. Results from other methods were generally in good agreement with those from the NFC method within the uncertainties of other methods claimed in other literatures, but values obtained from the Sader method were differed by up to 40% from the NFC values, which is 2 times worse than the known uncertainty.     

Dynamic analysis of tapping mode atomic force microscope (AFM) for critical dimension measurement

Transient dynamics of tapping mode atomic force microscope (AFM) for critical dimension measurement are analyzed. A simplified nonlinear model of AFM is presented to describe the forced vibration of the micro cantilever-tip system with consideration of both contact and non-contact transient behavior for critical dimension measurement. The governing motion equations of the AFM cantilever system are derived from the developed model. Based on the established dynamic model, motion state of the AFM cantilever system is calculated utilizing the method of averaging with the form of slow flow equations. Further analytical solutions are obtained to reveal the effects of critical parameters on the system dynamic performance. In addition, features of dynamic response of tapping mode AFM in critical dimension measurement are studied, where the effects of equivalent contact stiffness, quality factor and resonance frequency of cantilever on the system dynamic behavior are investigated. Contact behavior between the tip and sample is also analyzed and the frequency drift in contact phase is further explored. Influence of the interaction between the tip and sample on the subsequent non-contact phase is studied with regard to different parameters. The dependence of the minimum amplitude of tip displacement and maximum phase difference on the equivalent contact stiffness, quality factor and resonance frequency are investigated. This study brings further insights into the dynamic characteristics of tapping mode AFM for critical dimension measurement, and thus provides guidelines for the high fidelity tapping mode AFM scanning.     

Analysis of simulated scanning of atomic-scale silicon surface by atomic force microscopy

This study constructs a contact-mode atomic force microscopy (AFM) simulation measurement model with constant force mode to simulate and analyze the outline scanning measurement by AFM. The simulation method is that when the probe passes the surface of sample, the action force of the atom of sample received by the atom of the probe can be calculated by using Morse potential. Through calculation, the equivalent force on the cantilever of probe can be acquired. By using the deflection angle equation for the cantilever of probe developed and inferred by this study, the deflection angle of receiving action force can be calculated. On the measurement point, as the deflection angle reaches a fixed deflection angle, the scan height of this simulation model can be acquired. By scanning in the right order, the scan curve of the simulation model can be obtained. By using this simulation measurement model, this study simulates and analyzes the scanning of atomic-scale surface outline. Meanwhile, focusing on the tip radii of different probes, the concept of sensitivity analysis is employed to investigate the effects of the tip radius of probe on the atomic-scale surface outline. As a result, it is found from the simulation on the atomic-scale surface that within the simulation scope of this study, when the tip radius of probe is greater than 12 nm, the effects of single atom on the scan curve of AFM can be better decreased or eliminated.     

Fabrication of ionic liquid thin film by nano-inkjet printing method using atomic force microscope cantilever tip

We demonstrate the fabrication of thin films of ionic liquid (IL), 1-butyl-3-methyl-imidazolium tetrafluoborate, by nano-inkjet printing method using an atomic force microscope (AFM) cantilever. The IL filled in a pyramidal hollow of the AFM cantilever tip was extracted from an aperture at the bottom of the hollow and deposited onto a Pt substrate when the bias voltage was applied between the cantilever and the substrate. We succeeded in fabricating IL thin films with a thickness of 4 nm. The areas and thicknesses of IL thin films were controlled by the fabrication conditions in this method, which is also useful for the investigations of nanometer-scale properties of ionic liquid.     

A force-matching method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers

We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(1 0 0) and a 100-nm-thick film of gold deposited on Si(1 0 0). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.     

Investigating ultra-thin lubricant layers using resonant friction force microscopy

The ultrasonic friction mode of an atomic force microscope is a scanning probe technique allowing one to analyze the load and velocity dependence of friction. The technique is based on evaluation of the resonance behavior of an AFM cantilever when in contact with a vibrating sample surface. The effect of load and lateral displacement of the sample surface on the shape of the torsional resonance spectra of the AFM cantilever is evaluated under dry and lubricated sliding conditions. A characteristic flattening of the torsional resonance curve has been observed at large surface displacements, resulting from the onset of sliding friction in the AFM cantilever–sample surface contact. An analytical model describing torsional cantilever vibrations in Hertzian contact with a sample surface is presented, and numerical simulations have been carried out in order to confirm that the flattening of the resonance curve occurs with the onset of the sliding friction in the contact.     

A torsional resonance mode AFM for in-plane tip surface interactions

Changing the method of tip/sample interaction leads to contact, tapping and other dynamic imaging modes in atomic force microscopy (AFM) feedback controls. A common characteristic of these feedback controls is that the primary control signals are based on flexural deflection of the cantilever probes, statically or dynamically. We introduce a new AFM mode using the torsional resonance amplitude (or phase) to control the feedback loop and maintain the tip/surface relative position through lateral interaction. The torsional resonance mode (TRmode™) provides complementary information to tapping mode for surface imaging and studies. The nature of tip/surface interaction of the TRmode facilitates phase measurements to resolve the in-plane anisotropy of materials as well as measurements of dynamic friction at nanometer scale. TRmode can image surfaces interleaved with TappingMode™ with the same probe and in the same area. In this way we are able to probe samples dynamically in both vertical and lateral dimensions with high sensitivity to local mechanical and tribological properties. The benefit of TRmode has been proven in studies of water adsorption on HOPG surface steps. TR phase data yields approximately 20 times stronger contrast than tapping phase at step edges, revealing detailed structures that cannot be resolved in tapping mode imaging. The effect of sample rotation relative to the torsional oscillation axis of the cantilever on TR phase contrast has been observed. Tip wear studies of TRmode demonstrated that the interaction forces between tip and sample could be controlled for minimum tip damage by the feedback loop.     

Improving tapping mode atomic force microscopy with piezoelectric cantilevers

This article summarizes improvements to the speed, simplicity and versatility of tapping mode atomic force microscopy (AFM). Improvements are enabled by a piezoelectric microcantilever with a sharp silicon tip and a thin, low-stress zinc oxide (ZnO) film to both actuate and sense deflection. First, we demonstrate self-sensing tapping mode without laser detection. Similar previous work has been limited by unoptimized probe tips, cantilever thicknesses, and stress in the piezoelectric films. Tests indicate self-sensing amplitude resolution is as good or better than optical detection, with double the sensitivity, using the same type of cantilever. Second, we demonstrate self-oscillating tapping mode AFM. The cantilever's integrated piezoelectric film serves as the frequency-determining component of an oscillator circuit. The circuit oscillates the cantilever near its resonant frequency by applying positive feedback to the film. We present images and force-distance curves using both self-sensing and self-oscillating techniques. Finally, high-speed tapping mode imaging in liquid, where electric components of the cantilever require insulation, is demonstrated. Three cantilever coating schemes are tested. The insulated microactuator is used to simultaneously vibrate and actuate the cantilever over topographical features. Preliminary images in water and saline are presented, including one taken at 75.5 μm/s—a threefold improvement in bandwidth versus conventional piezotube actuators.     

多模态动态原子力显微镜系统

动态原子力显微镜(atomic force microscope,AFM)是通过检测悬臂谐振状态的变化来对物体表面形貌进行测量的。通过对谐振状态的三种因素即振幅、相位、频率的检测,动态AFM可以分为三种工作模式,即振幅反馈、相位反馈与频率反馈模式,这三种反馈模式有着不同的扫描特点。基于硅悬臂具有高阶谐振的特性,动态原子力显微镜可以在悬臂工作于高阶谐振状态时对物体进行扫描。综合上述工作模式研制了一套多模态动态AFM,可以在三种反馈模式、不同阶谐振状态下对物体进行扫描测量。利用该系统在不同反馈模式、不同阶谐振状态下进行了扫描测试,结果显示,系统在各模式下具有亚纳米分辨力,其中在相位反馈模式,悬臂二阶谐振时可达到最优灵敏度与分辨力,分别为17.5V/μm和0.29nm,在最优灵敏度与分辨力状态下对光栅试样进行了三维扫描,得到光栅的三维形貌图。     

High resolution surface morphology measurements using EBSD cross-correlation techniques and AFM

The surface morphology surrounding wedge indentations in (0 0 1) Si has been measured using electron backscattered diffraction (EBSD) and atomic force microscopy (AFM). EBSD measurement of the lattice displacement field relative to a strain-free reference location allowed the surface uplift to be measured by summation of lattice rotations about the indentation axis. AFM was used in intermittent contact mode to determine surface morphology. The height profiles across the indentations for the two techniques agreed within 1 nm. Elastic uplift theory is used to model the data.     

Direct measurement of tapping force with a cantilever deflection force sensor

An experimental set up dedicated to the measurement of atomic force microscope tapping force was developed. In the set-up, a standard TappingMode™ probe cantilever was used to tap another cantilever equipped with its own low noise and high sensitivity deflection detection system for force measurement. The amplitude and phase change of the tapping lever as well as the deflection of the sensing lever were simultaneously recorded as a function of tip/surface separation. Since the deflection of the sensing cantilever reflects the average force over one interaction cycle, we measured the total average force quantitatively after calibrating the spring constant and deflection sensitivity of the sensing lever. Considerable effort was made to achieve the same force curve in the tapping force measurement as occur during imaging of conventional samples such that the detected tapping force reflects the same interaction of the imaging process.     

Novel operation mode for eliminating influence of inclination angle and friction in atomic force microscopy

The accuracy of topography imaging in contact force mode of atomic force microscopy (AFM) depends on the one-to-one corresponding relationship between the cantilever deflection and the tip–sample distance, whereas such a relationship cannot be always achieved in the presence of friction and incline angle of sample surface. Recently, we have developed a novel operation mode in which we keep the van der Waals force as constant instead of the applied normal force, to eliminate the effect of inclination angle and friction on topography imaging in the contact force mode. We have improved our AFM to enable the new operation mode for validation. Comparative experiments have been performed and the results have shown that the effect of friction and inclination angle on topography imaging in contact mode of AFM can be eliminated or at least decreased effectively by working in the new operation mode we present.     

Uncertainty contribution of tip-sample angle to AFM lateral measurements

AFM measurements are very important for quality control in the photovoltaic, microfluidic, electronic or micro-optic industries. This work proposes an algorithm to complete the uncertainty evaluation of AFM systems along the XY-axis under conditions where tolerance of curved surfaces must be controlled. This algorithm is also tested for tilt angles between tip and sample from 0° to 9° using an experimental arrangement which consists of an AFM instrumented with an inclinometer and four step height standards.Results show good agreement between the theoretical model and experimental results for samples with larger steps TGZ03 (465 nm) and TGZ11 (1416 nm), but with poor results for the smaller samples TGZ01 (17.6 nm) and TGZ02 (73.1 nm). An angle of 9° shows an error of about 3% in the horizontal determination of the step dimension, but it could increase to 47% for a tilt angle of 30° according to the theoretical model.The angle error between tip and sample is included in the uncertainty budget using a uniform distribution. An evaluation is performed in a theoretical rolling machine for imprint lithography where a step must be measured with nominal dimensions of 3 μm—X-axis and 1 μm—Z-axis. An assumed tip-sample angle is assumed that changes from 0° to 22.5° (curved form) and produces an uncertainty contribution to the X measurement of 55.7 nm. This uncertainty is important and must be considered to guarantee tolerances in quality control of curved form products.     

Dual resonance excitation system for the contact mode of atomic force microscopy

We propose an improved system that enables simultaneous excitation and measurements of at least two resonance frequency spectra of a vibrating atomic force microscopy (AFM) cantilever. With the dual resonance excitation system it is not only possible to excite the cantilever vibrations in different frequency ranges but also to control the excitation amplitude for the individual modes. This system can be used to excite the resonance frequencies of a cantilever that is either free of the tip-sample interactions or engaged in contact with the sample surface. The atomic force acoustic microscopy and principally similar methods utilize resonance frequencies of the AFM cantilever vibrating while in contact with the sample surface to determine its local elastic modulus. As such calculation demands values of at least two resonance frequencies, two or three subsequent measurements of the contact resonance spectra are necessary. Our approach shortens the measurement time by a factor of two and limits the influence of the AFM tip wear on the values of the tip-sample contact stiffness. In addition, it allows for in situ observation of processes transpiring within the AFM tip or the sample during non-elastic interaction, such as tip fracture.     

Calibration of tapping AFM cantilevers and uncertainty estimation: Comparison between different methods

We present a comparative study between three different methods for the spring constant calibration of silicon beam-shaped Atomic Force Microscope (AFM) cantilevers, used in tapping AFM mode in air. The geometries of these levers can be quite different from the standard rectangular cross section. We examine a method that combines the knowledge of cantilever dimensions and eigenfrequencies (Cleveland formula), the Sader method and we build cantilever models based on Finite Element Analysis (FEA). We demonstrate that with accurate measurement of dimensions, resonance frequency and quality factor, the Cleveland formula yields a combined cantilever stiffness uncertainty of approximately ±7% and the Sader method an uncertainty of ±5%. We also use FEA to show that when trying to approximate a realistic trapezoidal 3D tipped geometry, there exists a systematic overestimation in cantilever stiffness of ±2%, compared to when considering a simple rectangular cross section. Our constructed FE models are able to account for inhomogeneities in material properties as well as the influence of the added reflective coating in the cantilever stiffness estimation.