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.     

Prototype cantilevers for quantitative lateral force microscopy

Prototype cantilevers are presented that enable quantitative surface force measurements using contact-mode atomic force microscopy (AFM). The "hammerhead" cantilevers facilitate precise optical lever system calibrations for cantilever flexure and torsion, enabling quantifiable adhesion measurements and friction measurements by lateral force microscopy (LFM). Critically, a single hammerhead cantilever of known flexural stiffness and probe length dimension can be used to perform both a system calibration as well as surface force measurements in situ, which greatly increases force measurement precision and accuracy. During LFM calibration mode, a hammerhead cantilever allows an optical lever "torque sensitivity" to be generated for the quantification of LFM friction forces. Precise calibrations were performed on two different AFM instruments, in which torque sensitivity values were specified with sub-percent relative uncertainty. To examine the potential for accurate lateral force measurements using the prototype cantilevers, finite element analysis predicted measurement errors of a few percent or less, which could be reduced via refinement of calibration methodology or cantilever design. The cantilevers are compatible with commercial AFM instrumentation and can be used for other AFM techniques such as contact imaging and dynamic mode measurements.     

Harnessing bifurcations in tapping-mode atomic force microscopy to calibrate time-varying tip-sample force measurements

Torsional harmonic cantilevers allow measurement of time-varying tip-sample forces in tapping-mode atomic force microscopy. Accuracy of these force measurements is important for quantitative nanomechanical measurements. Here we demonstrate a method to convert the torsional deflection signals into a calibrated force wave form with the use of nonlinear dynamical response of the tapping cantilever. Specifically the transitions between steady oscillation regimes are used to calibrate the torsional deflection signals.     

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.     

Topography imaging with a heated atomic force microscope cantilever in tapping mode

This article describes tapping mode atomic force microscopy (AFM) using a heated AFM cantilever. The electrical and thermal responses of the cantilever were investigated while the cantilever oscillated in free space or was in intermittent contact with a surface. The cantilever oscillates at its mechanical resonant frequency, 70.36 kHz, which is much faster than its thermal time constant of 300 micros, and so the cantilever operates in thermal steady state. The thermal impedance between the cantilever heater and the sample was measured through the cantilever temperature signal. Topographical imaging was performed on silicon calibration gratings of height 20 and 100 nm. The obtained topography sensitivity is as high as 200 microVnm and the resolution is as good as 0.5 nmHz(1/2), depending on the cantilever power. The cantilever heating power ranges 0-7 mW, which corresponds to a temperature range of 25-700 degrees C. The imaging was performed entirely using the cantilever thermal signal and no laser or other optics was required. As in conventional AFM, the tapping mode operation demonstrated here can suppress imaging artifacts and enable imaging of soft samples.     

Exploiting cantilever curvature for noise reduction in atomic force microscopy

Optical beam deflection is a widely used method for detecting the deflection of atomic force microscope (AFM) cantilevers. This paper presents a first order derivation for the angular detection noise density which determines the lower limit for deflection sensing. Surprisingly, the cantilever radius of curvature, commonly not considered, plays a crucial role and can be exploited to decrease angular detection noise. We demonstrate a reduction in angular detection shot noise of more than an order of magnitude on a home-built AFM with a commercial 450 μm long cantilever by exploiting the optical properties of the cantilever curvature caused by the reflective gold coating. Lastly, we demonstrate how cantilever curvature can be responsible for up to 45% of the variability in the measured sensitivity of cantilevers on commercially available AFMs.     

Development of dual-probe atomic force microscopy system using optical beam deflection sensors with obliquely incident laser beams

We developed a dual-probe (DP) atomic force microscopy (AFM) system that has two independently controlled probes. The deflection of each cantilever is measured by the optical beam deflection (OBD) method. In order to keep a large space over the two probes for an objective lens with a large numerical aperture, we employed the OBD sensors with obliquely incident laser beams. In this paper, we describe the details of our developed DP-AFM system, including analysis of the sensitivity of the OBD sensor for detection of the cantilever deflection. We also describe a method to eliminate the crosstalk caused by the vertical translation of the cantilever. In addition, we demonstrate simultaneous topographic imaging of a test sample by the two probes and surface potential measurement on an α-sexithiophene (α-6T) thin film by one probe while electrical charges were injected by the other probe.     

Dual frequency atomic force microscopy on charged surfaces

The cantilever is mechanically driven at two resonant frequencies in a bimodal atomic force microscope (AFM). To generate the feedback signal for topography measurement the deflection signal is demodulated at one frequency and for compositional surface mapping at the other. In particular, the second mode amplitude and phase signals are used to map surface forces such as the van der Waals interaction. On electrically charged surfaces both, van der Waals forces and electrostatic forces contribute to the second eigenmode signal. The higher eigenmode signal in bimodal AFM reflects the local distribution of electrical charges. Mechanically driven bimodal AFM thus also provides a valuable tool for compositional mapping based on surface charges.     

Lateral force microscope calibration using a modified atomic force microscope cantilever

A proof-of-concept study is presented for a prototype atomic force microscope (AFM) cantilever and associated calibration procedure that provide a path for quantitative friction measurement using a lateral force microscope (LFM). The calibration procedure is based on the method proposed by Feiler et al. [Rev. Sci. Instrum. 71, 2746 (2000)] but allows for calibration and friction measurements to be carried out in situ and with greater precision. The modified AFM cantilever is equipped with lateral lever arms that facilitate the application of normal and lateral forces, comparable to those acting in a typical LFM friction experiment. The technique allows the user to select acceptable precision via a potentially unlimited number of calibration measurements across the full working range of the LFM photodetector. A microfabricated version of the cantilever would be compatible with typical commercial AFM instrumentation and allow for common AFM techniques such as topography imaging and other surface force measurements to be performed.     

Quantitative measurement of in-plane cantilever torsion for calibrating lateral piezoresponse force microscopy

A simple quantitative measurement procedure of in-plane cantilever torsion for calibrating lateral piezoresponse force microscopy is presented. This technique enables one to determine the corresponding lateral inverse optical lever sensitivity (LIOLS) of the cantilever on the given sample. Piezoelectric coefficient, d(31) of BaTiO(3) single crystal (-81.62 ± 40.22 pm/V) which was calculated using the estimated LIOLS was in good agreement with the reported value in literature.     

Expanded beam deflection method for simultaneous measurement of displacement and vibrations of multiple microcantilevers

Here we present an extension of optical beam deflection (OBD) method for measuring displacement and vibrations of an array of microcantilevers. Instead of focusing on the cantilever, the optical beam is either focused above or below the cantilever array, or focused only in the axis parallel to the cantilevers length, allowing a wide optical line to span multiple cantilevers in the array. Each cantilever reflects a part of the incident beam, which is then directed onto a photodiode array detector in a manner allowing distinguishing between individual beams. Each part of reflected beam behaves like a single beam of roughly the same divergence angle in the bending sensing axis as the incident beam. Since sensitivity of the OBD method depends on the divergence angle of deflected beam, high sensitivity is preserved in proposed expanded beam deflection (EBD) method. At the detector, each spot's position is measured at the same time, without time multiplexing of light sources. This provides real simultaneous readout of entire array, unavailable in most of competitive methods, and thus increases time resolution of the measurement. Expanded beam can also span another line of cantilevers allowing monitoring of specially designed two-dimensional arrays. In this paper, we present first results of application of EBD method to cantilever sensors. We show how thermal noise resolution can be easily achieved and combined with thermal noise based resonance frequency measurement.     

Non-optical bimorph-based tapping-mode force sensing method for scanning near-field optical microscopy

A non‐optical bimorph‐based tapping‐mode force sensing method for tip–sample distance control in scanning near‐field optical microscopy is developed. Tapping‐mode force sensing is accomplished by use of a suitable piezoelectric bimorph cantilever, attaching an optical fibre tip to the extremity of the cantilever free end and fixing the guiding portion of the fibre to a stationary part near the tip to decouple it from the cantilever. This method is mainly characterized by the use of a bimorph, which carries out simultaneous excitation and detection of mechanical vibration at its resonance frequency owing to piezoelectric and anti‐piezoelectric effects, resulting in simplicity, compactness, ease of implementation and lack of parasitic optical background. In conjugation with a commercially available SPM controller, tapping‐mode images of various samples, such as gratings, human breast adenocarcinoma cells, red blood cells and a close‐packed layer of 220‐nm polystyrene spheres, have been obtained. Furthermore, topographic and near‐field optical images of a layer of polystyrene spheres have also been taken simultaneously. The results suggest that the tapping‐mode set‐up described here is reliable and sensitive, and shows promise for biological applications.     

Feedback based simultaneous correction of imaging artifacts due to geometrical and mechanical cross-talk and tip-sample stick in atomic force microscopy

This paper presents a feedback scheme that simultaneously corrects, in real time, for the imaging artifacts caused by cantilever and photosensor misalignments as well as misinterpretations in relative lateral position of the tip with respect to the sample due to the tip-sample stick in atomic force microscopy (AFM). The optical beam bounce method, typically used in AFM for imaging, is sensitive to inaccuracies of cantilever geometry and the relative misalignment of the laser source, cantilever, and the laser sensitive diode from the intended design. These inaccuracies, which contribute to the geometrical cross-talk between the normal and the lateral signals, become prominent at the atomic and subnanometer scales, and thereby impede high resolution imaging studies. The feedback scheme accounts for these artifacts and makes imaging insensitive to, in fact, practically independent of these inaccuracies. This scheme counteracts the lateral twisting dynamics of the cantilever, and as a result, it avoids the misinterpretation problem of the relative lateral position of the cantilever tip from the sample and thereby avoids the corresponding imaging artifacts that are typically prominent in contact mode friction force microscopy (FFM). The feedback scheme consists of simultaneously regulating the normal as well as the lateral cantilever deflection signal at their respective set points. This not only removes the imaging artifacts due to geometrical misalignments, mechanical cross-talk, and irregular sliding but also the corresponding compensatory control signal gives a more accurate real time measure of the lateral interaction force between the sample and the cantilever as compared to the lateral deflection signal used in FFM. Experimental results show significant improvement, and in some cases, practical elimination of the artifacts. The design and implementation of a split piezoassembly needed for the lateral actuation for the feedback scheme are also presented.     

Optimization of adhesion mode atomic force microscopy resolves individual molecules in topography and adhesion.

The force sensor of an atomic force microscope (AFM) is sensitive enough to measure single molecular binding strengths by means of a force-distance curve. In order to combine high-force sensitivity with the spatial resolution of an AFM in topography mode, adhesion mode has been developed. Since this mode generates a force-distance curve for every pixel of an image, the measurement speed in liquid is limited by the viscous drag of the cantilever. We have equipped our adhesion mode AFM with a cantilever that has a low viscous drag in order to reach pixel frequencies of 65 Hz. Optimized filtering techniques combined with an auto-zero circuitry that reduces the drift in the deflection signal, limited high- and low-frequency fluctuations in the height signal to 0.3 nm. This reduction of the height noise, in combination with a thermally stabilized AFM, allowed the visualization of individual molecules on mica with an image quality comparable to tapping mode. The lateral resolution in both the topography and the simultaneously recorded adhesion image are only limited by the size of the tip. Hardware and software position feedback systems allows individual molecules to be followed in time during more than 30 min with scan sizes down to 60 x 60 nm2.     

Implementation of a piezoresistive MEMS cantilever for nanoscale force measurement in micro/nano robotic applications

The nanoscale sensing and manipulation have become a challenging issue in micro/nanorobotic applications. In particular, a feedback sensor-based manipulation is necessary for realizing an efficient and reliable handling of particles under uncertain environment in a micro/ nano scale. This paper presents a piezoresistive MEMS cantilever for nanoscale force measurement in microrobotics. A piezoresistive MEMS cantilever enables sensing of gripping and contact forces in nanonewton resolution by measuring changes in the stress-induced electrical resistances. The calibration of a piezoresistive MEMS cantilever is experimentally carried out. In addition, as part of the work on nanomanipulation with a piezoresistive MEMS cantilever, the analysis on the interaction forces between a tip and a material, and the associated manipulation strategies are investigated. Experiments and simulations show that a piezoresistive MEMS cantilever integrated into a microrobotic system can be effectively used in nanoscale force measurements and a sensor-based manipulation.     

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.     

Oscillation-induced static deflection in scanning force microscopy

Employing an atomic force microscope (AFM) in conjunction with a quartz crystal microbalance, we have investigated how a high-frequency lateral oscillation of the substrate influences the imaging process of the AFM. It was found that the time-averaged deflection of the cantilever (both vertical and lateral) changed when the oscillation of the quartz resonator was turned on. The vertical-tip-substrate distance increased, while the lateral force of sliding decreased at the same time. A mode of imaging based on this effect was demonstrated. The oscillation was periodically interrupted at a rate of 73 Hz and the corresponding periodic modulation of the deflection was filtered and amplified using lock-in amplifiers. Slowly scanning the sample and displaying the outputs of the lock-in amplifiers versus x and y produced an image of the oscillation-induced static (OIS) deflection. Various mechanisms by which a lateral oscillation can generate a time-averaged vertical force are discussed. The fact that the vertical OIS deflection scaled linearly with amplitude and, also, that the OIS deflection was stronger on the sloped portions of the sample than on the flat regions, suggests a geometric interpretation. We term the phenomenon "cobble stone effect." Experiments in liquids showed that the generation of an OIS deflection required immediate contact between the sample and the tip: a search for an OIS deflection in the presence of a liquid-filled gap between the sample and the tip yielded a negative result. Hydrodynamic forces are thereby ruled out as dominating factors.     

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.     

High-sensitivity detection of proteins using gel electrophoresis and atomic force microscopy

We have developed a method to detect specific proteins with a high sensitivity using a gel electrophoresis method and force measurement of atomic force microscopy (AFM). Biotinylated proteins were separated by electrophoresis and fixed with cross-linking chemicals on the gel, followed by direct force measurement between the biotinylated proteins on the gel and a streptavidin-modified tip of an AFM cantilever. We were able to achieve a high enough sensitivity to detect the picogram order of the biotinylated proteins by evaluating the frequency of the interaction force larger than 100 pN in the force profile, which corresponds to the rupture force of interaction between streptavidin and biotin.     

Development of a microlateral force sensor and its evaluation using lateral force microscopy

A microlateral force sensor (MLFS) was developed and evaluated using atomic force microscopy (AFM). The sensor was attached to a sensing table supported by a suspension system. The lateral motion of the sensing table was activated by a comb actuator. The driving voltage to the comb actuator was controlled to maintain a constant position of the sensing table by detecting the tunneling current at a detector, which consisted of two electrodes where the bias voltage was applied. An AFM was used to apply a lateral force to the sensing table of the sensor. When the probe of a cantilever was pressed against the sensing table and a raster scanning was conducted, the driving voltage of the comb actuator changed to compensate the friction force between the probe and sensing table. AFM measurements of an asperity array on the sensing table were conducted, and a lateral force microscopy image (LFM) was obtained from the change in driving voltage. The image by MLFS was very similar to the LFM image that was conventionally obtained from torsion of the cantilever. The LFM image strongly correlated with the gradient image calculated from the AFM topographic image. The force sensitivity of the MLFS was determined by comparing the LFM image obtained by using the MLFS with the tangential force derived from the gradient of the AFM image.