Experimental observation of contact mode cantilever dynamics with nanosecond resolution

Euler-Bernoulli theory accurately predicts atomic force microscope cantilever shape during non-equilibrium snap-to-contact motion

We prove that the Euler-Bernoulli elastic beam theory can be reliably used to describe the dynamics of an atomic force microscope cantilever during the far from equilibrium snap-to-contact event. In conventional atomic force microscope operation, force-separation curves are obtained by post-processing voltage versus time traces produced by measuring one point on the cantilever close to the hanging end. In this article, we assess the validity of the Euler-Bernoulli equation during the snap-to-contact event. The assessment is based on a direct comparison between experiment and theory. The experiment uses Doppler vibrometry to measure displacement versus time for many points along the long axis of the cantilever. The theoretical algorithm is based on a solution of the Euler-Bernoulli equation to obtain the full shape of the cantilever as a function of time. The algorithm uses as boundary conditions, experimentally obtained information only near the hanging end of the cantilever. The solution is obtained in a manner that takes into account non-equilibrium motion. Within experimental error, the theory agrees with experiment indicating that the Euler-Bernoulli theory is appropriate to predict the cantilever kinematics during snap-to-contact. Since forces on the tip can be obtained from the instantaneous shape of the cantilever, this work should allow for computation of tip-sample forces during the snap-to-contact event from a conventional force-distance measured input.

Development of a 3-PRR Precision Tracking System with Full Closed-Loop Measurement and Control

A 3-PRR (three links with each link consisting of a prismatic pair and two rotating pairs) parallel platform was designed for application in a vacuum environment. To meet the requirement of high tracking accuracy of the 3-PRR parallel platform, a full closed-loop control precision tracking system with laser displacement sensors and linear grating encoders was analysed and implemented. Equally-spaced laser displacement sensors and linear grating encoders were adopted not only for measurement but also for feedback control. A feed-forward control method was applied for comparison before conducting the closed-loop feedback control experiments. The closed-loop control experiments were conducted by adopting the PI (proportion and integration) feedback control and RBF (radial basis function) neural network control algorithms. The experimental results demonstrate that the feed-forward control, PI feedback control, and RBF neural-network control algorithms all have a better control effect than that of semi-closed-loop control, which proves the validity of the designed full closed-loop control system based on the combination of laser displacement sensors and linear grating encoders.

Large area high-speed metrology SPM system

We present a large area high-speed measuring system capable of rapidly generating nanometre resolution scanning probe microscopy data over mm(2) regions. The system combines a slow moving but accurate large area XYZ scanner with a very fast but less accurate small area XY scanner. This arrangement enables very large areas to be scanned by stitching together the small, rapidly acquired, images from the fast XY scanner while simultaneously moving the slow XYZ scanner across the region of interest. In order to successfully merge the image sequences together two software approaches for calibrating the data from the fast scanner are described. The first utilizes the low uncertainty interferometric sensors of the XYZ scanner while the second implements a genetic algorithm with multiple parameter fitting during the data merging step of the image stitching process. The basic uncertainty components related to these high-speed measurements are also discussed. Both techniques are shown to successfully enable high-resolution, large area images to be generated at least an order of magnitude faster than with a conventional atomic force microscope.

Opportunities in high-speed atomic force microscopy

The atomic force microscope (AFM) has become integrated into standard characterisation procedures in many different areas of research. Nonetheless, typical imaging rates of commercial microscopes are still very slow, much to the frustration of the user. Developments in instrumentation for "high-speed AFM" (HSAFM) have been ongoing since the 1990s, and now nanometer resolution imaging at video rate is readily achievable. Despite thorough investigation of samples of a biological nature, use of HSAFM instruments to image samples of interest to materials scientists, or to carry out AFM lithography, has been minimal. This review gives a summary of different approaches to and advances in the development of high-speed AFMs, highlights important discoveries made with new instruments, and briefly discusses new possibilities for HSAFM in materials science.

Phase and amplitude patterns in DySEM mappings of vibrating microstructures

We use a dynamic scanning electron microscope (DySEM) to analyze the movement of oscillating micromechanical structures. A dynamic secondary electron (SE) signal is recorded and correlated to the oscillatory excitation of scanning force microscope (SFM) cantilever by means of lock-in amplifiers. We show, how the relative phase of the oscillations modulate the resulting real part and phase pictures of the DySEM mapping. This can be used to obtain information about the underlying oscillatory dynamics. We apply the theory to the case of a cantilever in oscillation, driven at different flexural and torsional resonance modes. This is an extension of a recent work (Schröter et al 2012 Nanotechnology 23 435501), where we reported on a general methodology to distinguish nonlinear features caused by the imaging process from those caused by cantilever motion.

Analytical and numerical analysis of imaging mechanism of dynamic scanning electron microscopy

The direct observation of small oscillating structures with the help of a scanning electron beam is a new approach to study the vibrational dynamics of cantilevers and microelectromechanical systems. In the scanning electron microscope, the conventional signal of secondary electrons (SE, dc part) is separated from the signal response of the SE detector, which is correlated to the respective excitation frequency for vibration by means of a lock-in amplifier. The dynamic response is separated either into images of amplitude and phase shift or into real and imaginary parts. Spatial resolution is limited to the diameter of the electron beam. The sensitivity limit to vibrational motion is estimated to be sub-nanometer for high integration times. Due to complex imaging mechanisms, a theoretical model was developed for the interpretation of the obtained measurements, relating cantilever shapes to interaction processes consisting of incident electron beam, electron-lever interaction, emitted electrons and detector response. Conclusions drawn from this new model are compared with numerical results based on the Euler-Bernoulli equation.

Improving the signal-to-noise ratio of high-speed contact mode atomic force microscopy

During high-speed contact mode atomic force microscopy, higher eigenmode flexural oscillations of the cantilever have been identified as the main source of noise in the resultant topography images. We show that by selectively filtering out the frequencies corresponding to these oscillations in the time domain prior to transforming the data into the spatial domain, significant improvements in image quality can be achieved.

Modelling oscillatory flexure modes of an atomic force microscope cantilever in contact mode whilst imaging at high speed

Understanding the modal response of an atomic force microscope is important for the identification of image artefacts captured using contact-mode atomic force microscopy (AFM). As the scan rate of high speed AFM increases, these modes present themselves as ever clearer noise patterns as the frequency of cantilever vibration falls under the frequency of pixel collection. An Euler-Bernoulli beam equation is used to simulate the flexural modes of the cantilever of an atomic force microscope as it images a hard surface in contact mode. Theoretical results are compared with experimental recordings taken in the high speed regime, as well as previous analytical results. It is shown that the model can capture the mode shapes and resonance properties of the first four eigenmodes.

High-speed atomic force microscopy in slow motion--understanding cantilever behaviour at high scan velocities

Using scanning laser Doppler vibrometer we have identified sources of noise in contact mode high-speed atomic force microscope images and the cantilever dynamics that cause them. By analysing reconstructed animations of the entire cantilever passing over various surfaces, we identified higher eigenmode oscillations along the cantilever as the cause of the image artefacts. We demonstrate that these can be removed by monitoring the displacement rather than deflection of the tip of the cantilever. We compare deflection and displacement detection methods whilst imaging a calibration grid at high speed and show the significant advantage of imaging using displacement.

Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator

Dynamic atomic force microscopy (dAFM) continues to grow in popularity among scientists in many different fields, and research on new methods and operating modes continues to expand the resolution, capabilities, and types of samples that can be studied. But many promising increases in capability are accompanied by increases in complexity. Indeed, interpreting modern dAFM data can be challenging, especially on complicated material systems, or in liquid environments where the behavior is often contrary to what is known in air or vacuum environments. Mathematical simulations have proven to be an effective tool in providing physical insight into these non-intuitive systems. In this article we describe recent developments in the VEDA (virtual environment for dynamic AFM) simulator, which is a suite of freely available, open-source simulation tools that are delivered through the cloud computing cyber-infrastructure of nanoHUB (www.nanohub.org). Here we describe three major developments. First, simulations in liquid environments are improved by enhancements in the modeling of cantilever dynamics, excitation methods, and solvation shell forces. Second, VEDA is now able to simulate many new advanced modes of operation (bimodal, phase-modulation, frequency-modulation, etc.). Finally, nineteen different tip-sample models are available to simulate the surface physics of a wide variety different material systems including capillary, specific adhesion, van der Waals, electrostatic, viscoelasticity, and hydration forces. These features are demonstrated through example simulations and validated against experimental data, in order to provide insight into practical problems in dynamic AFM.