A high-bandwidth amplitude estimation technique for dynamic mode atomic force microscopy.

While often overlooked, one of the prerequisites for high-speed amplitude modulation atomic force microscopy is a high-bandwidth amplitude estimation technique. Conventional techniques, such as RMS to DC conversion and the lock-in amplifier, have proven useful, but offer limited measurement bandwidth and are not suitable for high-speed imaging. Several groups have developed techniques, but many of these are either difficult to implement or lack robustness. In this contribution, we briefly outline existing amplitude estimation methods and propose a new high-bandwidth estimation technique, inspired by techniques employed in microwave and RF circuit design, which utilizes phase cancellation to significantly improve the performance of the lock-in amplifier. We conclude with the design and implementation of a custom circuit to experimentally demonstrate the improvements and discuss its application in high-speed and multifrequency atomic force microscopy.

Control of the higher eigenmodes of a microcantilever: applications in atomic force microscopy.

While conventional techniques in dynamic mode atomic force microscopy typically involve the excitation of the first flexural mode of a microcantilever, situations arise where the excitation of higher modes may result in image artefacts. Strong nonlinear coupling between the cantilever modes in liquid environments may result in image artefacts, limiting the accuracy of the image. Similar observations have been made in high-speed contact mode AFM. To address this issue, we propose the application of the modulated-demodulated control technique to attenuate problematic modes to eliminate the image artefacts. The modulated-demodulated control technique is a high-bandwidth technique, which is well suited to the control of next generation of high-speed cantilevers. In addition to potential improvements in image quality, a high-bandwidth controller may also find application in multifrequency AFM experiments. To demonstrate the high-bandwidth nature of the control technique, we construct an amplitude modulation AFM experiment in air utilizing low amplitude setpoints, which ensures that harmonic generation and nonlinear coupling of the modes result in image artefacts. We then utilize feedback control to highlight the improvement in image quality. Such a control technique appears extremely promising in high-speed atomic force microscopy and is likely to have direct application in AFM in liquids.

Sensorless enhancement of an atomic force microscope micro-cantilever quality factor using piezoelectric shunt control.

The image quality and resolution of the Atomic Force Microscope (AFM) operating in tapping mode is dependent on the quality (Q) factor of the sensing micro-cantilever. Increasing the cantilever Q factor improves image resolution and reduces the risk of sample and cantilever damage. Active piezoelectric shunt control is introduced in this work as a new technique for modifying the Q factor of a piezoelectric self-actuating AFM micro-cantilever. An active impedance is placed in series with the tip oscillation voltage source to modify the mechanical dynamics of the cantilever. The benefit of using this control technique is that it removes the optical displacement sensor from the Q control feedback loop to reduce measurement noise in the loop and allows for a reduction in instrument size.

Diagonal control design for atomic force microscope piezoelectric tube nanopositioners.

Atomic Force Microscopes (AFM) are used for generating surface topography of samples at micro to atomic resolutions. Many commercial AFMs use piezoelectric tube nanopositioners for scanning. Scanning rates of these microscopes are hampered by the presence of low frequency resonant modes. When inadvertently excited, these modes lead to high amplitude mechanical vibrations causing the loss of accuracy, while scanning, and eventually to break down of the tube. Feedback control has been used to damp these resonant modes. Thereby, enabling higher scanning rates. Here, a multivariable controller is designed to damp the first resonant mode along both the x and y axis. Exploiting the inherent symmetry in the piezoelectric tube, the multivariable control design problem is recast as independent single-input single-output (SISO) designs. This in conjunction with integral resonant control is used for damping the first resonant mode.

Resonant control of an atomic force microscope micro-cantilever for active Q control.

Active Q control may be used to modify the effective quality (Q) factor of an atomic force microscope (AFM) micro-cantilever when operating in tapping mode. The control system uses velocity feedback to obtain an effective cantilever Q factor to achieve optimal scan speed and image resolution for the imaging environment and sample type. Time delay of the cantilever displacement signal is the most common method of cantilever velocity estimation. Spill-over effects from unmodeled dynamics may degrade the closed loop system performance, possibly resulting in system instability, when time delay velocity estimation is used. A resonant controller is proposed in this work as an alternate method of velocity estimation. This new controller has guaranteed closed loop stability, is easy to tune, and may be fitted into existing commercial AFMs with minimal modification. Images of a calibration grating are obtained using this controller to demonstrate its effectiveness.

Invited review article: high-speed flexure-guided nanopositioning: mechanical design and control issues.

Recent interest in high-speed scanning probe microscopy for high-throughput applications including video-rate atomic force microscopy and probe-based nanofabrication has sparked attention on the development of high-bandwidth flexure-guided nanopositioning systems (nanopositioners). Such nanopositioners are designed to move samples with sub-nanometer resolution with positioning bandwidth in the kilohertz range. State-of-the-art designs incorporate uniquely designed flexure mechanisms driven by compact and stiff piezoelectric actuators. This paper surveys key advances in mechanical design and control of dynamic effects and nonlinearities, in the context of high-speed nanopositioning. Future challenges and research topics are also discussed.

Note: Piezoelectric strain voltage sensing at ultra-low frequencies.

Piezoelectric sensors have emerged as a versatile tool for measurement of various quantities such as pressure, acceleration, strain, or force across many industrial applications. When mechanically strained, electric charges are produced inside a piezoelectric transducer. These charges result in an electric field that may be measured as a voltage difference between two electrodes, from which the strain can be inferred. To measure this voltage the sensor must be interfaced with an external device that would typically have a finite input impedance. This, together with the capacitive nature of the piezoelectric sensor, results in an inability to measure strain at low frequencies. We propose a method, based on using a varactor diode in an oscillator circuit, which can result in accurate measurements of the piezoelectric voltage at ultra-low frequencies. We demonstrate successful measurements at 1 mHz.

High-speed cycloid-scan atomic force microscopy.

A key hurdle in achieving high scan speeds in atomic force microscopes is that the probe is required to be scanned over the sample in a zig-zag raster pattern. The fast axis of the AFM scanner must track a signal that contains frequencies beyond its mechanical bandwidth. Consequently, fast raster scans generate distortions in the resulting image. We propose a smooth cycloid-like scan pattern that allows us to achieve scan speeds much higher than a raster scan. We illustrate how the proposed method can be implemented on a commercial AFM with minimal modifications.