Compensator design for improved counterbalancing in high speed atomic force microscopy

Damping and tracking control of nanopositioning stages with double delayed position feedback

This paper presents a new damping control scheme for piezoelectric nanopositioning stages with double delayed position feedback (DDPF). The DDPF in the inner loop is proposed to suppress vibration of the nanopositioning stage, which leads to a double time-delay system. A new numerical differential method is proposed to determine the parameters of the DDPF with pole placement. Then, a high-gain proportional-integral (PI) controller is designed in the outer loop to achieve a low level of tracking errors, which includes the hysteresis nonlinearity, disturbance, and modeling uncertainties. Experimental tests with various control schemes are conducted on a piezoelectric nanopositioning stage to verify the effectiveness of the proposed method. Experimental results reveal that the control bandwidth of the system is improved from 79 Hz (with the PI controller), 416 Hz (with the conventional delayed position feedback based controller), and 422 Hz (with the recursive delayed position feedback based controller) to 483 Hz (with the proposed controller).

Development of a flexure-based nano-actuator for high-frequency high-resolution directional sensing with atomic force microscopy

Scanning probe microscopies typically rely on the high-precision positioning of a nanoscale probe in order to gain local information about the properties of a sample. At a given location, the probe is used to interrogate a minute region of the sample, often relying on dynamical sensing for improved accuracy. This is the case for most force-based measurements in atomic force microscopy (AFM) where sensing occurs with a tip oscillating vertically, typically in the kHz to MHz frequency regime. While this approach is ideal for many applications, restricting dynamical sensing to only one direction (vertical) can become a serious limitation when aiming to quantify the properties of inherently three-dimensional systems, such as a liquid near a wall. Here, we present the design, fabrication, and calibration of a miniature high-speed scanner able to apply controlled fast and directional in-plane vibrations with sub-nanometer precision. The scanner has a resonance frequency of ∼35 kHz and is used in conjunction with a traditional AFM to augment the measurement capabilities. We illustrate its capabilities at a solid-liquid interface where we use it to quantify the preferred lateral flow direction of the liquid around every sample location. The AFM can simultaneously acquire high-resolution images of the interface, which can be superimposed with the directional measurements. Examples of sub-nanometer measurements conducted with the new scanner are also presented.

The new FAST module: A portable and transparent add-on module for time-resolved investigations with commercial scanning probe microscopes

Time resolution is one of the most severe limitations of scanning probe microscopies (SPMs), since the typical image acquisition times are in the order of several seconds or even few minutes. As a consequence, the characterization of dynamical processes occurring at surfaces (e.g. surface diffusion, film growth, self-assembly and chemical reactions) cannot be thoroughly addressed by conventional SPMs. To overcome this limitation, several years ago we developed a first prototype of the FAST module, an add-on instrument capable of driving a commercial scanning tunneling microscope (STM) at and beyond video rate frequencies. Here we report on a fully redesigned version of the FAST module, featuring improved performance and user experience, which can be used both with STMs and atomic force microscopes (AFMs), and offers additional capabilities such as an atom tracking mode. All the new features of the FAST module, including portability between different commercial instruments, are described in detail and practically demonstrated.

High-speed atomic force microscope with a combined tip-sample scanning architecture

A high-speed atomic force microscope (HS-AFM) based on a tip-sample combined scanning architecture is presented. In this system, the X-scanner, which is separated from the AFM head, carries the sample and scans along the fast-axis. The Y and Z scanners integrated in the AFM head oscillate an ultrashort cantilever probe and scan in the other two dimensions. The optical beam deflection method is improved to enable the laser to track the probe over a wide scan range. A novel probe holder realizes easy exchange and alignment of the probe. Due to the separation of the X and Y scanners, both appear with better dynamic performance and carrying capacity. Experiments show that the HS-AFM established in this work can achieve a line rate of up to 100 Hz with the basic proportional-integral-derivative control algorithm and linear driving. The permissible sample size and mass can be as large as several centimeters and above 40 g.

Nanoscale Poroelasticity of the Tectorial Membrane Determines Hair Bundle Deflections

Stereociliary imprints in the tectorial membrane (TM) have been taken as evidence that outer hair cells are sensitive to shearing displacements of the TM, which plays a key role in shaping cochlear sensitivity and frequency selectivity via resonance and traveling wave mechanisms. However, the TM is highly hydrated (97% water by weight), suggesting that the TM may be flexible even at the level of single hair cells. Here we show that nanoscale oscillatory displacements of microscale spherical probes in contact with the TM are resisted by frequency-dependent forces that are in phase with TM displacement at low and high frequencies, but are in phase with TM velocity at transition frequencies. The phase lead can be as much as a quarter of a cycle, thereby contributing to frequency selectivity and stability of cochlear amplification.

High-speed large area atomic force microscopy using a quartz resonator

A high-speed atomic force microscope for scanning large areas, utilizing a quartz bar driven close to resonance to provide the motion in the fast scan axis is presented. Images up to 170 × 170 μm² have been obtained on a polydimethylsiloxane (PDMS) grating in 1 s. This is provided through an average tip-sample velocity of 28 cm s^-1 at a line rate of 830 Hz. Scan areas up to 80 × 80 μm² have been obtained in 0.42 s with a line rate of 1410 Hz. To demonstrate the capability of the scanner the spherulitic crystallization of a semicrystalline polymer was imaged in situ at high speed.

Design and control of multi-actuated atomic force microscope for large-range and high-speed imaging

This paper presents the design and control of a high-speed and large-range atomic force microscopy (AFM). A multi-actuation scheme is proposed where several nano-positioners cooperate to achieve the range and speed requirements. A simple data-based control design methodology is presented to effectively operate the AFM scanner components. The proposed controllers compensate for the coupled dynamics and divide the positioning responsibilities between the scanner components. As a result, the multi-actuated scanner behavior is equivalent to that of a single X-Y-Z positioner with large range and high speed. The scanner of the designed AFM is composed of five nano-positioners, features 6 μm out-of-plane and 120 μm lateral ranges and is capable of high-speed operation. The presented AFM has a modular design with laser spot size of 3.5 μm suitable for small cantilever, an optical view of the sample and probe, a conveniently large waterproof sample stage and a 20 MHz data throughput for high resolution image acquisition at high imaging speeds. This AFM is used to visualize etching of calcite in a solution of sulfuric acid. Layer-by-layer dissolution and pit formation along the crystalline lines in a low pH environment is observed in real time.

A miniaturized, high frequency mechanical scanner for high speed atomic force microscope using suspension on dynamically determined points

One of the major limitations in the speed of the atomic force microscope (AFM) is the bandwidth of the mechanical scanning stage, especially in the vertical (z) direction. According to the design principles of "light and stiff" and "static determinacy," the bandwidth of the mechanical scanner is limited by the first eigenfrequency of the AFM head in case of tip scanning and by the sample stage in terms of sample scanning. Due to stringent requirements of the system, simply pushing the first eigenfrequency to an ever higher value has reached its limitation. We have developed a miniaturized, high speed AFM scanner in which the dynamics of the z-scanning stage are made insensitive to its surrounding dynamics via suspension of it on specific dynamically determined points. This resulted in a mechanical bandwidth as high as that of the z-actuator (50 kHz) while remaining insensitive to the dynamics of its base and surroundings. The scanner allows a practical z scan range of 2.1 μm. We have demonstrated the applicability of the scanner to the high speed scanning of nanostructures.

Aggrecan nanoscale solid-fluid interactions are a primary determinant of cartilage dynamic mechanical properties

Poroelastic interactions between interstitial fluid and the extracellular matrix of connective tissues are critical to biological and pathophysiological functions involving solute transport, energy dissipation, self-stiffening and lubrication. However, the molecular origins of poroelasticity at the nanoscale are largely unknown. Here, the broad-spectrum dynamic nanomechanical behavior of cartilage aggrecan monolayer is revealed for the first time, including the equilibrium and instantaneous moduli and the peak in the phase angle of the complex modulus. By performing a length scale study and comparing the experimental results to theoretical predictions, we confirm that the mechanism underlying the observed dynamic nanomechanics is due to solid-fluid interactions (poroelasticity) at the molecular scale. Utilizing finite element modeling, the molecular-scale hydraulic permeability of the aggrecan assembly was quantified (kaggrecan = (4.8 ± 2.8) × 10(-15) m(4)/N·s) and found to be similar to the nanoscale hydraulic permeability of intact normal cartilage tissue but much lower than that of early diseased tissue. The mechanisms underlying aggrecan poroelasticity were further investigated by altering electrostatic interactions between the molecule's constituent glycosaminoglycan chains: electrostatic interactions dominated steric interactions in governing molecular behavior. While the hydraulic permeability of aggrecan layers does not change across species and age, aggrecan from adult human cartilage is stiffer than the aggrecan from newborn human tissue.

Note: High-speed Z tip scanner with screw cantilever holding mechanism for atomic-resolution atomic force microscopy in liquid

High-speed atomic force microscopy has attracted much attention due to its unique capability of visualizing nanoscale dynamic processes at a solid/liquid interface. However, its usability and resolution have yet to be improved. As one of the solutions for this issue, here we present a design of a high-speed Z-tip scanner with screw holding mechanism. We perform detailed comparison between designs with different actuator size and screw arrangement by finite element analysis. Based on the design giving the best performance, we have developed a Z tip scanner and measured its performance. The measured frequency response of the scanner shows a flat response up to ∼10 kHz. This high frequency response allows us to achieve wideband tip-sample distance regulation. We demonstrate the applicability of the scanner to high-speed atomic-resolution imaging by visualizing atomic-scale calcite crystal dissolution process in water at 2 s/frame.

High-bandwidth AFM-based rheology is a sensitive indicator of early cartilage aggrecan degradation relevant to mouse models of osteoarthritis

Murine models of osteoarthritis (OA) and post-traumatic OA have been widely used to study the development and progression of these diseases using genetically engineered mouse strains along with surgical or biochemical interventions. However, due to the small size and thickness of murine cartilage, the relationship between mechanical properties, molecular structure and cartilage composition has not been well studied. We adapted a recently developed AFM-based nano-rheology system to probe the dynamic nanomechanical properties of murine cartilage over a wide frequency range of 1 Hz to 10 kHz, and studied the role of glycosaminoglycan (GAG) on the dynamic modulus and poroelastic properties of murine femoral cartilage. We showed that poroelastic properties, highlighting fluid-solid interactions, are more sensitive indicators of loss of mechanical function compared to equilibrium properties in which fluid flow is negligible. These fluid-flow-dependent properties include the hydraulic permeability (an indicator of the resistance of matrix to fluid flow) and the high frequency modulus, obtained at high rates of loading relevant to jumping and impact injury in vivo. Utilizing a fibril-reinforced finite element model, we estimated the poroelastic properties of mouse cartilage over a wide range of loading rates for the first time, and show that the hydraulic permeability increased by a factor ~16 from knormal=7.80×10(-16)±1.3×10(-16) m(4)/N s to kGAG-depleted=1.26×10(-14)±6.73×10(-15) m(4)/N s after GAG depletion. The high-frequency modulus, which is related to fluid pressurization and the fibrillar network, decreased significantly after GAG depletion. In contrast, the equilibrium modulus, which is fluid-flow independent, did not show a statistically significant alteration following GAG depletion.

Adaptive AFM scan speed control for high aspect ratio fast structure tracking

Improved imaging rates in Atomic Force Microscopes (AFM) are of high interest for disciplines such as life sciences and failure analysis of semiconductor wafers, where the sample topology shows high aspect ratios. Also, fast imaging is necessary to cover a large surface under investigation in reasonable times. Since AFMs are composed of mechanical components, they are associated with comparably low resonance frequencies that undermine the effort to increase the acquisition rates. In particular, high and steep structures are difficult to follow, which causes the cantilever to temporarily loose contact to or crash into the sample. Here, we report on a novel approach that does not affect the scanner dynamics, but adapts the lateral scanning speed of the scanner. The controller monitors the control error signal and, only when necessary, decreases the scan speed to allow the z-piezo more time to react to changes in the sample's topography. In this case, the overall imaging rate can be significantly increased, because a general scan speed trade-off decision is not needed and smooth areas are scanned fast. In contrast to methods trying to increase the z-piezo bandwidth, our method is a comparably simple approach that can be easily adapted to standard systems.

High-speed imaging upgrade for a standard sample scanning atomic force microscope using small cantilevers

We present an atomic force microscope (AFM) head for optical beam deflection on small cantilevers. Our AFM head is designed to be small in size, easily integrated into a commercial AFM system, and has a modular architecture facilitating exchange of the optical and electronic assemblies. We present two different designs for both the optical beam deflection and the electronic readout systems, and evaluate their performance. Using small cantilevers with our AFM head on an otherwise unmodified commercial AFM system, we are able to take tapping mode images approximately 5-10 times faster compared to the same AFM system using large cantilevers. By using additional scanner turnaround resonance compensation and a controller designed for high-speed AFM imaging, we show tapping mode imaging of lipid bilayers at line scan rates of 100-500 Hz for scan areas of several micrometers in size.

Multi-actuation and PI control: a simple recipe for high-speed and large-range atomic force microscopy

High speed atomic force microscopy enables observation of dynamic nano-scale processes. However, maintaining a minimal interaction force between the sample and the probe is challenging at high speed specially when using conventional piezo-tubes. While rigid AFM scanners are operational at high speeds with the drawback of reduced tracking range, multi-actuation schemes have shown potential for high-speed and large-range imaging. Here we present a method to seamlessly incorporate additional actuators into conventional AFMs. The equivalent behavior of the resulting multi-actuated setup resembles that of a single high-speed and large-range actuator with maximally flat frequency response. To achieve this, the dynamics of the individual actuators and their couplings are treated through a simple control scheme. Upon the implementation of the proposed technique, commonly used PI controllers are able to meet the requirements of high-speed imaging. This forms an ideal platform for retroactive enhancement of existing AFMs with minimal cost and without compromise on the tracking range. A conventional AFM with tube scanner is retroactively enhanced through the proposed method and shows an order of magnitude improvement in closed loop bandwidth performance while maintaining large range. The effectiveness of the method is demonstrated on various types of samples imaged in contact and tapping modes, in air and in liquid.

Separate-type scanner and wideband high-voltage amplifier for atomic-resolution and high-speed atomic force microscopy

We have developed a liquid-environment atomic force microscope with a wideband and low-noise scanning system for atomic-scale imaging of dynamic processes at solid/liquid interfaces. The developed scanning system consists of a separate-type scanner and a wideband high-voltage amplifier (HVA). By separating an XY-sample scanner from a Z-tip scanner, we have enabled to use a relatively large sample without compromising the high resonance frequency. We compared various cantilever- and sample-holding mechanisms by experiments and finite element analyses for optimizing the balance between the usability and frequency response characteristics. We specifically designed the HVA to drive the developed scanners, which enabled to achieve the positioning accuracy of 5.7 and 0.53 pm in the XY and Z axes, respectively. Such an excellent noise performance allowed us to perform atomic-resolution imaging of mica and calcite in liquid. Furthermore, we demonstrate in situ and atomic-resolution imaging of the calcite crystal growth process in water.