Dynamic Mode Atomic Force Microscopy Research Articles

Probing Viscoelastic Properties and Interfaces in High-Density Polyethylene Vitrimers at the Nanoscale Using Dynamic Mode Atomic Force Microscopy.

Vitrimers are a new class of heterogeneous polymers that combine the best features of thermosets with those of thermoplastics. The introduction of cross-links strongly changes the viscoelastic behavior of vitrimer materials. However, the characterization and understanding of the nanostructures and interfaces in vitrimers resulting from dynamic cross-linking formation remain a major challenge. Here, using dynamic modes of atomic force microscopy (AFM), namely intermodulation AFM (ImAFM) and AFM-based dynamic mechanical analysis (AFM-nDMA), local viscoelastic properties and interfaces at the nanoscale length of high-density polyethylene (HDPE) vitrimer materials are reported. ImAFM imaging in combination with the k-means clustering algorithm clearly reveals two distinct phases in the vitrimer system with highly different viscoelastic properties. AFM-nDMA further provides quantitative nanoviscoelastic properties at the nanoscale to confirm that there is a cross-linking-rich aggregation area forming a nanosize network structure in the cross-linking-poor matrix phase. The cross-linking-rich region shows a similar elastic modulus but much higher adhesion force measured by AFM compared to the cross-linking-poor HDPE matrix. Furthermore, the frequency influence on the local viscoelastic properties of HDPE vitrimer at the nanoscale was initially screened. The observed HDPE vitrimer nanostructures and viscoelastic properties at the nanoscale also provide explanations on the observed bulk HDPE vitrimer crystallinity decrease and dimensional stability increase compared to HDPE. Therefore, probing the viscoelastic properties and interfaces of HDPE vitrimer provides important insights into understanding of the correlations between the vitrimer nanostructure and the bulk mechanical and rheological behaviors.

Control of quality factor of atomic force microscopy cantilever by cavity optomechanical effect

The effective quality factor of the cantilever plays a fundamental role in dynamic mode atomic force microscopy. Here we present a technique to modify the quality factor of an atomic force microscopy cantilever within a Fabry–Perot optical interferometer. The experimental setup uses two separate laser sources to detect and excite the oscillation of the cantilever. While the intensity modulation of the excitation laser drives the oscillation of the cantilever, the average intensity can be used to modify the quality factor via optomechanical force without changing the fiber-cantilever cavity length. The technique enables users to optimize the quality factor for different types of measurements without influencing the deflection measurement sensitivity. An unexpected frequency shift was observed and modelled as temperature dependence of the cantilever’s Young’s modulus, which was validated using finite element simulation. The model was used to compensate for the thermal frequency shift. The simulation provided relations between optical power, temperature, and frequency shift.

Revealing the static and dynamic nanomechanical properties of diatom frustules—Nature's glass lace

Diatoms are single cell microalgae enclosed in silica exoskeletons (frustules) that provide inspiration for advanced hybrid nanostructure designs mimicking multi-scale porosity to achieve outstanding mechanical and optical properties. Interrogating the structure and properties of diatoms down to nanometer scale leads to breakthrough advances reported here in the nanomechanical characterization of Coscinodiscus oculus-iridis diatom pure silica frustules, as well as of air-dried and wet cells with organic content. Static and dynamic mode Atomic Force Microscopy (AFM) and in-SEM nanoindentation revealed the peculiarities of diatom response with separate contributions from material nanoscale behavior and membrane deformation of the entire valve. Significant differences in the nanomechanical properties of the different frustule layers were observed. Furthermore, the deformation response depends strongly on silica hydration and on the support from the internal organic content. The cyclic loading revealed that the average compliance of the silica frustule is 0.019 m/N and increases with increasing number of cycles. The structure–mechanical properties relationship has a direct impact on the vibrational properties of the frustule as a complex micrometer-sized mechanical system. Lessons from Nature’s nanostructuring of diatoms open up pathways to new generations of nano- and microdevices for electronic, electromechanical, photonic, liquid, energy storage, and other applications.

Very-high-frequency probes for atomic force microscopy with silicon optomechanics

Atomic force microscopy (AFM) has been consistently supporting nanosciences and nanotechnologies for over 30 years and is used in many fields from condensed matter physics to biology. It enables the measurement of very weak forces at the nanoscale, thus elucidating the interactions at play in fundamental processes. Here, we leverage the combined benefits of micro/nanoelectromechanical systems and cavity optomechanics to fabricate a sensor for dynamic mode AFM at a frequency above 100 MHz. This frequency is two decades above the fastest commercial AFM probes, suggesting an opportunity for measuring forces at timescales unexplored thus far. The fabrication is achieved using very-large-scale integration technologies derived from photonic silicon circuits. The probe’s optomechanical ring cavity is coupled to a 1.55 μm laser light and features a 130 MHz mechanical resonance mode with a quality factor of 900 in air. A limit of detection in the displacement of 3 × 10−16 m/√Hz is obtained, enabling the detection of the Brownian motion of the probe and paving the way for force sensing experiments in the dynamic mode with a working vibration amplitude in the picometer range. When inserted in a custom AFM instrument embodiment, this optomechanical sensor demonstrates the capacity to perform force-distance measurements and to maintain a constant interaction strength between the tip and sample, an essential requirement for AFM applications. Experiments indeed show a stable closed-loop operation with a setpoint of 4 nN/nm for an unprecedented subpicometer vibration amplitude, where the tip–sample interaction is mediated by a stretched water meniscus.

Intermittent-contact local dielectric spectroscopy of nanostructured interfaces

Local dielectric spectroscopy (LDS) is a scanning probe method, based on dynamic-mode atomic force microscopy (AFM), to discriminate dielectric properties at surfaces with nanometer-scale lateral resolution. Until now a sub-10 nm resolution for LDS has not been documented, that would give access to the length scale of fundamental physical phenomena such as the cooperativity length related to structural arrest in glass formers (2–3 nm). In this work, LDS performed by a peculiar variant of intermittent-contact mode of AFM, named constant-excitation frequency modulation, was introduced and extensively explored in order to assess its best resolution capability. Dependence of resolution and contrast of dielectric imaging and spectroscopy on operation parameters like probe oscillation amplitude and free amplitude, the resulting frequency shift, and probe/surface distance-regulation feedback gain, were explored. By using thin films of a diblock copolymer of polystyrene (PS) and polymethylmethacrylate (PMMA), exhibiting phase separation on the nanometer scale, lateral resolution of at least 3 nm was demonstrated in both dielectric imaging and localized spectroscopy, by operating with optimized parameters. The interface within lamellar PS/PMMA was mapped, with a best width in the range between 1 and 3 nm. Changes of characteristic time of the secondary (β) relaxation process of PMMA could be tracked across the interface with PS.

Low Latency Demodulation for High-Frequency Atomic Force Microscopy Probes

One prerequisite for high-speed imaging in dynamic-mode atomic force microscopy (AFM) is the fast demodulation of the probe signal. In this contribution, we present the amplitude and phase estimation method based on the acquisition of four points per oscillation, with the sampling frequency being phase-locked on the probe actuation. The method is implemented on a RedPitaya platform, with its clock being generated from the actuation signal of the probe. Experimental characterizations using square-modulated sine waves show that latency of 500 ns is achieved with a carrier frequency of 10 MHz, which is ten times faster compared with a state-of-the-art lock-in amplifier. A tracking bandwidth greater than 200 kHz is obtained experimentally. The method is eventually applied to a close-loop AFM scan realized using a 15-MHz AFM probe, showing its suitability for high-frequency oscillating probes.

Subnanometer-scale imaging of nanobio-interfaces by frequency modulation atomic force microscopy.

Recently, there have been significant advancements in dynamic-mode atomic force microscopy (AFM) for biological applications. With frequency modulation AFM (FM-AFM), subnanometer-scale surface structures of biomolecules such as secondary structures of proteins, phosphate groups of DNAs, and lipid-ion complexes have been directly visualized. In addition, three-dimensional AFM (3D-AFM) has been developed by combining a high-resolution AFM technique with a 3D tip scanning method. This method enabled visualization of 3D distributions of water (i.e. hydration structures) with subnanometer-scale resolution on various biological molecules such as lipids, proteins, and DNAs. Furthermore, 3D-AFM also allows visualization of subnanometer-scale 3D distributions of flexible surface structures such as thermally fluctuating lipid headgroups. Such a direct local information at nano-bio interfaces can play a critical role in determining the atomic- or molecular-scale model to explain interfacial structures and functions. Here, we present an overview of these recent advancements in the dynamic-mode AFM techniques and their biological applications.

AFM Microcantilever With a Collocated AlN Sensor-Actuator Pair: Enabling Efficient Q-Control for Dynamic Imaging

This manuscript presents a novel microcantilever with an embedded piezoelectric sensor-actuator pair for dynamic atomic force microscopy (AFM). The transducer pair is constructed from a two-layered AlN stack. Stacking the piezoelectric transducers in this manner leads to a minimal feedthrough from actuation to sense electrode, granting a high dynamic range frequency response for dynamic mode AFM. The cantilever’s design allows for dual mode operation at 1st and 2nd resonance modes. High resolution tapping mode imaging results are reported, while the cantilever is operated at these modes. A feedback control loop is used to modify quality factor of the 1st mode of the cantilever, using a positive position feedback (PPF) controller. A faster response time is achieved by reducing the ${Q}$ -factor, enabling the cantilever to track the topography at a higher scan rate. Results of bimodal AFM imaging are reported, using amplitude changes of the 1st mode for surface topography, while material properties are encoded in phase changes of the 2nd mode. [2020-0096]

Amplitude noise spectrum of a lock-in amplifier: Application to microcantilever noise measurements

The lock-in amplifier is a crucial component in many applications requiring high-resolution displacement sensing; it's purpose is to estimate the amplitude and phase of a periodic signal, potentially corrupted by noise, at a frequency determined by a reference signal. Where the noise can be approximated by a stationary Gaussian process, such as thermal force noise and electronic sensor noise, this article derives the amplitude noise spectral density of the lock-in-amplifier output. The proposed method is demonstrated by predicting the demodulated noise spectrum of a microcantilever for dynamic-mode atomic force microscopy to determine the cantilever on-resonance thermal noise, the cantilever tracking bandwidth and the electronic noise floor. The estimates are shown to closely match experimental results over a wide range of operating conditions.

High Dynamic Range AFM Cantilever With a Collocated Piezoelectric Actuator-Sensor Pair

We present a novel approach to fundamentally eliminate electrical feedthrough (cross-talk) signal in self-sensing piezoelectric microcantilevers, used in dynamic mode atomic force microscopy (AFM). The probe is an Si microcantilever on which a two-layer piezoelectric stack transducer is microfabricated. The top transducer in the stack functions as an actuator, while the bottom transducer is used as a deflection sensor. This arrangement leads to a collocated actuator-sensor pair that co-exist on the same surface area. We report experimental results that establish the sensor’s ability to capture the full dynamic range of the cantilever with minimal feedthrough from the actuator. [2019-0143]

Atomic force microscopy phase imaging of epitaxial graphene films

Dynamic mode atomic force microscopy phase imaging is known to produce distinct contrast between graphene areas of different atomic thickness. But the intrinsic complexity of the processes controlling the tip motion and the phase angle shift excludes its use as an independent technique for a quantitative type of analysis. By investigating the relationship between the phase shift, the tip-surface interaction, and the thickness of the epitaxial graphene areas grown on silicon carbide, we shed light on the origin of such phase contrast, and on the complex energy dissipation processes underlying phase imaging. In particular, we study the behavior of phase shift and energy dissipation when imaging the interfacial buffer layer, single-layer, and bilayer graphene regions as a function of the tip-surface separation and the interaction forces. Finally, we compare these results with those obtained on differently-grown quasi free standing single- and bilayer graphene samples.

An optimization framework for the design of piezoelectric AFM cantilevers

To facilitate further miniaturization of atomic force microscopy (AFM) cantilevers and to eliminate the standard optical beam deflection sensor, integrated piezoelectric actuation and sensing on the chip level is a promising option. This article presents a topology optimization method for dynamic mode AFM cantilevers that maximizes the sensitivity of an integrated piezoelectric sensor under stiffness and resonance frequency constraints. Included in the formulation is a new material model C-SIMP (connectivity and solid isotropic material with penalization) that extends the SIMP model to explicitly include the penalization of unconnected structures. Example cantilever designs demonstrate the potential of the topology optimization method. The results show, firstly, the C-SIMP material model significantly reduces connectivity issues and, secondly, arbitrary cantilever topologies can produce increases in sensor sensitivity or resonance frequency compared to a rectangular topology.

Lyapunov Estimator for High-Speed Demodulation in Dynamic Mode Atomic Force Microscopy

In dynamic mode atomic force microscopy (AFM), the imaging bandwidth is governed by the slowest component in the open-loop chain consisting of the vertical actuator, cantilever, and demodulator. While the common demodulation method is to use a lock-in amplifier (LIA), its performance is ultimately bounded by the bandwidth of the postmixing low-pass filters. This brief proposes an amplitude and phase estimation method based on a strictly positive real Lyapunov design approach. The estimator is designed to be of low complexity while allowing for high bandwidth. In addition, suitable gains for high performance are suggested such that no tuning is necessary. The Lyapunov estimator is experimentally implemented for amplitude demodulation and shown to surpass the LIA in terms of tracking bandwidth and noise performance. High-speed AFM images are presented to corroborate the results.

Fidelity Measurement on Signal Detection Algorithms With Application to AFM Imaging

Many signal processing and decision making algorithms reported in contemporary literature characterize the performance of the proposed methods utilizing decision error rates. However there is significant need for strategies that provide quantitative assessment of the fidelity of decisions made by the algorithms. This paper develops novel techniques utilizing which fidelity measures can be assigned quantitatively on some prevalent signal detection algorithms. The developed fidelity measurement methods with the detection algorithms are employed for topography imaging utilizing dynamic mode atomic force microscope (AFM). The AFM is a versatile metrology tool for interrogating material at the nano-scale. In spite of its remarkable achievements, a key issue that remains largely unaddressed is the assessment of fidelity of the measurement data. The developed paradigm facilitates user specific priority for either detection of sample features with high decision confidence or on not missing detection of true features. The fidelity measures presented here are suitable for real-time implementation. A detailed comparative study is presented to characterize the proposed signal detection algorithms and fidelity measurement techniques under practical AFM applications. Comprehensive simulation and experimental data corroborate the effectiveness of proposed methods.

Design and fabrication of a flexural harmonic AFM probe with an exchangeable tip

While harmonic probes are essential characterization tools in dynamic mode Atomic Force Microscopy, precise fabrication of harmonic probes is a challenge, and their replacement is relatively expensive. This paper reports the design, fabrication and evaluation of harmonic AFM probes with exchangeable tips that address these issues. The probe comprises a cantilever of non-uniform geometry that carries an exchangeable tip held by a liquid meniscus. The cantilever and the liquid meniscus interface are designed so that the tip is held firmly and the tip exchange can be performed with precise control over its position and orientation. A systematic approach is proposed for the design and fabrication of probes with specified eigen-frequencies. The approach consists of adopting an appropriate initial geometry, and iteratively modifying its dimensions so that the specified eigen-frequencies are achieved. To correct for errors in fabrication of the designed probe, an iterative fabrication scheme is also proposed. To facilitate implementation of this scheme, a simple lumped parameter model is developed for the overall probe. The proposed approach is employed to design and fabricate a harmonic probe with exchangeable tip whose first two flexural eigen-frequencies are in the ratio 1:4. Finally, the fabricated probe is evaluated, and the ratio of eigen-frequencies is found to match the desired harmonic ratio to an accuracy of over 99.8%.

High-speed dynamic-mode atomic force microscopy imaging of polymers: an adaptive multiloop-mode approach.

Adaptive multiloop-mode (AMLM) imaging to substantially increase (over an order of magnitude) the speed of tapping-mode (TM) imaging is tested and evaluated through imaging three largely different heterogeneous polymer samples in experiments. It has been demonstrated that AMLM imaging, through the combination of a suite of advanced control techniques, is promising to achieve high-speed dynamic-mode atomic force microscopy imaging. The performance, usability, and robustness of the AMLM in various imaging applications, however, is yet to be assessed. In this work, three benchmark polymer samples, including a PS–LDPE sample, an SBS sample, and a Celgard sample, differing in feature size and stiffness of two orders of magnitude, are imaged using the AMLM technique at high-speeds of 25 Hz and 20 Hz, respectively. The comparison of the images obtained to those obtained by using TM imaging at scan rates of 1 Hz and 2 Hz showed that the quality of the 25 Hz and 20 Hz AMLM imaging is at the same level of that of the 1 Hz TM imaging, while the tip–sample interaction force is substantially smaller than that of the 2 Hz TM imaging.

Toward quantitative estimation of material properties with dynamic mode atomic force microscopy: a comparative study

In this article, we explore methods that enable estimation of material properties with the dynamic mode atomic force microscopy suitable for soft matter investigation. The article presents the viewpoint of casting the system, comprising of a flexure probe interacting with the sample, as an equivalent cantilever system and compares a steady-state analysis based method with a recursive estimation technique for determining the parameters of the equivalent cantilever system in real time. The steady-state analysis of the equivalent cantilever model, which has been implicitly assumed in studies on material property determination, is validated analytically and experimentally. We show that the steady-state based technique yields results that quantitatively agree with the recursive method in the domain of its validity. The steady-state technique is considerably simpler to implement, however, slower compared to the recursive technique. The parameters of the equivalent system are utilized to interpret storage and dissipative properties of the sample. Finally, the article identifies key pitfalls that need to be avoided toward the quantitative estimation of material properties.

Radiation pressure excitation of a low temperature atomic force/magnetic force microscope for imaging in 4-300 K temperature range.

We describe a novel radiation pressure based cantilever excitation method for imaging in dynamic mode atomic force microscopy (AFM) for the first time. Piezo-excitation is the most common method for cantilever excitation, however it may cause spurious resonance peaks. Therefore, the direct excitation of the cantilever plays a crucial role in AFM imaging. A fiber optic interferometer with a 1310 nm laser was used both for the excitation of the cantilever at the resonance and the deflection measurement of the cantilever in a commercial low temperature atomic force microscope/magnetic force microscope (AFM/MFM) from NanoMagnetics Instruments. The laser power was modulated at the cantilever's resonance frequency by a digital Phase Locked Loop (PLL). The laser beam is typically modulated by ∼500 μW, and ∼141.8 nmpp oscillation amplitude is obtained in moderate vacuum levels between 4 and 300 K. We have demonstrated the performance of the radiation pressure excitation in AFM/MFM by imaging atomic steps in graphite, magnetic domains in CoPt multilayers between 4 and 300 K and Abrikosov vortex lattice in BSCCO(2212) single crystal at 4 K for the first time.

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions.

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip–sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surface as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young’s modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip–sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information.

High-sensitivity imaging with lateral resonance mode atomic force microscopy.

In the operation of a dynamic mode atomic force microscope, a micro-fabricated rectangular cantilever is typically oscillated at or near its mechanical resonance frequency. Lateral bending resonances of cantilevers are rarely used because the resonances are not expected to be detected by the beam-deflection method. In this work, we found that micro-cantilevers with a large tip produced an out-of-plane displacement in lateral resonance (LR), which could be detected with the beam-deflection method. Finite-element analysis indicated that the presence of a large tip is the major source of the out-of-plane coupling for the LR. We also imaged a heterogeneous sample by operating a cantilever in LR, torsional resonance, and tapping modes. LR mode yielded a small deformation and noise level in the height maps as well as a high contrast and small noise level in the phase maps. LR mode also had a resonance frequency that was orders of magnitude higher than that of tapping mode. Operation with LR mode may have the benefits of high-speed scanning, high-sensitivity imaging, and mapping of in-plane mechanical properties of the sample surface. In general, LR mode may become a powerful new atomic force microscopy technique for characterizing sample materials.