Tip-sample Interaction Force Research Articles

Novel hybrid interference and atomic force microscopy

Abstract A novel hybrid microscope which combines an interference microscopic (IM) and an atomic force microscopic (AFM) measurement mode is introduced. It is realised by adding an AFM probe to an IM, where the AFM probe can be mechanically switched in or out of the beam path of the IM. When the AFM cantilever is out of the beam path, the system works in the IM measurement mode for noncontact and fast optical measurements. When the AFM cantilever is in the beam path, it works in the AFM measurement mode, where the AFM tip interacts with sample surfaces for measurements. The deformation of the AFM cantilever induced by the tip-sample interaction force is detected from interference fringes, which are formed by the interference of the light beam reflected from the backside of the AFM cantilever and a reference beam in the IM. This novel design has a high-level synergy of AFM and IM technologies and provides several promising application potentials. For instance, it can bring high-resolution AFM measurements whenever and wherever needed in IM measurements, thus, to complement the lateral resolution limits of IM; The AFM measurement mode can provide measurement results with higher topography fidelity, thus, to offer in-situ reference areal surface metrology for IM measurements. In the paper, design concept, realisation of a prototype instrument, and experimental results illustrating the performance of the prototype instrument are detailed. 

Characterization of strongly coupled quartz tuning fork sensors for precision force measurement in atomic force microscopy

Miniaturized quartz tuning forks (QTFs) have been adopted as force sensors for non-contact atomic force microscopy (AFM). However, the coupled oscillation behaviors of the QTF prongs are not well understood, preventing quantitative measurement of the nanoscale tip-sample interaction forces. This article presents a lumped model that accurately delineates the coupled mechanical oscillations of QTF prongs, establishing rigorous relationships between experimental observables and tip-sample interaction forces. The first-order resonance spectra of a commercial QTF were fully characterized by correlating its piezoelectric response with the actual mechanical oscillation measured with a Fabry-Pérot interferometer. In order to uniquely determine the modeling parameters (i.e., the effective masses, spring constants, and damping constants), the experimental results were compared with the lumped model predictions while masses were added to one prong. The results reveal that the QTF’s center of mass is highly damped, preventing the observation of a symmetric resonance mode. In addition, the mass loading experiment demonstrates that the mechanical oscillations of the QTF prongs are strongly coupled, accounting for 59% (84%) of the effective stiffness at the in-plane (out-of-plane), antisymmetric resonance mode. We believe that the obtained QTF characterization results will pave the way for quantitative measurements of non-contact interaction forces in QTF-based AFM platforms, significantly improving the precision and reliability of nanoscale force measurements.

Heterodyne High-Harmonic Electrostatic Force Microscopy with Improved Spatial Resolution for Nanoscale Identification of Metallic/Semiconducting Carbon Nanotubes.

There are two main types of carbon nanotubes (CNTs): metallic and semiconducting. Naturally grown CNTs are randomly distributed, posing challenges in distinguishing between the two types. Here, a novel approach for nanoscale high-resolution imaging and identification of CNTs was introduced by incorporating the heterodyne technique into high-harmonic electrostatic force microscopy (HH-EFM) on an atomic force microscopy (AFM) platform. In the developed heterodyne HH-EFM, a more localized high-order gradient of tip-sample nonlinear interaction force is used as signal channels, resulting in an improved spatial resolution, compared to the conventional HH-EFM. Furthermore, the heterodyne HH-EFM also has the capability to visualize material carrier density and assess qualitative carrier transport performance. Our work not only presents a new approach to identifying/exploring electrical properties of low-dimensional nanomaterials but also provides a solution for optimizing resolution in long-range interaction-based functional AFM technologies.

Stiffness calibration of qPlus sensors at low temperature through thermal noise measurements.

Non-contact atomic force microscopy (nc-AFM) offers a unique experimental framework for topographical imaging of surfaces with atomic and/or sub-molecular resolution. The technique also permits to perform frequency shift spectroscopy to quantitatively evaluate the tip-sample interaction forces and potentials above individual atoms or molecules. The stiffness of the probe, k, is then required to perform the frequency shift-to-force conversion. However, this quantity is generally known with little precision. An accurate stiffness calibration is therefore mandatory if accurate force measurements are targeted. In nc-AFM, the probe may either be a silicon cantilever, a quartz tuning fork (QTF), or a length extensional resonator (LER). When used in ultrahigh vacuum (UHV) and at low temperature, the technique mostly employs QTFs, based on the so-called qPlus design, which actually covers different types of sensors in terms of size and design of the electrodes. They all have in common a QTF featuring a metallic tip glued at the free end of one of its prongs. In this study, we report the stiffness calibration of a particular type of qPlus sensor in UHV and at 9.8 K by means of thermal noise measurements. The stiffness calibration of such high-k sensors, featuring high quality factors (Q) as well, requires to master both the acquisition parameters and the data post-processing. Our approach relies both on numerical simulations and experimental results. A thorough analysis of the thermal noise power spectral density of the qPlus fluctuations leads to an estimated stiffness of the first flexural eigenmode of ≃2000 N/m, with a maximum uncertainty of 10%, whereas the static stiffness of the sensor without tip is expected to be ≃3300 N/m. The former value must not be considered as being representative of a generic value for any qPlus, as our study stresses the influence of the tip on the estimated stiffness and points towards the need for the individual calibration of these probes. Although the framework focuses on a particular kind of sensor, it may be adapted to any high-k, high-Q nc-AFM probe used under similar conditions, such as silicon cantilevers and LERs.

Calibration of the oscillation amplitude of quartz tuning fork-based force sensors with astigmatic displacement microscopy.

Quartz tuning forks and qPlus-based force sensors offer an alternative approach to silicon cantilevers for investigating tip-sample interactions in scanning probe microscopy. The high-quality factor (Q) and stiffness of these sensors prevent the tip from jumping to the contact, even at sub-nanometer amplitude. The qPlus configuration enables simultaneous scanning tunneling microscopy and atomic force microscopy, achieving spatial resolution and spectroscopy at the subatomic level. However, to enable precise measurement of tip-sample interaction forces, confidence in these measurements is contingent upon the accurate calibration of the spring constant and oscillation amplitude of the sensor. Here, we have developed a method called astigmatic displacement microscopy with picometer sensitivity.

Simultaneous detection of force and tunneling current in electrolyte solution by using qPlus sensor.

We have developed a sensor for simultaneous measurement of atomic force microscopy (AFM) and scanning tunneling microscopy (STM) under liquid environments. The sensor, which is based on the qPlus sensor, is equipped with an insulated conductive tip. Owing to its electrical insulation except for the tip apex, the developed sensor enabled simultaneous detection of tip-sample interaction force and tunneling current, suppressing the Faradaic leakage current. As a fundamental demonstration, we performed simultaneous AFM/STM imaging in an electrolyte solution by using the developed sensor.

The effect of sample viscoelastic properties and cantilever amplitudes on maximum repulsive force, indentation, and energy dissipation in bimodal AFM

Bimodal atomic force microscopy (AFM) uses two eigenfrequencies to map nanomechanical properties with high spatial and temporal resolution. To reliably map surface properties and to understand the links between experimental observables, energy dissipation, and viscoelastic properties considering the effects of nonconservative interaction forces is essential. To avoid damaging the sample, the maximum force between the tip and the surface and the maximum indentation of the tip into the sample needs to be controlled. In this work, we use both experiments and simulations to study how viscoelastic properties affect the cantilever response in bimodal AFM. We simulate the tip-sample interaction force, indentation, and energy dissipation for samples with different viscous properties. Under the tested operating conditions, we observe that more energy is dissipated in the higher eigenmode. The larger higher eigenmode free amplitude increases the energy dissipation in both eigenmodes. The larger energy dissipation increases the contrast of the bimodal AFM dissipation map. The simulations are cross-compared with experiments and similar trends are observed. This work is important for understanding and optimizing bimodal AFM measurements on samples with significant viscoelastic responses, such as cells, tissues, and polymers.

Hybrid mode atomic force microscopy of phase modulation and frequency modulation.

We propose hybrid phase modulation (PM)/frequency modulation (FM) atomic force microscopy (AFM) to increase the imaging speed of AFM in high-Q environments. We derive the relationship between the phase shift, the frequency shift and the tip-sample interaction force from the equation of motion for the cantilever in high-Q environments. The tip-sample conservative force is approximately given by the sum of the conservative force with respect to the phase shift in the PM mode and that with respect to the frequency shift in the FM mode. We preliminarily demonstrate that the hybrid PM/FM-AFM is a new and very promising AFM operation mode that can increase imaging speed.

Exploring Nanomechanical Properties of Soot Particle Layers by Atomic Force Microscopy Nanoindentation

In this work, an experimental investigation of the nanomechanical properties of flame-formed carbonaceous particle layers has been performed for the first time by means of Atomic Force Microscopy (AFM). To this aim, carbon nanoparticles with different properties and nanostructures were produced in ethylene/air laminar premixed flames at different residence times. Particles were collected on mica substrates by means of a thermophoretic sampling system and then analyzed by AFM. An experimental procedure based on the combination between semi-contact AFM topography imaging, contact AFM topography imaging and AFM force spectroscopy has been implemented. More specifically, a preliminary topological characterization of the samples was first performed operating AFM in semi-contact mode and then tip-sample interaction forces were measured in contact spectroscopy mode. Finally, semi-contact mode was used to image the indented surface of the samples and to retrieve the projected area of indents. The hardness of investigated samples was obtained from the force–distance curves measured in spectroscopy mode and the images of intends acquired in semi-contact mode. Moreover, the Young’s modulus was measured by fitting the linear part of the retraction force curves using a model based on the Hertz theory. The extreme force sensitivity of this technique (down to nNewton) in addition to the small size of the probe makes it extremely suitable for performing investigation of mechanical properties of materials at the nanoscale. The experimental procedure was successfully tested on reference materials characterized by different plastic behavior, e.g., polyethylene naphthalate and highly oriented pyrolytic graphite. Both hardness and Young’s modulus values obtained from AFM measurements for different soot particle films were discussed.

Confronting interatomic force measurements.

The quantitative interatomic force measurements open a new pathway to materials characterization, surface science, and chemistry by elucidating the tip-sample interaction forces. Atomic force microscopy is the ideal platform to gauge interatomic forces between the tip and the sample. For such quantitative measurements, either the oscillation frequency or the oscillation amplitude and the phase of a vibrating cantilever are recorded as a function of the tip-sample separation. These experimental quantities are subsequently converted into the tip-sample interaction force, which can be compared with interatomic force laws to reveal the governing physical phenomena. Recently, it has been shown that the most commonly applied mathematical conversion techniques may suffer a significant deviation from the actual tip-sample interaction forces. To avoid the assessment of unphysical interatomic forces, the use of either very small (i.e., a few picometers) or very large oscillation amplitudes (i.e., a few nanometers) has been proposed. However, the use of marginal oscillation amplitudes gives rise to another problem as it lacks the feasibility due to the adverse signal-to-noise ratios. Here, we show a new mathematical conversion principle that confronts interatomic force measurements while preserving the oscillation amplitude within the experimentally achievable and favorable limits, i.e., tens of picometers. Our theoretical calculations and complementary experimental results demonstrate that the proposed technique has three major advantages over existing methodologies: (I) eliminating mathematical instabilities of the reconstruction of tip-sample interaction force, (II) enabling accurate conversion deep into the repulsive regime of tip-sample interaction force, and (III) being robust to the uncertainty of the oscillation amplitude and the measurement noise. Due to these advantages, we anticipate that our methodology will be the nucleus of a reliable evaluation of material properties with a more accurate measurement of tip-sample interaction forces.

Neural Network for Surface-Profile Estimation of Atomic Force Microscope

This paper describes a methodology for implementing an identification algorithm for an atomic force microscope to estimate a surface profile of a sample. A microbeam of the atomic force microscope is modeled as an Euler-Bernoulli beam. A tip-sample interaction force used here is a piecewise function described by the attractive van der Waals force and the repulsive Derjaguin-Muller-Toporov force which can represent the indentation made by a tip of the microbeam into the sample surface. The identification of the instantaneous gap between the tip of the undeformed microbeam and the sample surface is implemented on line based on a trained input-output recurrent network. With the measured cantilevered-beam-tip motion supplied to the recurrent network, the recurrent network is going to compute the estimated gap. The approach being used in this study is in contrast to the conventional approach in that it is based on the signal in the time domain instead of in the frequency domain; therefore, the number of steps involved is fewer. When comparing the proposed approach with the adaptive-tracking controllers based on adaptive control Lyapunov functions, the proposed approach outperforms the adaptive-tracking controllers significantly. Whereas the adaptive-tracking controllers require much more measured signals to supply to the controllers and the parameter estimator. Instead, the proposed approach has to store two units in the tapped-delay-line memory while the identification algorithm is running.

A new insight into the vibrational modeling of contact mode for atomic force microscope beams in various immersion ambiances.

In this article, the vibrations of V-shaped beam as the most usable atomic force microscope (AFM) beam in contact mode has been modeled using finite element method. This work is a fundamental issue for contact resonance AFM. We have considered carbon tetrachloride (CCL4 ), methanol, acetone, water, and vacuum the immersion ambiences. For modeling of the beam dynamics, both of the Timoshenko and Euler-Bernoulli beam principles have been used. For presenting the best theoretical model all specifications for AFM beam and sample surface has been assumed. The outcomes show that by raising the interaction force between AFM beam and sample surface, the resonant frequency increases. By diluting the liquid surroundings, the resonant frequency and amplitude of frequency response functions (FRF) of vertical movement increase. The amplitude of FRF increases by raising the beam thickness and rectangular part breadth, but reduces by increasing the rectangular and tapered part lengths. The resonant frequency reduces by boosting the rectangular and tapered parts lengths and rectangular part width, but raises by increasing the beam thickness. Theoretical model in attendance and lack of tip-sample interaction force have been evaluated with experimental works for vacuum and water as the immersion ambiances. Results show good agreement.

Modeling of non-contact atomic force microscope with two-term excitations

The goal of this article is to study the dynamical behavior of atomic force microscope cantilever in its non-contact mode of operation. The lumped parameter model is used to construct the mathematical model of the cantilever. The tip of the cantilever is excited by two harmonic terms and is in interaction with the sample surface. The Van der Waals force, tip-sample interaction force, makes the system nonlinear. Using multiple scales method, the frequency response equation is found. The effects on the amplitude of excitations, the damping coefficient, and initial sample – tip distance is studied and presented as the results.

Calibration of T-shaped atomic force microscope cantilevers using the thermal noise method.

The tip-sample interaction force measurements in atomic force microscopy (AFM) provide information about materials' properties with nanoscale resolution. The T-shaped cantilevers used in Torsional-Harmonic AFM allow measuring the rapidly changing tip-sample interaction forces using the torsional (twisting) deflections of the cantilever due to the off-axis placement of the sharp tip. However, it has been difficult to calibrate these cantilevers using the commonly used thermal noise-based calibration method as the mechanical coupling between flexural and torsional deflections makes it challenging to determine the deflection sensitivities from force-distance curves. Here, we present thermal noise-based calibration of these T-shaped AFM cantilevers by simultaneously analyzing flexural and torsional thermal noise spectra, along with deflection signals during a force-distance curve measurement. The calibration steps remain identical to the conventional thermal noise method, but a computer performs additional calculations to account for mode coupling. We demonstrate the robustness of the calibration method by determining the sensitivity of calibration results to the laser spot position on the cantilever, to the orientation of the cantilever in the cantilever holder, and by repeated measurements. We validated the quantitative force measurements against the known unfolding force of a protein, the I91 domain of titin, which resulted in consistent unfolding force values among six independently calibrated cantilevers.

NONLINEAR VIBRATIONS OF THE IMMERSED DAGGER-SHAPED ATOMIC FORCE MICROSCOPE CANTILEVER IN DIFFERENT LIQUIDS STUDIED BY EXPERIMENTAL AND THEORETICAL METHODS

In this paper, the nonlinear dynamic behavior of an immersed dagger-shaped atomic force microscope cantilever in different liquids has been investigated for the first time. The Timoshenko beam theory, which considers rotatory inertia and shear deformation effects, has been used for modeling the cantilever. The nonlinear tip-sample interaction force has been modeled by using the Hertzian contact theory. Water, methanol, acetone, and carbon tetrachloride are considered as the immersion environments. In most cases, the softening behavior has been observed for the cantilever. The resonant frequency is found to decrease with an increase in the liquid viscosity. The experimental results have been compared with the theoretical predictions and are found to be in good agreement.

Dynamic analysis of atomic force microscope in tapping mode

The Atomic force microscope (AFM) is an enormously valuable tool in a wide variety of applications because of its function to depict in different mediums with the sub-nano-meter resolution, and also manipulating objects with nano-meter-scale features and measuring forces with better than pico-newton resolution. In this paper, the lumped parameter model is used to construct the mathematical model of the AFM cantilever. The cantilever tip, excited by the harmonic external force, is under the influence of the tip-sample interaction force. Since, we consider the AFM in the operation mode named dynamic contact mode, the Deryagin-Muller-Toporov (DMT) force is considered as the interaction force between the cantilever tip and the surface of the sample. DMT force causes non-linearity. To solve the equation of motion, the Van der Pol method is used to obtain the frequency response equation to investigate the non-linearity effect as well as the amplitude of the excitation on the response. The stability of steady state motion is investigated.

Analysis of Dynamic Behavior of V-Shaped Atomic Force Microscope Cantilever in Contact and Tapping Modes by Considering Various Immersion Surroundings

In atomic force microscope (AFM) as a powerful device for scanning the samples, a cantilever is used to sense the variations of its dynamic characteristics due to the tip–sample interaction. Theoretical models that can accurately simulate the surface-coupled dynamics of the cantilever are necessary for quantifiable and qualitative explanation and understanding of measured results. A good understanding of the dynamics of AFM cantilevers vibrating in liquid is needed for the interpretation of scanning images, selection of AFM operating conditions and evaluation of sample’s mechanical properties. In this paper, the amplitude of frequency response functions (FRF) of vertical and rotational movements for a V-shaped atomic force microscope beam immersed in various surroundings has been surveyed for the first time. For rising the precision of theoretical model, we have considered all needful details for the beam and sample. The amplitude of FRF of vertical and rotational movements and resonant frequency of beam have been surveyed by supposing cantilever thickness, breadth and length, the angle between cantilever and sample surface, tip height and normal and lateral tip–sample interaction force. In this study, carbon tetrachloride (CCL4), methanol, acetone, water and air have been considered as surroundings. The results show that an increase in the tip–sample interaction force considerably raises the amount of resonant frequency. By increasing the liquid viscosity, the amplitude of FRF for vertical and rotational movements and resonant frequency reduce. Moreover, the amplitude of FRF of vertical and rotational movements is reduced by raising the rectangular and tapered parts lengths, but increased by raising the rectangular part breadth and cantilever thickness. The resonant frequency goes down by increasing the rectangular and tapered parts lengths and rectangular part breadth, but increases by rising the cantilever thickness. In this paper, we have tried to model the realistic dynamic behavior of V-shaped AFM beam in contact and tapping modes with the most accuracy. Results show good agreement. Based on the experimental results, the present theoretical model can forestall better the realistic behavior of tapping mode than the contact mode for V-shaped AFM cantilever. Based on the complexity of the V-shaped AFM cantilever, this study has been done for the first time in both of the contact and tapping modes.

Nanomechanical 3D Depth Profiling of Collagen Fibrils in Native Tendon

Connective tissue displays a large compositional and structural complexity that involves multiple length scales. In particular, on the molecular and the nanometer level, the elementary processes that determine the biomechanics of collagen fibrils in connective tissues are still poorly understood. Here, we use atomic force microscopy (AFM) to determine the three-dimensional (3D) depth profiles of the local nanomechanical properties of collagen fibrils and their embedding interfibrillar matrix in native (unfixed), hydrated Achilles tendon of sheep and chickens. AFM imaging in air with controlled humidity preserves the tissue's water content, allowing the assembly of collagen fibrils to be imaged in high resolution beneath an approximately 5-10 nm thick layer of the fluid components of the interfibrillar matrix. We collect pointwise force-distance (FD) data and amplitude-phase-distance (APD) data, from which we construct 3D depth profiles of the local tip-sample interaction forces. The 3D images reveal the nanomechanical morphology of unfixed, hydrated collagen fibrils in native tendon with a 0.1 nm depth resolution and a 10 nm lateral resolution. We observe a diversity in the nanomechanical properties among individual collagen fibrils in their adhesive and in their repulsive, viscoelastic mechanical response as well as among the contact points between adjacent collagen fibrils. This sheds new light on the role of interfibrillar bonds and the mechanical properties of the interfibrillar matrix in the biomechanics of tendon.

Experimental and theoretical studies of frequency response function of dagger‐shaped atomic force microscope cantilever in different immersion environments

In this study, the amplitude of frequency response functions of vertical and rotational displacements and resonant frequency of a dagger-shaped atomic force microscope cantilever have been investigated. To increase the accuracy of theoretical model, all necessary details for cantilever and sample surface have been taken into account. In this paper, carbon tetrachloride (CCL4 ), methanol, acetone, water and air have been considered as the environments. In the most cases, presence and absence of tip-sample interaction force have studied. For a sample cantilever immersed in air, both of the Euler-Bernoulli and Timoshenko beam theories have been compared. The results indicate that the tip-sample interaction force raises the resonant frequency. Increasing the liquid viscosity leads to a decrease in the resonant frequency and the amplitude of frequency response functions of vertical and rotational displacements. Increasing the rectangular and tapered parts lengths, decreases the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements. By increasing the cantilever thickness the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements increases. Theoretical model for air and water has been compared with experimental work. Results show good agreement.

Observer Design for Topography Estimation in Atomic Force Microscopy Using Neural and Fuzzy Networks

In this study, a novel artificial intelligence-based approach is presented to directly estimate the surface topography. To this aim, performance of different artificial intelligence-based techniques, including the multi-layer perceptron neural, radial basis function neural, and adaptive neural fuzzy inference system networks, in estimation of the sample topography is investigated. The results demonstrate that among the designed observers, the multi-layer perceptron method can estimate surface characteristics with higher accuracy than the other methods. In the classical imaging techniques, the scanning speed of atomic force microscope is restricted due to the time required by the oscillating tip to reach the steady state motion while the closed-loop controller tries to maintain the tip vibration amplitude at a set-point value. To address this issue, we have proposed an innovative imaging technique that not only eliminates the need to a closed-loop controller but also estimates the surface topography very quick and accurate compared to the conventional imaging method. Also, the proposed technique is capable of simultaneous estimation of the topography, Hamaker parameter, and the tip-sample interaction force.