Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method (original) (raw)
Related papers
MODELING AND DYNAMIC ANALYSIS OF ATOMIC FORCE MICROSCOPE BASED ON EULER-BERNOULLI BEAM THEORY
2009
Operation of atomic force microscope in dynamic mode has received great attention due to its ability to image compliant materials and also due to the fact that it can prevent the tip and sample damages during scanning. In this paper a model is proposed for AFM microcantilever-tip system based on Euler-Bernoulli beam theory and is solved numerically in order to study the behavior of a continuous cantilever beam in dynamic mode subject to changes in tip mass, cantilever density, length and the interaction force between the cantilever-tip and the sample. This is accomplished by linearizing the surface coupling force.
Numerical modelling of electrostatic force microscopes considering charge and dielectric constant
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2009
Purpose-The purpose of this paper is to present a hybrid numerical simulation approach for the calculation of potential and electric field distribution considering charge and dielectric constant. Design/methodology/approach-Each numerical method has its own advantages and disadvantages. The idea is to overcome the disadvantages of the corresponding numerical method by coupling with other numerical methods. An augmented finite element method (FEM), linear FEM and boundary element method are used with an efficient coupling. Findings-The simulation model of microstructured devices is not so simple. During the simulation various types of problems will occur. It is found that by using several numerical methods these problems can be overcome and the calculation can be performed efficiently. Research limitations/implications-The present approach can be applied in 2D cases. But, in 3D cases the calculation of augmented FEM in a spherical coordinate becomes quite elaborate. Practical implications-The proposed hybrid numerical simulation approach can be applied for the simulation of the electrostatic force microscope (EFM) which is a very high-resolution measuring tool in nanotechnology. This approach can be applied also to other micro-electro-mechanical systems. Originality/value-Since the scanning process of the EFM is dynamic, it requires the updating of the FEM mesh in each calculation time step. In the present paper, the mesh updating is achieved by an arbitrary Lagrangian-Eulerian (ALE) method. The proposed numerical approach can be applied for the simulation of the EFM including this remeshing algorithm ALE.
Multimode and multitone analysis of the dynamic mode operation of the Atomic Force Microscope
2013 American Control Conference, 2013
This article investigates the multimode model of the cantilever beam during probe based imaging. It develops a framework to quantify the effects of different material properties like dissipativity and stiffness in a near tapping mode operation of Atomic Force Microscope (AFM), which is the primary mode of imaging soft matter, when excitation consists of more than one sinusoids. Averaging theory forms an important basis and provides the theoretical foundations. Effect of dissipative and stiffness properties of the sample on the forces experienced by probe is modeled as changes in parameters of an equivalent linear time invariant model, of the cantileversample system. It is shown that this model can be extended to the case when multiple modes of the cantilever participate in the nonlinear interaction with the sample forces.
Simulation of atomic force microscopy operation via three-dimensional finite element modelling
Nanotechnology, 2009
Numerical modelling of atomic force microscopy cantilever designs and experiments is presented with the aim of exploring friction mechanisms at the microscale. As a starting point for this work, comparisons between finite element (FE) models and previously reported mathematical models for stiffness calibration of cantilevers (beam and V-shaped) are presented and discrepancies highlighted. A colloid probe (comprising a plain cantilever on which a particle is adhered) model was developed, and its normal and shear interaction were investigated, exploring the response of the probe accounting for inevitable imperfections in its manufacture. The material properties of the cantilever had significant impact on both the normal response and the lateral response. The sensitivity of the mechanical response in both directions was explored and it was found to be higher in terms of normal rather than lateral sensitivity. In lateral measurements, generic response stages were identified, comprising a first stage of twisting, followed by lateral bending, and then slipping. This was present in the two cantilever types explored (beam and V-shaped). Additionally, a model was designed to explore the dynamic sensitivity by comparing the simulation of a hysteresis loop with a previously reported experiment, and the results show good agreement in the response pattern. The ability to simulate the scan over an inclined surface representing the flank of an asperity was also demonstrated.
2013
In this paper, simulation results for the electrostatic force between an Atomic Force Microscope (AFM) sensor and the surface of a dielectric are presented for different bias voltages on the tip:. The aim is to analyse force-distance curves as AFM detection mode for electrostatic charges. The sensor is composed of a cantilever supporting a conical tip terminated by a spherical apex; the effect of the cantilever is neglected here. Our model of force curve has been developed using the Finite Volume Method. The scheme is based on the Polynomial Reconstruction Operator -PRO-scheme. First results of the computation of electrostatic force for different tipsample distances, 0 to 600 nm, and for different DC voltage stress applied to the tip, 6 to 25 V, are shown and compared with experimental data in order to validate our approach.
Physical Review B, 2003
Dynamic force curves of an atomic force microscope in the presence of attractive van der Waals and electrostatic forces are analytically treated using a variational method taking into account nonlinear tip-sample coupling. This approach allows describing and understanding the motion of a voltage-biased tip observed in experimental approach-retract curves in dynamic mode. The solutions predict a hysteretic behavior in the force curves for both amplitude and phase of oscillation. This hysteresis diminishes and disappears with increasing tip-sample voltage. The tip-surface system is modeled as a plane capacitor with an effective area of interaction. The analytical solution clearly accounts for the apparent height measured in topographical scanning due to the presence of charges on the sample. It also furnishes an estimation of the quantity of excess charges on the sample surface measured in the experiment. There, an estimated 360 electrons were injected into a SiO 2 surface. Additionally, at the onset of electrostatic coupling, an abrupt transition from intermittent contact to noncontact regime is experimentally evidenced by a jump of the phase from one branch of solution to the other. This phase contrast represents an easy way to distinguish and to choose between intermittent contact and noncontact regime.
Modeling forces between the probe of atomic microscope and the scanning surface
Neural Computing and Applications, 2018
Atomic force microscope (AFM) is usually used to study the properties and surface structure of nanoscale materials. AFMs have three major abilities: force measurement, imaging, and manipulation. In the force measurement, AFM can be used to measure the forces between the probe and the sample as a function of their mutual separation. AFM compared to scanning electron microscope has a single image scan size; also the scanning speed of AFM is also a limitation. AFM images can also be affected by nonlinearity, hysteresis, creep of the piezoelectric material, and cross talk between the x, y, and z axes that may require software enhancement and filtering. Due to the nature of AFM probes, they cannot normally measure steep walls or overhangs in surface. In this study, the force between the Probe of Atomic Microscope and the surface is simulated by using force measurement ability of AFM and artificial neural network. The experimental data are used for training of artificial neural networks. The best model was found to be a feed-forward backpropagation network, with Logsig, Tansig and Tansig transfer functions in successive layers, respectively, and 3 and 2 neurons in the first and second hidden layers. According to the results, the proposed neural network is well capable of modeling the behavior of AFM probes in noncontact mode.
Design of mechanical components for vibration reduction in an atomic force microscope
Review of Scientific Instruments, 2011
Vibration is a key factor to be considered when designing the mechanical components of a high precision and high speed atomic force microscope (AFM). It is required to design the mechanical components so that they have resonant frequencies higher than the external and internal vibration frequencies. In this work, the mechanical vibration in a conventional AFM system is analyzed by considering its mechanical components, and a vibration reduction is then achieved by reconfiguring the mechanical components. To analyze the mechanical vibration, a schematic of the lumped model of the AFM system is derived and the vibrational influences of the AFM components are experimentally examined. Based on this vibration analysis, a reconfigured AFM system is proposed and its effects are compared to a conventional system through a series of simulations and experiments.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2018
Characterization and analysis of sample surfaces with nanometer order topologies is essential to study properties such as roughness, resistance, molecular arrangements, failure, among others. Therefore, in recent decades, atomic force microscope (AFM) has become an essential tool, since it has the ability to get 3D nanometer order images of surfaces from some predefined kind of interaction. In order to understand the dynamics and improve the operation of base-cantilever-tip-sample AFM systems, several mathematical models were proposed in the literature. However, it seems that there is still a need of representative and parametric models able to capture material and geometric properties of the cantilever beam and piezoceramic base actuator. Hence, this work focuses on the development and analysis of a parametric model capable of properly representing the dynamics of an AFM cantilever beam when subjected to realistic operation conditions, using a finite element model for the cantilever beam and accounting for translational and rotational inertia of the probe tip and for the piezoceramic actuator that excites and controls the beam motion. All material and geometrical properties for the system (cantilever beam, probe tip and piezoceramic actuator) can be parametrized. Experimental SEM images and frequency responses of a real AFM cantilever beam are used to verify the model and also to define its parameters with very satisfactory results. A dynamic analysis of the cantilever beam when subjected to tip-sample nonlinear interaction forces is performed to develop a proper reduced-order model. The interaction forces were modeled using Lennard Jones potentials. Then, an analysis of the dynamic response of the cantilever beam for varying tip-sample initial distances is performed. Besides the appearance of the expected nonlinear behavior due to the tip-sample interaction forces, it is observed that the closer the sample is to the beam tip, the smaller is the tip displacement amplitude. Based on this observation, an analysis is performed to assess the correlation between the tip displacement and the surface topology of a diamond sample with satisfactory results.
Variational treatment of electrostatic interaction force in atomic force microscopy
Zeitschrift für angewandte Mathematik und Physik, 2007
In this paper we introduce the mathematical model for the electrostatic interaction force between an atomic force microscope (AFM) tip and a sample surface. We formulate the electrostatic potential problem in Sobolev spaces and find the corresponding weak solution in terms of the integral potential, which can be approximated numerically by generalized Fourier series and used to find the interaction force between an AFM tip and a sample surface. The formulation of the problem in a weak (Sobolev) space setting allows us to determine the force for AFM tips of arbitrary shape. Efficiency of the method is illustrated using numerical examples for the spherical and tetrahedral AFM tips.