Geometric parameters effect of the atomic force microscopy smart piezoelectric cantilever on the different rough surface topography quality by considering the capillary force

Nowadays, the atomic force microscopy (AFM) is widely used in the nanotechnology as a powerful nano‐robot. The surface topography in Nanoscale is by far one of the most important usages of the AFM device. Hence, in this article, the vibration motion of a piezoelectric rectangular cross‐section micro‐cantilever (MC) which oscillates in the moist environment has been examined based on the Timoshenko beam theory. After extracting the MC governing equations according to Hamilton's principle, the finite element method has been used to discretize the motion equations. The surface topography has been simulated for various roughness forms in the tapping and non‐contact modes by considering the effects of the Van der Waals, capillary and contact forces. Also, the experimental results obtained from the glass surface topography have been simulated. The results illustrate that the time delay in higher natural frequencies in the tapping mode is shorter in comparison with the non‐contact mode, especially, for the lower natural frequencies. The sensitivity analysis of the natural frequencies, topography depth and time delay have been simulated. Results indicate that the most effective parameter is the MC length. In the first mode, the first section length has the highest effect on the surface topography time delay, also, in the second vibration mode; the most effective parameter on the time delay is the MC tip length based on the simulation results.     

The effect of surface roughness on the vibration behavior of AFM piezoelectric MC in the vicinity of sample surface in air environment based on MCS theory

Recent developments in the field of piezoelectric materials have led to the increasing use of piezoelectric materials in a variety of Atomic Force Microscopy (AFM). Utilizing piezoelectric layer as a sensor and actuator not only reduces the size of microscope but also enhances the quality of surface topography in Micro and Nano scales. In the current study, the effect of surface roughnesson the vibration behavior of AFM piezoelectric micro cantilever (MC) has been investigated in Micro and Nano scales according to the types of the surface roughness. Furthermore, the micro cantilever modelling has been schemed based on the Modified Couple Stress (MCS) theoryin order to model the vibration amplitude of AFM piezoelectric MC that precisely indicates the measured surface roughness. Besides, according to the various modelling of surface roughness, the effect of roughness radius on the minimum and maximum amplitude of Piezoelectric MC has been studied based on the geometry of roughness in air environment. In this environment, the effect of environmental forces including van der Waals, Capillary and contact forces on the vibration amplitude of MC forms the basis of surface topography which has, also, been studied in this article. Moreover, the present study intends to investigate the effect of surface roughness on the vibrating amplitude of MC in both the Tapping and Non-Contact Modes.     

Analysis of the atomic force microscopy vibration behavior using the Timoshenko theory by multi‐scale method in the air environment

This article deals with the modeling and simulation of the vibration behavior of piezoelectric micro‐cantilever (MC) based on the Timoshenko theory and using multi‐scale (MTS) method in the air environment. In this regard, the results are compared with the previous literature, such as the finite element method and the MTS method. The analysis of the piezoelectric MC vibrating behavior is investigated in a dynamical mode including non‐contact and tapping modes. The dynamics of this system is affected by interferential forces between probe tip and sample surface, such as van der Waals, capillary, and contact forces. According to the results, the forces applied to the probe tip reduce the amplitude and the resonance frequency. The simulation of surface topography in non‐contact mode and tapping for rectangular and wedge‐shaped roughness in the air environment are presented. Various experiments have been conducted in Ara research Company using the atomic force microscopy device in the amplitude mode. In the NSC15 Cantilever, the first natural frequency is derived from the results of the MC simulation based on Timoshenko beam theory, the practical results are 295.85 and 296.12 kHz, and the error rate is 0.09; at higher natural frequencies, the error rate has been increased. The γ _f coefficient is a measure of the nonlinear effects on the system; the effect of the piezoelectric length and width on γ _f coefficient is also investigated.     

Effects of geometrical dimensions and liquid properties on frequency response of resonating microcantilevers in the vicinity of a surface

Frequency response of an atomic force microscopy cantilever immersed in liquid near a surface strongly depends on the hydrodynamic forces specially the squeezed film damping, mechanical properties of the liquid including the dynamic viscosity and the density and the geometrical dimensions of the cantilever. For a slightly inclined magnetically oscillated cantilever with the approximate hydrodynamic forces acting on it, the analytical solution of the equation of motion has already been acquired. In this paper, the effects of geometrical dimensions of the cantilever on the resonance frequency, the motion amplitude and the quality factor are observed and then any increase in the kinematic viscosity of the liquid is studied through the simulation of the oscillatory motion of the cantilever. The acquired amplitude–frequency curves indicate that with an appropriate proportion between the cantilever dimensions, it is possible to optimize the quality factor for extremely small tip-sample separations. Also, if the thickness is increased and the width is reduced with the cross section area being held constant, the resonance will occur at higher frequency and the quality factor will be enhanced. Adding glycerol to water will result in the reduction of resonance frequency of the cantilever near the surface due to the viscous friction and squeezed film damping. Consequently the quality factor is decreased as a result of viscosity increase in the simulations.     

FEM analysis of the vibrational motion of oblique piezoelectric microcantilever in the vicinity of a sample surface in liquid

This article examines an oblique Microcantilever (MC) with an extended piezoelectric layer in liquid. The study of hydrodynamic force in MC which has been floated in viscous fluid is considered as paramount importance. To model the Vibrational motion, the Hamilton's principle has been used. For this purpose, the Vibrational motion equation has been modeled by considering the continuous beam based on the Euler–Bernoulli beam theory in liquid. Furthermore, using the Galerkin method and the Newmark algorithm, the differential equations of the MC has been solved. In this modeling, the inter-atomic forces between the MC tip and the sample surface have been considered in addition to the hydrodynamic and squeeze forces. The simulation results illustrate a reduction in the sensitivity of the vibrational motion under the effect of the squeeze force during the angularization of the MC. Moreover, the results illustrate that by reducing the MC distance from the sample surface, the Vibration amplitude decreases due to the increase in the fluid squeeze force. At the end, it has been shown that the time delay in sample surface topography in liquid substantially decreases in comparison with the air.     

Modeling and simulation of AFM cantilever with two piezoelectric layers submerged in liquid over rough surfaces

In this paper, the vibration of an atomic force microscope (AFM) cantilever in tapping mode with two whole piezoelectric layers submerged in liquid medium is investigated. In the performed modeling, the sample surface has been considered as rough, and to show these surface asperities, two models of Rumpf and Rabinovich have been employed for analyzing the attractive Van der Waals force. This paper has been organized in two sections. The first section deals with the functioning of cantilever over rough surfaces, which accompanies the changes of the attractive Van der Waals force, and the second section involves the changes in the Van der Waals force which lead to a change in the liquid medium. The cantilever is totally submerged in the liquid. To show the effect of liquid on cantilever, first, only the cantilever tip is immersed in the liquid and it is dynamically analyzed. Then, the cantilever is totally submerged and then taken out of the liquid, so that the additional mass and damping of the cantilever could be calculated. In these two manners of cantilever immersion in liquid, the effects of the added mass and damping on the cantilever can be measured. When a cantilever vibrates totally in liquid, since the mass and damping of the liquid that is present on the cantilever cannot be determined, first, the cantilever's natural frequency in liquid is estimated in the laboratory and then by using this frequency and the cantilever stiffness (which is not medium-dependent and is always considered as constant), the additional mass and damping of the cantilever are determined.