تجزیه و تحلیل حساسیت از دستکاری فشار نانوذرات توسط AFM در یک فرایند قوی کنترل شده

This paper investigates the sensitivity of nanoparticle parameters in a robust controlled process, by a compatible nanomanipulation model consisting of all effective phenomena in nanoscale. The dynamic model of nanoparticle displacement utilizes the Lund–Grenoble (LuGre) friction model, since it demonstrates pre-slip displacement, friction delay, various forces of failure and the stick-slip movement, with respect to other presented models. Also, the interaction force between nanoparticle and AFM cantilever tip are modeled by using the Derjaguin model. Sliding mode control (SMC) approach is used to provide the desired substrate motion trajectory, despite the challenges in the piezoelectric substrate motion control, consisting of thermal drift, hysteresis, and other uncertainties. In this paper, the dynamic model of nanoparticle manipulation is expressed to determine the nanoparticle behavior for substrate movement with desired trajectory and the effect of pre-process selections of the result of the manipulation. Depending on obtained diagrams for parameters sensitivity, the prediction of manipulation result is more precise, and also this is effective on choosing of proper initial condition and parameter selection in pushing purposes. Finally, it can be used to adjust proper pushing time and input for an accurate and successful pushing and assembly. It also provides a real-time visualization during micro/nanomanipulation and increases complexity of the resulting created structures.

Nanomanipulation deals with the controlled manipulation of micro/nano-objects and it is the basic approach for building useful devices from nanoscale components such as atoms/molecules in top-down or bottom-up fabrication techniques [1]. In this way, some researchers have focused on modeling and its applications to motion analysis of nanoparticles or the probe tip [2], [3], [4], [5] and [6]. The AFM probe consists of a cantilever and a tapered tip, and it is used as a manipulator. Manipulation of nanoparticles has been widespread of interest for last years, and dynamic modeling is a basic tool for understanding the pushing procedure at real time. The initial model for pushing was provided by Falvo et al., but in this model, the forces due to the scale changing were not considered [2]. The first model that considered the surface forces and contact deformations was proposed by Sitti and Hashimoto [3]. It used JKR theory of contact mechanics in which a discrete system model is used to design teleoperated control of pushing. Tafazzoli and Sitti presented a more satisfactory model for the nanoparticles’ pushing process [4]. They tried to simulate a real-time nanomanipulation. Using this model, Korayem and Zakeri studied pushing of nanoparticles and developed the model to obtain the sensitivity of pushing critical force and critical time due to variations of geometrical and material parameters [5]. In later models, researchers have presented some different approaches to fulfill the prior deficiencies. Being more focused on the interaction forces between AFM probe, sample and tip displacement modeling, recent studies are in a better agreement with experimental results. Babahosseini et al. has solved the interaction force's problem, but the lack of exactness in cantilever modeling for more desirable trajectories of substrate displacement still remains [6]. Landolsi and Ghorbel provided a new modeling of tip displacement that is much more compatible with the dynamics of nanoparticle, and the results of this kind of modeling is more reliable [7]. On the other hand, since the AFMs were made for imaging with constant speed of substrate movement, there has been always a tendency to perform this process with such an approach from the early works [3] and [4]. However, the proficiency of manipulation using AFM requires a more flexible method which can undergo any desired controlled motion. In this work, AFM probe and nanoparticle dynamics are modeled according to the most compatible and exact approaches and later, interaction and friction forces are investigated and modeled. Then, the frequent used piezoelectric actuated stage model is expressed and a robust observer–base controller for displacement in nano scale is designed, using sliding mode control approach (SMC), considering all probable uncertainties and manipulation requirements. Then, the behavior of nanoparticle in this process, regarding to contact and friction forces is studied under the dynamic model of probe and particle. Dependency of friction force and other variables to the substrate velocity, nanoparticle size and material, cantilever types and control parameters are analyzed and compared.

A modified model for nanoparticle displacement in AFM pushing manipulation was presented in this paper, which is suitable for calculations of manipulation parameters for an inconstant substrate motion. In order to present a precise substrate movement trajectory with the least possible error, considering the elements affecting the piezoelectric substrate spatial resolution, a VSC controller was chosen to compensate the negative effect of these elements. Indefinite parameters in manipulation process, hysteresis and drift are kind of uncertainties and disturbances improved by designing a robust sliding mode controller. This controller used an observer to calculate the immeasurable state of velocity in substrate motion to use it as input voltage of the piezoelectric substrate. After getting the expected result from presented control method, manipulation process and sensitivity of parameters were deeply investigated. Implementation of LuGre friction model provided the actual stick-slip displacement pattern by means of the presented dynamic model of nanoparticle and AFM probe. Providing the proper results regarding to the experimental data, other parameters in nano scale were calculated and sensitivity of nanoparticle dynamics were studied. Considering the velocity of substrate movement, increment of manipulation velocity resulted in decrease of parameters maximum and the increase of minimums after the movement starts. Then, the effect of nanoparticle size and sensitivity of displacement and contact variables to the variations was studied. According to the results of this study, smaller particle had a swifter movement; as the increase of nanoparticle mass and radius resulted in decrease of stick-slip motion frequency, but the effect on contact force and penetration depth extremums was insignificant. Next, the changes of nanoparticle substance on manipulation process were investigated. The manipulation was simulated with mentioned parameters of different materials, and had corresponding effect on manipulation variables. Since manipulation is procured by AFM cantilever and tip, cantilever type selection and the effect of cantilever stiffness was studied later. The sensitivity of friction force, contact force, penetration depth and contact load to these changes was investigated and the nanoparticle movement trajectory and critical time were calculated. Finally, the changes of λ on both substrate motion and nanoparticle displacement were presented and discussed. The presented automated manipulation process using sliding mode controller, performs the manipulation task with the required robustness. We believe that, this method opens a new chapter, which could be followed by some experiments that will show the effectiveness and exactness of this approach better. Different displacement goals are easily selected with this approach. According to the presented modeling of the whole process, prediction of the nanoparticle behavior and the changes in other parameters during the process are possible, and our idea is that, this approach provides a step forward to the understanding of nano world parameters and forces, besides the real process, and before the process is performed. This provides the chance of controlling the process according to the desired variations on parameters for special applications, and to fabricate more complex structures in an accurate and successful pushing manipulation in future works.