13 research outputs found
Dynamics and control of Atomic Force Microscopy
No full textThe technique of Atomic Force Microscopy (AFM) is one of the major inventions of the twentieth century which substantially contributed to our understanding of the nanoscale world. In contrast to other microscopy techniques, the AFM does not operate based on the electromagnetic waves, but nano-mechanical interactions between the sample surface and a sharp probe. Therefore, its resolution is not fundamentally limited to the diffraction limit of light, but the sharpness of the probe tip which can be as small as a few atoms. The images and data obtained by AFM have had crucial importance for the scientists in the fields of biology, material science, and experimental physics. However, AFM experiments have always involved some challenges. Particularly, the limited imaging speed, and the probability of damaging the samples hinder scientists from extracting the necessary information on the samples. Besides its applications as a research tool, the AFM could potentially solve some of the challenges in semiconductor industry as a metrology and inspection tool, however, the aforementioned limitations are even more restrictive for any industrial use. Therefore, it is imperative to develop apparatus and methods which can increase the speed and reliability of AFM. In this thesis, we try to understand the physics of AFM and contribute to its development towards a potential industrial and clinical tool, from the perspective of dynamics and control of its cantilever.Computational Design and Mechanic
Identification of Probe of an Atomic Force Microscope Using Curve Fitting
No full textIn recent years the Tapping Mode-Atomic Force Microscope (TM-AFM) has become one of the most important tools for imaging on the nanometer scale. In comparison with other contemporary technologies, the AFMs have been able to obtain atomic resolution both in high vacuum and liquid environments thus affirming their supremacy. The AFM can be perceived as a combination of a mechanical profilometer, where mechanical springs are used to sense the forces, and a Scanning tunneling microscope, where piezo-electric transducers are used for scanning. The AFM is widely used to generate a topographical image of the sample surface and also to study certain characteristics of the sample. The latter is aided by measuring the forces between the sample surface and the tip of the probe.The non-linear, rapidly changing and hysteretic behavior of the tip-sample forces makes their accurate estimation extremely difficult in dynamic AFM. Moreover, the cantilever probe responds to an average of the different forces acting on the probe tip. Since several permutations of different forces can give the same periodic average, the accurate estimation of each of these forces has been evidently impossible. However, some probes exist for which the motion of the cantilever consists of super harmonic components of the tip-sample forces which provide more information about the tip-sample forces. Nevertheless the construction of these cantilevers is challenging and time consuming. Knowledge of the dynamic properties of the cantilever facilitates one to study its behaviour to a particular input. Since different forces act at different tip sample distances, a more mathematical approach towards tip-sample force estimation which includes the dynamic characteristics of the cantilever is necessary. The accurate knowledge of the cantilever dynamics is extremely important for precise estimation of tip-sample forces, deduction of mechanical properties, controller synthesis etc. Therefore in this research, the techniques to identify the state space matrices is explored. One, rather old but an immensely useful identification method are the black box identification techniques. These techniques can be used to accurately estimate the fully parameterized state space matrices of the system. The main difficulty arises in estimating these parameters specially in the absence of one of the inputs (tip-sample interactions). In this thesis research, an algorithm is developed to identify the fully parameterized state space matrices. A secondary cantilever of very high fundamental resonance frequency is used as a force sensor. This force sensor set up along with the periodic property of the tip-sample forces during TM-AFM is used to reconstruct the tip-sample interaction forces. Using the estimated tip-sample forces, a transfer function between the cantilever deflection and the estimated force is identified using a curve fitting technique. The curve fitting technique uses iterative least squares to reduce the two norm between the experimental frequency response and the frequency response estimated using the identified transfer function.Mechanical Engineering | Systems and Contro
Topology optimization of constrained eigenfrequencies
No full textHigh performance machines such as those used in the semiconductor industry, robotics or racing engines have lots of fast moving parts. The dynamic properties of these moving parts are crucial to the performance of the machine. Therefore these moving parts have to be carefully designed which is often a very time consuming iterative process. In this thesis a general method to optimize the dynamic properties of a structure utilizing topology optimization is investigated. More specifically, the method will be focused on the optimization of eigenfrequencies whilst achieving specific ratios between eigenfrequencies,as dynamic performance requirements are often linked to such criteria. We refer to this class of topology optimization problems as problems involving constrained eigenfrequencies. A particular case of interest is the desired multiplicity of two or more eigenfrequencies, that is a ratio of 1. Several crucial aspects of the topology optimization of eigenfrequencies are investigated, these are the material interpolation methods, mode tracking techniques, multiplicity problems and obtaining a discrete design. By comparing different material interpolation methods, a clear view on the effects of different methods is obtained, leading to solid arguments for selecting a linear material interpolation method for topology optimization of eigenfrequencies. A simple yet effective method of tracking theeigenmodes during the optimization process combined with a solution for the multiplicity problems is presented and verified to show similar results as a more complex analytical approach. A new method of obtaining a discrete design without applying penalization or modification of the eigenvalue problemhas been developed using a modified objective function. This method shows promising results and is a good candidate for replacing the material interpolation penalization method. By combining these results, a general and capable framework for the topology optimization of constrained eigenfrequencies is obtained. Using the presented framework, a practical application of the method is given by the design of a cantilever used in an atomic force microscope. Feasible and well-performing designs have been generated, both from a functional and manufacturing point of view.Mechanical Engineering | Precision and Microsystems Engineerin
Transient Tip-Sample Interactions in High-Speed AFM Imaging of 3D nano structures
No full textThe maximum amount of repulsive force applied to the surface plays a very important role in damage of tip or sample in Atomic Force Microscopy(AFM). So far, many investigations have focused on peak repulsive forces in tapping mode AFM in steady state conditions. However, it is known that AFM could be more damaging in transient conditions. In high-speed scanning, and in presence of 3D nano structures (such as FinFET), the changes in topography appear in time intervals shorter than the response time of the cantilever. In this case, the tip may crush into the sample by exerting much higher forces than for the same cantilever-sample distance in steady state situations.In this study the effects of steep upward steps in topography on the tip-sample interactions have been investigated, and it has been found that the order(s) of magnitude higher forces can be applied. The information on the worst case scenario obtained by this method can be used for selection of operation parameters and probe design to minimize damage in high-speed imaging. The numerically obtained results have been verified with the previous works in steady state regime. Based on this investigation the maximum safe scanning speed has been obtained for a case study
Minimizing tip-sample forces and enhancing sensitivity in atomic force microscopy with dynamically compliant cantilevers
No full textDue to the harmonic motion of the cantilever in Tapping Mode Atomic Force Microscopy, it is seemingly impossible to estimate the tip-sample interactions from the motion of the cantilever. Not directly observing the interaction force, it is possible to damage the surface or the tip by applying an excessive mechanical load. The tip-sample interactions scale with the effective stiffness of theprobe. Thus, the reduction of the mechanical load is usually limited by the manufacturability of low stiffness probes. However, the one-to-one relationship between spring constant and applied force only holds when higher modes of the cantilever are not excited. In this paper, it is shown that, by passively tuning higher modes of the cantilever, it is possible to reduce the peak repulsive force.These tuned probes can be dynamically more compliant than conventional probes with the same static spring constant. Both theoretical and experimental results show that a proper tuning of dynamic modes of cantilevers reduces the contact load and increases the sensitivity considerably.Moreover, due to the contribution of higher modes, the tuned cantilevers provide more information on the tip-sample interaction. This extra information from the higher harmonics can be used for mapping and possibly identification of material properties of samples
Topology optimization involving constrained eigenfrequencies
No full textHigh performance machines such as those used in the semiconductor industry, robotics or racing engines have lots of fast moving parts. The dynamic properties of these moving parts are crucial to the performance of the machine. Therefore these moving parts have to be carefully designed which is often a very time consuming iterative process. In this thesis a general method to optimize the dynamic properties of a structure utilizing topology optimization is investigated. More specifically, the method will be focused on the optimization of eigenfrequencies whilst achieving specific ratios between eigenfrequencies,as dynamic performance requirements are often linked to such criteria. We refer to this class of topology optimization problems as problems involving constrained eigenfrequencies. A particular case of interest is the desired multiplicity of two or more eigenfrequencies, that is a ratio of 1. Several crucial aspects of the topology optimization of eigenfrequencies are investigated, these are the material interpolation methods, mode tracking techniques, multiplicity problems and obtaining a discrete design. By comparing different material interpolation methods, a clear view on the effects of different methods is obtained, leading to solid arguments for selecting a linear material interpolation method for topology optimization of eigenfrequencies. A simple yet effective method of tracking the eigenmodes during the optimization process combined with a solution for the multiplicity problems is presented and verified to show similar results as a more complex analytical approach. A new method of obtaining a discrete design without applying penalization or modification of the eigenvalue problem has been developed using a modified objective function. This method shows promising results and is a good candidate for replacing the material interpolation penalization method. By combining these results, a general and capable framework for the topology optimization of constrained eigenfrequencies is obtained. Using the presented framework, a practical application of the method is given by the design of a cantilever used in an atomic force microscope. Feasible and well-performing designs have been generated, both from a functional and manufacturing point of view
Transient tip-sample interactions in high-speed AFM imaging of 3D nano structures
No full textThe maximum amount of repulsive force applied to the surface plays a very important role in damage of tip or sample in Atomic Force Microscopy(AFM). So far, many investigations have focused on peak repulsive forces in tapping mode AFM in steady state conditions. However, it is known that AFM could be more damaging in transient conditions. In high-speed scanning, and in presence of 3D nano structures (such as FinFET), the changes in topography appear in time intervals shorter than the response time of the cantilever. In this case, the tip may crush into the sample by exerting much higher forces than for the same cantilever-sample distance in steady state situations. In this study the effects of steep upward steps in topography on the tip-sample interactions have been investigated, and it has been found that the order(s) of magnitude higher forces can be applied. The information on the worst case scenario obtained by this method can be used for selection of operation parameters and probe design to minimize damage in high-speed imaging. The numerically obtained results have been verified with the previous works in steady state regime. Based on this investigation the maximum safe scanning speed has been obtained for a case studyComputational Design and Mechanic
A comprehensive model for transient behavior of tapping mode atomic force microscope
No full textMany investigations have focused on steady-state nonlinear dynamics of cantilevers in tapping mode atomic force microscopy (TM-AFM). However, a transient dynamic model—which is essential for a model-based control design—is still missing. In this paper, we derive a mathematical model which covers both the transient and steady-state behavior. The steady-state response of the proposed model has been validated with existing theories. Its transient response, however, which is not covered with existing theories, has been successfully verified with experiments. Besides enabling model-based control design for TM-AFM, this model can explain the high-end aspects of AFM such as speed limitation, image quality, and eventual chaotic behavior.Computational Design and MechanicsTeam Jan-Willem van Wingerde
Chaos: The speed limiting phenomenon in dynamic atomic force microscopy
No full textThis paper investigates the closed-loop dynamics of the Tapping Mode Atomic Force Microscopy using a new mathematical model based on the averaging method in Cartesian coordinates. Experimental and numerical observations show that the emergence of chaos in conventional tapping mode AFM strictly limits the imaging speed. We show that, if the controller of AFM is tuned to be faster than a certain threshold, the closed-loop system exhibits a chaotic behavior. The presence of chaos in the closed-loop dynamics is confirmed via bifurcation diagrams, Poincaré sections, and Lyapunov exponents. Unlike the previously detected chaos due to attractive forces in the AFM, which can be circumvented via simple changes in operation parameters, this newly identified chaos is seemingly inevitable and imposes an upper limit for the closed-loop bandwidth of the AFM
Chaos: The speed limiting phenomenon in dynamic atomic force microscopy
No full textThis paper investigates the closed-loop dynamics of the Tapping Mode Atomic Force Microscopy using a new mathematical model based on the averaging method in Cartesian coordinates. Experimental and numerical observations show that the emergence of chaos in conventional tapping mode AFM strictly limits the imaging speed. We show that, if the controller of AFM is tuned to be faster than a certain threshold, the closed-loop system exhibits a chaotic behavior. The presence of chaos in the closed-loop dynamics is confirmed via bifurcation diagrams, Poincaré sections, and Lyapunov exponents. Unlike the previously detected chaos due to attractive forces in the AFM, which can be circumvented via simple changes in operation parameters, this newly identified chaos is seemingly inevitable and imposes an upper limit for the closed-loop bandwidth of the AFM.Computational Design and MechanicsDynamics of Micro and Nano System
