| Nanoscience and nanotechnology is one of the most potential areas in the frontier science and high-tech research.During the development of nanoscience and nanotechnology,a series of scanning probe microscopes have been developed into core tools for detecting the structure,properties and functions of micro-nanoscale materials.Among them,atomic force microscopy(AFM)is widely used in chemistry,materials,physics,biology and other nano-related disciplines due to its unique advantages.AFM has made important contributions to the rapid development of nanoscience.Micro-cantilever probe system is the core component of AFM,and its dynamic behavior determines the rapidity,stability and accuracy of AFM imaging.The ultimate goal of the AFM theory is to give analytical or numerical relationships between the observed quantity of the micro-cantilever system and the properties of the sample.Based on these analytical or numerical relationships,the results of the AFM experiments can be interpreted and the optimal experimental scheme can be determined.Therefore,the theoretical research on dynamic characteristics of the micro-cantilever system is one of the hotspots concerned by researchers in recent years.Although the previous theoretical work has achieved great success in explaining the dynamic behavior of the micro-cantilever system,it has its limitations.The main limitations are as follows.The accurate analytical results of the dynamic evolution process,the dynamic oscillation degree and the response speed can not be determined quantitatively by the previous theoretical framework and methods,which will greatly limit the AFM imaging speed.On the other hand,the stability and steady-state margin of the micro-cantilever system can not be judged quantitatively by the previous theoretical methods,which will greatly limit the AFM imaging quality.In addition,due to the limitations of manufacturing technology,the dynamic characteristics of the system can not be improved effectively by adjusting the internal parameters of the micro-cantilever system.Aiming at solving these key problems,the dynamic characteristics of the micro-cantilever system are addressed in depth.The work of this paper mainly includes the following parts:(1)It is proposed to solve the dynamic equation of the micro-cantilever system by using automatic control theory of the complex system.The dynamic differential equation of the micro-cantilever system can be transformed into the mathematical model in the complex domain of Laplace space.The influence of the structure and parameters of the micro-cantilever system on the steady-state and dynamic characteristics can be analyzed comprehensively.The correction methods can be proposed to improve the dynamic characteristics of the micro-cantilever system effectively.(2)The time-domain dynamic characteristics of the micro-cantilever system have been studied in detail.By using automatic control theory,the stability of the system is strictly proved.The analytical expressions of the micro-cantilever deflection in time domain are derived.The analytical results of the dynamic overshoot,regulation time and the steady-state error of the micro-cantilever system are obtained.These analytical results play an important role in evaluating the stability,rapidity and accuracy of AFM.The effects of the internal parameters,the external excitation signals and the interaction forces between tip and sample surface on the time-domain dynamic behavior of the micro-cantilever system are discussed respectively.The theoretical and experimental results show that these key physical quantities have a profound impact on the steady-state and dynamic behavior of the micro-cantilever system in time domain,which are beneficial for AFM imaging quality and imaging speed.(3)It is proposed to solve the motion equation of the micro-cantilever system with tapping mode AFM by using the frequency domain analysis method.The analytical expressions of the amplitude-frequency and phase-frequency characteristics of the micro-cantilever system are deduced in detail.The stability of the system is strictly proved by using the frequency domain characteristics of the micro-cantilever system.From the point of the engineering technology,the relative stability of the micro-cantilever system is directly measured by the steady-state margin,and the analytical results of the relative stability are deduced.The influence of the key parameters on the frequency domain characteristics of the system is discussed in detail theoretically and experimentally.These results provide an important theoretical guidance for determining the better experimental scheme.The frequency domain analysis method is compared with the traditional theoretical methods and the experimental results.The results show that the automatic control theory has a great advantage in solving the dynamic mode AFM.The frequency domain analysis method is used to study the resonance characteristics of the microcantilever system in the liquid environment and the theoretical results are compared with the experimental results.It is found that the theoretical results are agree with the experimental results.(4)The external correction methods are proposed to optimize the design of the micro-cantilever system and to improve the stability,accuracy and rapidity of AFM.The series correction,the feedback correction and the composite correction schemes for the micro-cantilever system are introduced in detail.In each scheme,the composition of the passive network and the active network of the correction device are given,and the time domain and frequency domain characteristics of the correction are discussed.The internal parameters of each specific correction scheme are calculated in detail.The dynamic characteristics of the micro-cantilever system before and after correction are compared in depth.The theoretical and experimental results show that the dynamic characteristics of the micro-cantilever system can be improved with these external correction schemes.(5)The dynamic characteristics can also be improved by adjusting the quality factor of the micro-cantilever.Based on automatic control theory,the internal correction optimization methods,such as self-excitation,are addressed in detail.The stability of the micro-cantilever system with self-excitation is proved by using the stability criterion in frequency domain.The analytical results of the frequency characteristics are obtained.The results show that self-excitation method can significantly change the effective quality factor of the micro-cantilever,and can increase the amplitude of steady-state resonance or accelerate the dynamic response speed of the system.The resonant feedback control technique is proposed to control the steady-state stability,the dynamic oscillation degree and the response speed.Moreover,by using this control technique,the influence of higher order poles can be eliminated and the spillover effect can be prevented.(6)By using the simulation platform of the micro-cantilever system,the main theoretical results of most chapters are simulated and verified.Moreover,some theoretical results are compared with the experimental results.It is found that the analytical results have high accuracy. |
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