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Dynamic & Vibration Analysis of AFM Probe Affected by the Non Uniform Potential Field

Kahrobaiyan, Mohammad Hossein | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40362 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Ahmadian, Mohammad Taghi
  7. Abstract:
  8. Atomic force microscope (AFM) has a significant capability of imaging surface topography on an atomic scale. It is also widely used for Nanolithography in MEMS/NEMS (micro/nanoelectromechanical systems). Conventional AFMs consist of a cantilever with a sharp conical or pyramidal tip located at the free end of the cantilever that plays an important role in AFM measurements. Scanning across a surface, AFM interacts with the sample surface through its tip. Although the dynamic behavior of the AFM cantilever is complicated, the researchers have been interested in studying AFM dynamic behavior because it has a great influence on the surface imaging process. The imaging rate and contrast of topographic images are notably influenced by the resonant frequency and sensitivity of AFMs respectively. So it is important for researchers to study the resonant frequency and sensitivity of an AFM cantilever. Although the conventional AFMs have a significant capability of nano-scale surface measurements, their probe tips cannot come in close proximity to the sidewalls, no matter how sharp they are. Therefore, no accurate nano-scale measurements at sidewalls and edges can be achieved by these conventional AFMs.In addition,regarding the increasing applications of micro-structures such as micro nozzles, micro gears, micro holes and micro trenches which all of them have sidewalls and edges, researchers proposed an assembled cantilever probe (ACP) for AFMs in order to determine the topography images and also the roughness and waviness of sidewalls and edges of these micro-structures. This ACP comprises a horizontal microcantilever, a vertical assembled probe located at the free end of the horizontal microcantilever and a tip located at the free end of the vertical extension. In this thesis, the nonlinear vibration of an AFM with an assembled cantilever probe is investigated. In order to achieve this goal, utilizing Hamilton principle, the governing partial differential equation (PDE) of the ACP motion and corresponding boundary conditions are obtained in the first step. In the next step, applying Galerkin and assuming mode method, the governing ordinary differential equation (ODE) of motion is derived. After that, using the perturbation techniques such as multiple scales and Lindsted-Poincare method, the governing nonlinear ODE of the system is solved analytically and the time and frequency responses are delineated in some figures. Furthermore, the influences of the system parameters such as the geometrical one on the frequency response of the system are assessed. In addition to the nonlinear vibration investigation, the torsional sensitivity and resonant frequency of the ACP are studied in this thesis and the effects of the geometrical parameters on them are investigated. Finally, in order to optimize the flexural sensitivity of the ACP, it is assumed that the horizontal microcantilever is made of functionally graded materials (FGMs) and the influences of the FGM properties distribution function on the resonant frequency and sensitivity are assessed. The results show that for each contact stiffness, there is a unique properties distribution function using that the sensitivity will be maximized and consequently the high quality and high contrast images can be obtained
  9. Keywords:
  10. Atomic Force Microscopy (AFM) ; Sensitivity ; Functionally Graded Materials (FGM) ; Resonant Frequencies ; Assembled Contilever Probe ; Non-Uniform Potential Field

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