טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentHornstein Sharon
SubjectNonlinear Spatio-Temporal Dynamics of the Scan Process in
Atomic Force Microscopy
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oded Gottlieb
Full Thesis textFull thesis text - English Version


Abstract

Atomic Force Microscopy (AFM) belongs to the scanning probe devices, used to map surface features down to molecular and atomic resolutions and enables a quantitative estimation of atomic interaction forces. The essence of the AFM is a moving microcantilever, manufactured with a fine tip at its free end, which is brought into close proximity with a sample. The interaction forces between the tip atoms and those of the sample are used for creation of a spatial map of the surface. The advantages of the AFM over the alternative Scanning Electron Microscope (SEM) are its abilities to create a true three dimensional topographic imaging of the scanned sample, to work in wide environmental conditions that vary from ambient air to vacuum, as well as in liquids, which is essential for imaging of biomolecules and living organisms.

The growing demand for detection of sub-atomic features increased the need for development of contemporary scanning techniques, which have broadened the applications of the classical AFM from planar to spatial operation. These include torsional resonance and lateral excitation modes. Moreover, much attention has put on developing novel excitation techniques that utilize the rich modal content of the AFM cantilever and consist of a few frequencies that match the beam’s resonances. Consequently, due to the nonlinear nature of the beam, internal resonances between different modes of the beam can arise and lead to vibrations of higher modes or induce motion at different directions.

Thus, the objectives of this research include derivation and theoretical analyses of a spatial continuous model for a 3D AFM microbeam that consistently incorporates the nonlinear atomic interaction, and the dynamic conditions of the scan process and its control. The model considered is obtained using the extended Hamilton's principle, which was reduced to a set of 5 degree-of-freedom system for the vertical and lateral flexure and longitudinal torsion of the beam. Asymptotic analysis of the weakly nonlinear system response and numerical analysis of strongly nonlinear dynamics, depict nonlinear phenomena with energy transfer between the planer and torsional modes. The scan motion in the horizontal direction is considered in this research via a reduced order 2 DOF model, which captures the main features of the continuous one. The rigid-body model is used as the dynamic system for a classical controller, and a closed-loop response to a periodic triangular input in the scan direction is examined.