טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentHornstein Sharon
SubjectNonlinear Dynamics, Stability and Control of The Scan
Process in Atomic Force Microscopy
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oded Gottlieb


Abstract

Atomic force microscopy (AFM) is a modern imaging technique that is used to map surfaces down to atomic resolution and enables a quantitative estimation of atomic interaction forces. This is obtained by measuring a van der Waals like atomic interaction between a sample and a vibrating micro-cantilever, which has a sharp tip at its free end. The growing demand for detection of sub-atomic features increases the need for faster and accurate scanning. The accuracy of force estimation from measured data crucially depends on the quality of the mathematical model in use. A typically used model is that of a lumped mass system that reduces the microbeam to a linear spring with a nonlinear force. This model does not incorporate the dynamic boundary condition of the scan process and cannot resolve the rich dynamic response of the AFM system. Thus, the objectives of this research include derivation and analyses of a continuous model for a vibrating AFM microbeam that consistently incorporates the nonlinear atomic interaction and the dynamic conditions of the scan process. The model considered is obtained using the extended Hamilton's principle and the analysis includes both multiple-scales asymptotics of weakly nonlinear system and numerical analysis of strongly nonlinear dynamics, leading to 'jump-to-contact' of the tip with the sample. Results include analytical frequency response, periodic and quasiperiodic solutions and instabilities near primary, secondary and internal resonances. Analytical bounds are obtained using a global Melnikov-Holmes analysis and a local Moon-Chirikov overlap criterion. These bounds are compared with numerically obtained ‘jump-to-contact’ curves.