טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentWu Wei
SubjectNonlinear Dynamics of Microbeams for Atomic Force Microscopy
in Ultra-High Vacuum
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Oded Gottlieb
Professor Emeritus Arthur Shavit (Deceased)
Full Thesis textFull thesis text - English Version


Abstract

Atomic Force Microscopy (AFM) is a modern imaging technique that is used to map surfaces down to atomic resolution. It is an ideal instrument for mapping biological and nonconducting materials which cannot be done by any alternative methods. There are several AFM operation modes that incorporate a vibrating micro-cantilever with a sharp tip at its free end that is scanning a target sample. These include contact, noncontact, and tapping modes which enable a model based estimation of the atomic forces between the tip and sample. Recently, subatomic features have been obtained in the noncontact mode of AFM operation in very low temperature and ultra-high vacuum (UHV) conditions. However, the accuracy of quantitative force estimation from measured data crucially depends on the quality of the mathematical model in use. Typically used lumped-mass models cannot resolve the rich spatio-temporal dynamic response of the nonlinear AFM microbeam or accurately predict system instabilities in UHV. Thus, the objectives of this research include derivation, analysis, and validation of a continuous model for the vibrating AFM system that consistently incorporate nonlinear atomic interaction with both viscoelastic and temperature dependent thermophysical properties required for operation in UHV. The model considered includes coupled elastic and temperature fields which are reduced to a modal based nonlinear dynamical system. The analysis incorporates both multiple-scales asymptotics and numerical analysis for weakly and strongly nonlinear response respectively. Results include coexisting periodic solutions near primary resonance, and quasiperiodic modal energy transfer due to an internal resonance. An experiment with Al and Si cantilevers of larger scale (not MEMS) is conducted in UHV, where localized tip-sample interaction is obtained by magnets. Free vibration decay reveals conditions for coupled nonlinear thermo- and viscoelastic response which are then validated in forced vibration. Comparison of results with those reported in literature demonstrate the importance of nonlinear thermo- and viscoelastic continuum based models for accurate estimation of atomic interaction properties and prediction of dynamic 'jump-to-contact' instabilities.