Theory and Applications of Atomic Force Microscopy Microcantilevers.

The heart of a AFM is a sharp tip that interacts at the sample. The resonance frequency and the quality factor Q affects the responsiveness significantly. In this thesis, a variational method is used to calculate the deflection and the fundamental and harmonic resonance frequencies of commercial V-shaped and rectangular AFM cantilevers. Damping by environmental gases, including air, nitrogen, argon, and helium, affects the frequency of maximum response and to a much greater degree the quality factor Q. Damping in liquids is dominated by an increase in effective mass of the cantilever due to an added mass of the liquid being dragged with that cantilever. The response is given for AFM cantilevers subjected to harmonic excitation in the presence of fluid damping and force gradient at a surface. One-dimensional harmonic oscillator theory is adequate to describe the amplitude of the cantilever as a function of applied frequency for free and near-contact cases. Good agreement between theory and experiment is found as a function of tip-sample distance. In liquid environments, the behavior is dominated by hydrodynamic damping and a large added mass from the liquid. For tapping operation, acoustic excitation is used at frequencies well above the fundamental, so that even weak cantilever act with a high effective spring constant. In tapping operation, the tip briefly encounts the strong repulsive potential of the sample surface losing a small fraction of its energy. By modeling the interaction potential as an exponential, a transient and steady-state solution can be obtained. Adsorption-induced bending and resonance frequency change of an AFM cantilever can be used as the basis for novel chemical sensors. By simultaneously measuring bending and frequency characteristics, it is possible to decouple the effects of adsorption between spring constant and mass loading changes. It is theoretically shown how surface stress mechanically acts upon a cantilever. Also a simple harmonic oscillator is used to interpret how the surface stress could affect the spring constant of a cantilever. Moreover, this technique was used to investigate adsorption of chemical vapors such as mercury and moisture with picogram resolution.