Doctoral Dissertations

Guoyuan Chen

Date of Award

8-1995

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Physics

Major Professor

Robert J. Warmack

Committee Members

T. A. Callcott, R. J. Dunlap

Abstract

The ability of the atomic force microscope (AFM) to obtain high res-olution images in ambient conditions makes it a very powerful tool for surface studies. The AFM operates by sensing the interaction force between a cantilevered probe and the sample surface. By using a cantilever with a spring constant much less than the effective spring constants of the atoms in the sam-ple, sample damage can be avoided. However, other interaction forces such as capillary forces can produce undesirable deformation and permanent damage of the sample. Non-contact and tapping-mode AFM (TMAFM) show promise for imaging soft samples that may be deformed by continuous contact. The heart of a AFM is a sharp tip that interacts at the sample and is supported by a cantilever. The resonance frequency and the quality factor Q of the cantilever 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. The effective mass of V-shaped cantilevers is roughly half that calculated for the equivalent rectangular 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. Helium has the lowest viscosity, resulting in highest Q, and thus provides the best sensitivity in non-contact force microscopy. 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. To gain insight into the mechanisms of the TMAFM operating, one-dimensional harmonic oscillator theory is used to model TMAFM operation in the near-contact region in the presence of gases and liquids. The force derivative of the tip-sample interaction changes the vibration amplitude and frequency at maximum amplitude of the cantilever. Additionally, the interaction is hydrodynamically damped by fluid motion around the tip and the sample surface. Good agreement was found between theoretical and experimental amplitudes as a function of height. For a sample-driven TMAFM operating in fluids, the cantilever can be very soft and operated at frequencies well above the fundamen-tal. Under these conditions the cantilever and sample act with a high effective spring constant, much like that used in gaseous operation. The tip-sample in-teraction in the fluid is still mediated through the force derivative of the sample. For metals under water, a strong van der Waals interaction appears as a peak for driven frequencies below resonance, while for semiconductors and insulators, this peak is absent due to a weaker interaction. Tapping-mode scanning force microscopy in liquids is usually accom-plished by acoustic excitation of the cantilever because of the strong viscous damping. Contact of the tip with the sample surface results in the cantilever amplitude with an anharmonic response. This interaction is modeled as a viscous-damped, one-dimensional harmonic oscillator periodically perturbed by an exponential surface potential. Experimental results verify the validity of the model. Recently it has become clear that AFM cantilevers can be used for a variety of sensor applications. For example, 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 will be theoretically shown here how surface stress mechanically acts upon a cantilever. Also a simple harmonic oscillator is used to interpret how the surface stress affects 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.

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