Modeling the Dynamics of Atomic Force Microscope Cantilevers

Joshua Wiehn - M.S. Thesis Defense
Department of Engineering Mechanics
University of Nebraska - Lincoln
Advisor:  Dr. Joseph A. Turner

Date: Friday, November 9, 2001
Time: 1:30 p.m.
Place: N205 Walter Scott Engineering Center


The atomic force microscope (AFM) was initially developed to provide topography information of a sample surface. Advancements have led to the development of new measurement techniques that exploit the dynamic properties of the AFM cantilevers (probes). In this thesis, models are developed for various AFM cantilevers. These models provide information about the flexural and torsional vibrations modes of the cantilevers and their sensitivity to changes in the stiffness of the sample surface. Closed-form expressions are derived for cantilevers with constant cross-sections. For nonuniform AFM cantilevers, such as those with a triangular shape, the Rayleigh-Ritz method is used to develop an approximate solution. The interaction between the cantilever and the sample surface is approximated as a linear spring, such that linear vibration theory may be used for the analysis. This simplification restricts the results to experiments involving low-amplitude excitations. Comparisons between the models and experimental results are made and the limitations of the models are discussed. It is anticipated that these models will aid in the selection of cantilevers and the specific vibration modes necessary for obtaining optimal measurements using the AFM. From the resonance frequency measurements, information regarding the material properties of the sample surface may also be obtained.