6 August 2001 Sensitivity of atomic force microscope vibration modes to changes in surface stiffness
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Abstract
Advancements in atomic force microscopy have led to the development of new measurement techniques that take advantage of the different vibration modes of the cantilevers. Each vibration mode has a different sensitivity to the variations in surface stiffness. The cantilever interacts with the sample surface through the tip of the cantilever. This interaction is approximated as a linear spring such that linear vibration theory may be used for analysis. This simplification restricts the results to experiments involving low amplitude excitations. For imaging, a single vibration mode is selected for feedback control. The image contrast is directly controlled by the modal sensitivity of the cantilever. Low-stiffness cantilevers have typically been unusable for imaging of stiff materials because of the lack of sensitivity of the first flexural mode. In this article, a closed form solution of the modal sensitivity for flexural vibration modes is derived for cantilevers with constant cross-sections. For cantilevers with other shapes, an approximate solution is developed using the Rayleigh-Ritz method. For given nominal values of surface and AFM cantilever properties, the appropriate mode for highest contrast may be predicted.
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Joshua S. Wiehn, Joseph A. Turner, "Sensitivity of atomic force microscope vibration modes to changes in surface stiffness", Proc. SPIE 4328, Smart Structures and Materials 2001: Sensory Phenomena and Measurement Instrumentation for Smart Structures and Materials, (6 August 2001); doi: 10.1117/12.435536; https://doi.org/10.1117/12.435536
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