Sensitivity of atomic force microscope vibration modes to changes in surface stiffness

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.