Surface stress induced deflections of cantilever plates with applications to the atomic force microscope: Rectangular plates

Surface stress is a material property that underpins many physical processes, such as the formation of self-assembled monolayers and the deposition of metal coatings. Due to its extreme sensitivity, atomic force microscopy (AFM) has recently emerged as an important tool in the measurement of surface stress. Fundamental to this application is theoretical knowledge of the effects of surface stress on the deflections of AFM cantilever plates. In this article, a detailed theoretical study of the effects of surface stress on the deflections of rectangular AFM cantilever plates is given. This incorporates the presentation of rigorous finite element results and approximate analytical formulas, together with a discussion of their limitations and accuracies. In so doing, we assess the validity of Stoney’s equation, which is commonly used to predict the deflections of these cantilevers, and present new analytical formulas that greatly improve upon its accuracy.