In-plane deformation of cantilever plates with applications to lateral force microscopy

Abstract

The in-plane deformation of atomic force microscope (AFM) cantilevers under lateral loading is commonly assumed to have negligible effect in comparison to other deformation modes and ignored. In this article, we present a theoretical study of the behavior of cantilevers under lateral loading, and in so doing establish that in-plane deformation can strongly contribute to the total deformation, particularly for rectangular cantilevers of high aspect ratio (length/width). This has direct implications to lateral force microscopy, where the neglect of in-plane deformation can contribute to significant quantitative errors in force measurements and affect the interpretation of measurements. Consequently, criteria and approaches for minimizing the effects of in-plane deformation are presented, which will be of value to users and designers of AFM cantilevers. Accurate analytical formulas for the in-plane spring constants of both rectangular and V-shaped cantilevers are also presented.