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

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. © 2004 American Institute of Physics. @DOI: 10.1063/1.1667252#