Finite element analysis of V‐shaped cantilevers for atomic force microscopy under normal and lateral force loads

For the quantitative investigation of surface properties such as elasticity, friction and wear by atomic force microscopy (AFM), a quantitative determination of the forces acting on the probe during its motion along the sample surface is essential. In this article, a fully parameterized finite element model for V‐shaped cantilevers is presented and the three‐dimensional mechanical deformations of the AFM cantilever are investigated. Force constants and detection angles for tip displacements in the three spatial directions are calculated for widely used cantilevers. The limits of linearity according to Hook's law are studied. It is found that the AFM contact cantilevers investigated here show a linear bending behavior for tip displacements within a range below approx. 10 nm in lateral directions and 100 nm in the normal direction. Displacements within this range are typical for many AFM applications including force modulation techniques. For higher loads as used e.g. for surface modification, a significant deviation from linear behavior is observed.