Exact solutions of AFM scanning probes subjected to tip-sample forces

In this study, an analytical method for the static deflection of an AFM nonuniform probe subjected to tip-sample forces is presented. The effects of the Lennard-Jones and electrostatic noncontact forces and a contact force on the deflection of a cantilever are investigated. The contact force is simulated by the Derjaguin–Muller–Toporov model. In general, when an atomic force microscopy is used to measure a sample’s topography and properties, a jump phenomenon of a cantilever usually exists. Unfortunately, there is a lack of a complete and precise description about this jump phenomenon. This proposed ana-lytical method is helpful to investigate precisely the jump phenomenon. Moreover, the effects of several parameters on the jump phenomenon are studied. Finally, several simple and general relations between the deflection of beam and the tip-sample distance are presented. 1.