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 analytical 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.