Dynamics of a vibrating tip near or in intermittent contact with a surface

We discuss the stability of the tip motion in dynamic atomic force microscopy. A nonlinear dynamics analysis shows that the tip's phase space is divided in two basins of attraction. A phase space diagram dominated by either basin of attraction implies a stable motion while a substantial contribution from both basins is associated with instabilities. Because the dominance of a given basin of attraction depends on the tip-surface interaction potential and separation, stable and unstable motions are intrinsic features of an oscillating tip near or in intermittent contact with a surface.