Amplitude, deformation and phase shift in amplitude modulation atomic force microscopy: a numerical study for compliant materials

Numerical simulations were applied to investigate the motion of a tip interacting with a compliant sample. The dependence of the amplitude, deformation, contact time and phase shift on the mechanical properties of the sample, free oscillation amplitude and cantilever force constant were investigated. The compliance and surface adhesion energy favour the formation of an adhesion neck between tip and surface. The neck modifies the tip motion when its length is comparable to the free oscillation amplitude. The simulations also show that the tip may oscillate fully indented on the sample if large force constant cantilevers and amplitudes are used. A good compromise between stability and resolution is achieved by using low force constant cantilevers and large oscillation amplitudes. The agreement obtained between theory and experimental data supports the conclusions of the model.