Phase contrast in tapping-mode scanning force microscopy

The tapping-mode operation of a scanning force microscope represents an intermediate situation between contact and noncontact regimes. Its rapid development and expansion are due to lateral force minimization and its ability to give phase-contrast images of heterogeneous surfaces. Here, we calculate the phase shift between the cantilever excitation and its response as a function of the sample mechanical properties, tip-sample separation, and adhesion forces. We show that the phase shift that gives rise to phase-contrast images is associated with tip-sample interactions that involve energy dissipation such as adhesion energy hysteresis and viscoelasticity. Experimental phase-shift measurements performed on mica surfaces support the conclusions of the model.