Description of phase imaging in tapping mode atomic force microscopy by harmonic approximation

Tapping mode atomic force microscopy measurements were performed for an elastomer, polydimethylsiloxane, to obtain amplitudes and phase angles as a function of driving frequency at various driving and set-point amplitudes. The amplitude curves support the harmonic approximation that the vibrational characteristics of a tapping cantilever are essentially harmonic. Based on this approximation, we derived simple analytical formulas describing the phase shift, the predictions of which agree reasonably well with experiment. Our work shows that the phase shift is influenced by the dissipation energy as well as the resonance frequency shift associated with the tip-sample interaction, and suggests a simple way of estimating the dissipation energy. (C) 1998 Elsevier Science B.V. All rights reserved.