DESCRIPTION OF PHASE IMAGING IN TAPPING MODE ATOMIC-FORCE MICROSCOPY BY HARMONIC APPROXIMATION

Tapping mode atomic force microscopy measurements were performed for a n elastomer, polydimethylsiloxane, to obtain amplitudes and phase angl es as a function of driving frequency at various driving and set-point amplitudes. The amplitude curves support the harmonic approximation t hat the vibrational characteristics of a tapping cantilever are essent ially harmonic. Based on this approximation, we derived simple analyti cal formulas describing the phase shift, the predictions of which agre e reasonably well with experiment. Our work shows that the phase shift is influenced by the dissipation energy as well as the resonance freq uency shift associated with the tip-sample interaction, and suggests a simple way of estimating the dissipation energy. (C) 1998 Elsevier Sc ience B.V. All rights reserved.