Frequency shift and energy dissipation in non-contact atomic-force microscopy

Frequency shift as a function of tip-surface distance is investigated theoretically for a real experimental condition on Si 111.surface with a Si tip. Some different situations for the energy dissipation are considered: 1. without any energy dissipation; 2. with the energy dissipation of a constant Q-value of the cantilever system; 3. with the energy dissipation from the tip-induced relaxation besides that of 2., which is addressed approximately by a coupled-two-vibrator model. It is shown that the energy dissipation effect in 2. is negligible and the results from 1. and 2. are almost the same even for rather low Q-value G1000.. The situation 3.is indicated to be the one which can affect the frequency shift remarkably for small tip-surface distance. q2000 Elsevier Science B.V. All rights reserved