Time-averaged cantilever deflection in dynamic force spectroscopy

We theoretically and experimentally study a hitherto neglected effect in dynamic force spectroscopy. The time-averaged deflection of the cantilever and the frequency shift of its second flexural mode were measured for 11 oscillation amplitudes between 12.8 and 0.51 nm above a maximum protrusion of the atomically resolved topography on KBr(001). A small but measurable time-averaged deflection was observed and the magnitude increased with decreasing amplitude. Interaction force curves essentially coincident over the whole attractive range were obtained from the measured frequency shifts with a rms noise linearly decreasing with amplitude. The correction of the tip-sample distance with the measured time-averaged deflection changes the strength of the interaction force. The deflection calculated from the extracted interaction force agrees with the direct measurement and is approximately proportional to the frequency shift except at the smallest amplitudes.