Thermal frequency noise in low oscillation amplitude Dynamic Scanning Force Microscopy

摘要

Thermal fluctuation of the cantilever position sets a fundamental limit forthe precision of any Scanning Force Microscope. In the present work we analysehow these fluctuations limit the determination of the resonance frequency ofthe tip-sample system. The basic principles of frequency detection in DynamicScanning Force Microscopy are revised and the precise response of a typicalfrequency detection unit to thermal fluctuation of the cantilever is analysedin detail. A general relation for thermal frequency noise is found as afunction of measurement bandwidth and cantilever oscillation. For largeoscillation amplitude and low bandwidth, this relation converges to the resultknown from the literature, while for low oscillation amplitude and largebandwidth we find that the thermal frequency noise is equal to the width of theresonance curve and therefore stays finite, contrary to what is predicted bythe relation known so far. The results presented in this work fundamentallydetermine the ultimate limits of Dynamic Scanning Force Microscopy.