Thermal frequency noise in low oscillation amplitude Dynamic Scanning Force Microscopy

TL;DR

This paper analyzes how thermal fluctuations impose fundamental limits on frequency measurement precision in Dynamic Scanning Force Microscopy, revealing new insights into the thermal frequency noise behavior across different operational regimes.

Contribution

It provides a comprehensive analysis of thermal frequency noise, deriving a general relation that accounts for various oscillation amplitudes and bandwidths, extending previous literature.

Findings

Thermal frequency noise converges to known results at large oscillation amplitude and low bandwidth.

At low oscillation amplitude and large bandwidth, noise equals the resonance width and remains finite.

The work establishes fundamental limits for the precision of Dynamic Scanning Force Microscopy.

Abstract

Thermal fluctuation of the cantilever position sets a fundamental limit for the precision of any Scanning Force Microscope. In the present work we analyse how these fluctuations limit the determination of the resonance frequency of the tip-sample system. The basic principles of frequency detection in Dynamic Scanning Force Microscopy are revised and the precise response of a typical frequency detection unit to thermal fluctuation of the cantilever is analysed in detail. A general relation for thermal frequency noise is found as a function of measurement bandwidth and cantilever oscillation. For large oscillation amplitude and low bandwidth, this relation converges to the result known from the literature, while for low oscillation amplitude and large bandwidth we find that the thermal frequency noise is equal to the width of the resonance curve and therefore stays finite, contrary to what is predicted by the relation known so far. The results presented in this work fundamentally determine the ultimate limits of Dynamic Scanning Force Microscopy.