Determining cantilever stiffness from thermal noise
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Updated: May 12, 2026

Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid
Published on: December 2, 2022
Jannis Lübbe1, Matthias Temmen, Philipp Rahe
1Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany.
Abstract:
We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f n , quality factor Q n and specifically the stiffness k n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.
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