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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
Determining cantilever stiffness from thermal noise.
Jannis Lübbe1, Matthias Temmen, Philipp Rahe
1Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany.
This study presents a new method for determining cantilever stiffness (k n) from thermal noise, enhancing accuracy for applications like noncontact atomic force microscopy (NC-AFM). The technique offers practical applicability across a wide range of cantilever frequencies.
Area of Science:
- Physics
- Materials Science
- Nanotechnology
Background:
- Cantilever properties like eigenfrequency (f n), quality factor (Q n), and stiffness (k n) are crucial for various applications.
- Extracting these properties from thermal noise via power spectral density (PSD) analysis is a known method.
- However, traditional PSD analysis for stiffness determination can be complex and requires sophisticated spectral analysis.
Purpose of the Study:
- To critically discuss the extraction of intrinsic cantilever properties from thermal noise.
- To introduce a novel, simplified method for determining cantilever stiffness (k n).
- To demonstrate the practical applicability of the new method, especially for noncontact atomic force microscopy (NC-AFM).
Main Methods:
- Analysis of the power spectral density (PSD) of cantilever displacement fluctuations in contact with a thermal bath.
- Introduction of a new method involving spectral analysis of the demodulated oscillation signal of an excited cantilever.
- Experimental validation using cantilevers with eigenfrequencies from 50 kHz to 2 MHz.
Main Results:
- Successfully demonstrated the extraction of intrinsic cantilever properties (f n, Q n, k n) from thermal noise.
- Validated the practical applicability of the PSD analysis method for cantilevers in the 50 kHz to 2 MHz range.
- Showcased the effectiveness of the new demodulated signal analysis method for determining k n in the 10 Hz to 1 kHz range, independent of cantilever eigenfrequency.
Conclusions:
- The new method for determining cantilever stiffness (k n) from demodulated oscillation signals is effective and broadly applicable.
- This simplified spectral analysis is particularly advantageous for noncontact atomic force microscopy (NC-AFM) due to readily available instrumentation.
- The study provides a valuable tool for accurate characterization of micro- and nanomechanical resonators.
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