Elsevier

Surface Science

Volume 440, Issue 3, 10 October 1999, Pages L863-L867
Surface Science

Surface Science Letters
A simplified but intuitive analytical model for intermittent-contact-mode force microscopy based on Hertzian mechanics

https://doi.org/10.1016/S0039-6028(99)00861-4Get rights and content

Abstract

The forces acting on the substrate in intermittent-contact-mode (IC mode, tapping mode) atomic force microscopy are not accessible to a direct measurement. For an estimation of these forces, a simple analytical model is developed by considering only the shift of the cantilever resonance frequency caused by Hertzian (contact) forces. Based on the relationship between frequency shift and tip–sample force for large-amplitude frequency-modulation atomic force microscopy, amplitude and phase versus distance curves are calculated for the intermittent contact mode, and the forces on the substrate are calculated. The results show a qualitative agreement with numerical calculations, yielding typical maximal forces of 50–150 nN. When working above the unperturbed resonance, forces are found to be significantly larger than below the resonance.

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Acknowledgements

Fruitful discussions with S. Hembacher and J. Mannhart are gratefully acknowledged. This work was supported by the BMBF (project number 13N6918/1).

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