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

• Published in: Surface science Vol. 440; no. 3; pp. L863 - L867
• Main Authors: Bielefeldt, Hartmut, Giessibl, Franz J.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 10-10-1999; Amsterdam Elsevier Science; New York, NY
• Subjects: Atomic force microscopes; Atomic force microscopy; Exact sciences and technology; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Intermittent contact; Physics; Scanning probe microscopes, components and techniques; Tapping mode; Tapping mode; Atomic force microscopy; Intermittent contact; Simulation; Resonance frequency; Analytical method; Theoretical study; Tip surface interactions
• ISSN: 0039-6028; 1879-2758
• DOI: 10.1016/S0039-6028(99)00861-4

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.