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Theory of higher harmonics imaging in tapping-mode atomic force microscopy |
Li Yuan(李渊), Qian Jian-Qiang(钱建强)†, and Li Ying-Zi(李英姿) |
Department of Applied Physics, Beihang University, Beijing 100191, China |
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Abstract The periodic impact force induced by tip-sample contact in tapping mode atomic force microscope (AFM) gives rise to non-harmonic response of a micro-cantilever. These non-harmonic signals contain the full characteristics of tip-sample interaction. A complete theoretical model describing the dynamical behaviour of tip--sample system was developed in this paper. An analytic formula was introduced to describe the relationship between time-varying tip--sample impact force and tip motion. The theoretical analysis and numerical results both show that the time-varying tip--sample impact force can be reconstructed by recording tip motion. This allows for the reconstruction of the characteristics of the tip--sample force, like contact time and maximum contact force. It can also explain the ability of AFM higher harmonics imaging in mapping stiffness and surface energy variations.
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Received: 14 September 2009
Revised: 28 October 2009
Accepted manuscript online:
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PACS:
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07.79.Lh
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(Atomic force microscopes)
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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Fund: Project supported by the National
High-Tech Research and Development Program of China (Grant
No.~2007AA12Z128). |
Cite this article:
Li Yuan(李渊), Qian Jian-Qiang(钱建强), and Li Ying-Zi(李英姿) Theory of higher harmonics imaging in tapping-mode atomic force microscopy 2010 Chin. Phys. B 19 050701
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