Theory of higher harmonics imaging in tapping-mode atomic force microscopy

doi:10.1088/1674-1056/19/5/050701

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.

Keywords: tapping mode atomic force microscopy higher harmonics imaging

Received: 14 September 2009
Revised: 28 October 2009
Accepted manuscript online:

PACS:	07.79.Lh	(Atomic force microscopes)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)

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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