中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50701-050701.doi: 10.1088/1674-1056/19/5/050701

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

李渊, 钱建强, 李英姿   

  1. Department of Applied Physics, Beihang University, Beijing 100191, China
  • 收稿日期:2009-09-14 修回日期:2009-10-28 出版日期:2010-05-15 发布日期:2010-05-15
  • 基金资助:
    Project supported by the National High-Tech Research and Development Program of China (Grant No.~2007AA12Z128).

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)   

  1. Department of Applied Physics, Beihang University, Beijing 100191, China
  • Received:2009-09-14 Revised:2009-10-28 Online:2010-05-15 Published:2010-05-15
  • Supported by:
    Project supported by the National High-Tech Research and Development Program of China (Grant No.~2007AA12Z128).

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摘要： 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.

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.

Key words: tapping mode atomic force microscopy, higher harmonics imaging

中图分类号:  (Atomic force microscopes)

  • 07.79.Lh
02.60.Lj (Ordinary and partial differential equations; boundary value problems)