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

• Published in: Chinese physics B Vol. 19; no. 5; pp. 213 - 218
• Main Author: 李渊 钱建强 李英姿
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.05.2010
• Subjects: Atomic force microscopy; Contact; Dynamical systems; Higher harmonics; Imaging; Mathematical analysis; Mathematical models; Recording; 动力学行为; 原子力显微镜; 微悬臂梁; 接触时间; 相互作用; 轻敲模式; 高次谐波
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/19/5/050701

The periodic impact force induced by tip-sample contact in a tapping mode atomic force microscope （AFM） gives rise to the 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 timevarying 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.