Lin Shueei Muh
Department of Mechanical Engineering, Kun Shan University, Tainan, Taiwan 710-03, Republic of China.
Ultramicroscopy. 2007 Feb-Mar;107(2-3):245-53. doi: 10.1016/j.ultramic.2006.08.001. Epub 2006 Aug 28.
In a common environment of atomic force microscopy (AFM), a damping force occurs between a tip and a sample. The influence of damping on the dynamic response of a cantilever must be significant. Moreover, accurate theory is very helpful for the interpretation of a sample's topography and properties. In this study, the effects of damping and nonlinear interatomic tip-sample forces on the dynamic response of an amplitude-formulation AFM are investigated. The damping force is simulated by using the conventional Kelvin-Voigt damping model. The interatomic tip-sample force is the attractive van der Waals force. For consistance with real measurement of a cantilever, the mathematical equations of the beam theory of an AM-AFM are built and its analytical solution is derived. Moreover, an AFM system is also simplified into a mass-spring-damper model. Its exact solution is simple and intuitive. Several relations among the damping ratio, the response ratio, the frequency shift, the energy dissipation and the Q-factor are revealed. It is found that the resonant frequencies and the phase angles determined by the two models are almost same. Significant differences in the resonant quality factors and the response ratios determined by using the two models are also found. Finally, the influences of the variations of several parameters on the error of measuring a sample's topography are investigated.
在原子力显微镜（AFM）的常见环境中，探针与样品之间会产生阻尼力。阻尼对悬臂梁动态响应的影响必定很大。此外，精确的理论对于解释样品的形貌和特性非常有帮助。在本研究中，研究了阻尼和非线性原子间探针 - 样品力对振幅公式化AFM动态响应的影响。通过使用传统的开尔文 - 维格纳阻尼模型来模拟阻尼力。原子间探针 - 样品力为吸引性的范德华力。为了与悬臂梁的实际测量相一致，建立了振幅调制原子力显微镜（AM - AFM）梁理论的数学方程并推导了其解析解。此外，AFM系统也被简化为一个质量 - 弹簧 - 阻尼器模型。其精确解简单直观。揭示了阻尼比、响应比、频率偏移、能量耗散和品质因数之间的几种关系。发现由这两种模型确定的共振频率和相角几乎相同。还发现使用这两种模型确定的共振品质因数和响应比存在显著差异。最后，研究了几个参数的变化对测量样品形貌误差的影响。
