Gramazio Federico, Lorenzoni Matteo, Pérez-Murano Francesc, Rull Trinidad Enrique, Staufer Urs, Fraxedas Jordi
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
Instituto de Microelectrónica de Barcelona (IMB-CNM, CSIC), Campus UAB, 08193 Bellaterra, Barcelona, Spain.
Beilstein J Nanotechnol. 2017 Apr 19;8:883-891. doi: 10.3762/bjnano.8.90. eCollection 2017.
We present a combined theoretical and experimental study of the dependence of resonant higher harmonics of rectangular cantilevers of an atomic force microscope (AFM) as a function of relevant parameters such as the cantilever force constant, tip radius and free oscillation amplitude as well as the stiffness of the sample's surface. The simulations reveal a universal functional dependence of the amplitude of the 6th harmonic (in resonance with the 2nd flexural mode) on these parameters, which can be expressed in terms of a gun-shaped function. This analytical expression can be regarded as a practical tool for extracting qualitative information from AFM measurements and it can be extended to any resonant harmonics. The experiments confirm the predicted dependence in the explored 3-45 N/m force constant range and 2-345 GPa sample's stiffness range. For force constants around 25 N/m, the amplitude of the 6th harmonic exhibits the largest sensitivity for ultrasharp tips (tip radius below 10 nm) and polymers (Young's modulus below 20 GPa).
我们展示了一项关于原子力显微镜（AFM）矩形悬臂共振高次谐波与相关参数（如悬臂力常数、针尖半径、自由振荡幅度以及样品表面刚度）之间依赖关系的理论与实验相结合的研究。模拟结果揭示了第六谐波（与第二弯曲模式共振）的幅度对这些参数的通用函数依赖关系，这种关系可以用枪形函数来表示。该解析表达式可被视为从AFM测量中提取定性信息的实用工具，并且可以扩展到任何共振谐波。实验证实了在3 - 45 N/m的力常数范围和2 - 345 GPa的样品刚度范围内的预测依赖关系。对于约25 N/m的力常数，第六谐波的幅度对超尖针尖（针尖半径低于10 nm）和聚合物（杨氏模量低于20 GPa）表现出最大的灵敏度。
