Functional dependence of resonant harmonics on nanomechanical parameters in dynamic mode atomic force microscopy

Beilstein Journal of Nanotechnology

关键词: atomic force microscopy;    metrology;    multifrequency;    nanomechanics;   

DOI  :  10.3762/bjnano.8.90

学科分类：地球科学(综合)

来源: Beilstein - Institut zur Foerderung der Chemischen Wissenschaften

【 摘 要 】

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).

【 授权许可】

CC BY