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

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...

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Bibliographic Details
Published in:Beilstein journal of nanotechnology 2017, Vol.8 (1), p.883-891
Main Authors: Gramazio, Federico, Lorenzoni, Matteo, Pérez-Murano, Francesc, Rull Trinidad, Enrique, Staufer, Urs, Fraxedas, Jordi
Format: Article
Language:English
Subjects:
Amplitudes
Atomic force microscopes
Atomic force microscopy
Dependence
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Higher harmonics
metrology
Modulus of elasticity
multifrequency
nanomechanics
Nanoscience
Nanotechnology
Parameters
Simulation
Stiffness
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Summary: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).
ISSN:2190-4286
2190-4286
DOI:10.3762/bjnano.8.90