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

Beilstein Journal of Nanotechnology
Federico GramazioJordi Fraxedas

Abstract

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).

References

Jun 20, 1997·Chemical Reviews·Robert W. Carpick, Miquel Salmeron
Apr 1, 2006·Proceedings of the National Academy of Sciences of the United States of America·J FraxedasF Sanz
Oct 15, 2008·Physical Review Letters·Bernd Gotsmann, Mark A Lantz
Feb 4, 2012·The Review of Scientific Instruments·Daniel KiracofeArvind Raman
Apr 3, 2012·Nature Nanotechnology·Ricardo Garcia, Elena T Herruzo
May 9, 2012·The Review of Scientific Instruments·Sergio SantosNeil H Thomson
Oct 30, 2012·Physical Chemistry Chemical Physics : PCCP·A VerdaguerJ Fraxedas
Oct 31, 2015·Ultramicroscopy·Yongda YanXuesen Zhao

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Citations

Jan 23, 2018·Beilstein Journal of Nanotechnology·Weijie ZhangJiaru Chu
Dec 14, 2018·Beilstein Journal of Nanotechnology·Jesús S LacasaJaime Colchero

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Methods Mentioned

BETA
AFM

Software Mentioned

VEDA
Virtual Environment for Dynamic AFM ( VEDA )

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