Tapping mode of an atomic force microscope with a probe cantilever of a low spring constant

The work presents mathematical simulation results of tapping interaction of an atomic force microscope (AFM) probe with low (0.1 N/m) spring constant of its cantilever with samples of materials with the Young moduli of 0.01; 0.1; 1; 10 GPa under varying the characterizing samples surface energy Hamaker constant, oscillation amplitude of a piezoelectric element, and also the quality factor of the probe. The Johnson–Kendall–Roberts model was used to describe contact between the probe and a sample. Non-contact interaction was taken into account using the Lennard–Jones potential. It was defined that at lower values of the Hamaker constant, higher quality factor of the AFM probe, and higher oscillation amplitude of the piezoelectric generator, conditions for transition from mixed mode of probe–sample interaction, which is undesirable for obtaining AFM images, to purely elastic mode occur. However, for materials with the Young moduli of 1 and 10 GPa abrupt changes in probe characteristics occur, which are associated not with influence of surface adhesion, but with late onset steady-state mode of probe oscillation. In order to avoid non-steady state oscillation of the probe in tapping AFM mode, it is proposed to use probes with higher spring constant to obtain high-quality AFM images of material surfaces with the Young modulus of 1 GPa and higher. 

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