Abstract
The conventional design of harmonic AFM probe geometry is made in neglect of the effects of the size-dependency factor and the tip-sample interacting force. Obviously, the effect of these two factors on the natural frequencies of a probe is significant. In this study, the effects of the two factors on the integer-multiples relation among frequencies are investigated. In this study, the effects of the two factors on the integer-multiples relation among frequencies are investigated. It is discovered that, in general, the integer-multiples relations of the probe’s frequencies in the classical model does not be kept as the same as that in the system with the effect of the size-dependency factor under the same material and geometry properties of probe. In addition, when the probe is used to measure the sample, the deviation of the relations will happen. The smaller the tip-sample distance is, the larger the deviation of integer-multiples frequencies is. The analytical method is presented here such that during scanning a sample at some tip-sample distance, the material and geometry properties of the probe can be tuned to the integer-multiples relation of resonant frequencies. Moreover, five similarity conditions among the systems with and without the effects of size-dependency and the tip-sample interacting force are discovered. According to these conditions, the integer-multiples relation is kept in different systems.
Highlights
For high-speed AFM imaging, atomic force microscopy is often employed to measure the surface topography and material property of specimens, simultaneously. e dynamic response of the fundamental mode is conventionally used to measure the topography of the sample. e response of higher flexural modes of a cantilever is taken to measure some material properties [1,2,3,4,5,6]
Precise positioning of the attached mass could be technically not so easy to realize. e literatures [6, 9, 10] investigated the selective removal of the lever materials is more convenient than the previous one, which can be accomplished by changing the cantilever shape and cutting hole structures in the probe. e literatures [5, 11, 12] studied the cutting the boundary of probe cross section to tailor the frequency characteristics
No literature is devoted to design the harmonic probe with the integer-multiples relation of frequencies considering the effects of the size dependency and the tipsample interacting force during an AFM probe measuring a sample’s topography and properties
Summary
For high-speed AFM imaging, atomic force microscopy is often employed to measure the surface topography and material property of specimens, simultaneously. e dynamic response of the fundamental mode is conventionally used to measure the topography of the sample. e response of higher flexural modes of a cantilever is taken to measure some material properties [1,2,3,4,5,6]. Lin and Chang [13] designed the harmonic AFM probe with varying cross section in polynomial series based on the modified couple stress theory, neglecting the effect of the tip-sample interacting force. Lin et al [20] made assessment of the classical, modified couple stress, and strain gradient theories about size dependency effect on the resonant frequency of a conventional AFM uniform probe subjected to van der Waals force. No literature is devoted to design the harmonic probe with the integer-multiples relation of frequencies considering the effects of the size dependency and the tipsample interacting force during an AFM probe measuring a sample’s topography and properties. The design of linearly varying cross section of the probe with the integer-multiples relation of frequencies and these effects is proposed. The similarity conditions among the systems with and without the effects of sizedependency and the tip-sample interacting force are investigated
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