Abstract
We study the oscillatory behavior of qPlus sensors with a long tilted tip by means of finite element simulations. The vibration modes of a qPlus sensor with a long tip are quite different from those of a cantilever with a short tip. Flexural vibration of the tungsten tip will occur. The tip can no longer be considered as a rigid body that moves with the prong of the tuning fork. Instead, it oscillates both horizontally and vertically. The vibration characteristics of qPlus sensors with different tip sizes were studied. An optimized tip size was derived from obtained values of tip amplitude, ratio between vertical and lateral amplitude components, output current, and quality factor. For high spatial resolution the optimal diameter was found to be 0.1 mm.
Highlights
Quartz tuning forks are widely used in the watch industry because of their low frequency offset over a wide temperature range [1]
The values of fq and ftip are obtained by the simulation, and ftf is calculated by the method described in [27]
The oscillation characteristics of qPlus sensors with different dimensions of tungsten tips were studied by using the finite element method
Summary
Quartz tuning forks are widely used in the watch industry because of their low frequency offset over a wide temperature range [1]. Quartz tuning forks have a high elastic constant, a high quality factor (Q factor), and are self-sensing due to the piezoelectric effect [1]. A quartz tuning fork can be used as a force sensor. The central part of the “qPlus sensor” is a quartz tuning fork of which one prong is fixed onto a substrate and the other prong with an attached tip serves as a self-sensing cantilever [2]. J. Giessibl et al first used the qPlus sensor to measure the morphology of a grating
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