Numerical analysis of vibration modes of a qPlus sensor with a long tip

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.

Fundamental and higher eigenmodes of qPlus sensors with a long probe for vertical-lateral bimodal atomic force microscopy

“…They revealed the lateral tip oscillation in the second mode and demonstrated topographic imaging with the sensor. Afterward, Chen et al also reported a FEM study on the QTF sensors with an angled-attached long probe with various probe lengths and diameters 30 . In contrast, we found the lateral tip oscillation in the higher flexural mode of a qPlus sensor where a long probe was attached perpendicularly to the QTF prong (Fig.…”

“…First, the determination of the spring constant and oscillation amplitude is necessary for the quantitative analysis of tip-sample interaction. The effective spring constant of the qPlus sensor with a long probe was already analyzed by FEM 28,30,31 . Some methods to calibrate the amplitude of the higher mode of the qPlus sensor with a long probe were proposed, such as scanning electron microscopy 28,30 and laser Doppler vibrometry 31,32 .…”

“…The effective spring constant of the qPlus sensor with a long probe was already analyzed by FEM 28,30,31 . Some methods to calibrate the amplitude of the higher mode of the qPlus sensor with a long probe were proposed, such as scanning electron microscopy 28,30 and laser Doppler vibrometry 31,32 . Furthermore, analysis of piezoelectric sensitivity, which is the ratio of the output voltage signals to the tip oscillation am- plitude, is crucial because it determines the deflection noise density, which dominates the minimum detectable force gradient in AFM 33 .…”

“…There is another way to oscillate the probe apex laterally, which uses the higher eigenmodes of the QTF sensor with a long probe. 20,[28][29][30][31][32] Higuchi et al analyzed the eigenmodes of the QTF sensor with an angled-attached long probe by the nite element method (FEM). 28 They revealed the lateral tip oscillation in the second mode and demonstrated topographic imaging with the sensor.…”

“…31,32 Furthermore, the analysis of piezoelectric sensitivity, which is the ratio of the output voltage signals to the tip oscillation amplitude, is crucial because it determines the deection noise density, which dominates the minimum detectable force gradient in AFM. 33 Although several research groups have analyzed the piezoelectric current, 30 to the best of our knowledge, there have been no studies analyzing piezoelectric sensitivity.…”