Abstract
The time response of tuning-fork based sensors can be improved by operating them at higher eigenmodes because a measurement takes at least one oscillation cycle in dynamic force microscopy and the oscillation period of the second eigenmode is only about one sixth of the fundamental mode. Here we study the higher-order eigenmodes of quartz qPlus sensors [Bettac et al., Nanotechnology 20, 264009 (2009); Giessibl and Reichling, Nanotechnology 16, S118 (2005); Giessibl, Appl. Phys. Lett. 76, 1470 (2000); and Giessibl, Appl. Phys. Lett. 73, 3956 (1998)], their equivalent stiffness, and piezoelectric sensitivity, while paying special attention to the influence of the mass and rotary inertia of the sensing tip which is attached to the end of the qPlus quartz cantilever. A combination of theoretical modeling and scanning laser Doppler vibrometry is used to study the eigenmodes of qPlus sensors with tungsten tips. We find that the geometry of tungsten tips can greatly influence the shape, equivalent stiffness, and piezoelectric sensitivity of the second eigenmode of the quartz cantilever. At a critical tip length it is possible to theoretically achieve infinite equivalent stiffness and infinite piezoelectric sensitivity when the tip becomes a perfect node of vibration and beyond this critical tip length the second eigenmode loses its vibration node and the trajectory of the tip reverses with respect to the beam curvature. The findings have major implications for optimizing tip geometry for high-resolution imaging with qPlus sensors using higher eigenmodes.
Keywords
QUARTZ TUNING FORK; SURFACE
DOI
10.1063/1.3407511
Citation
Journal of Applied Physics 107, 104508 (2010)
Date of this Version
5-2010
Recommended Citation
Tung, Ryan C.; Wutscher, Thorsten; Martinez-Martin, David; Reifenberger, R.; Giessibl, Franz; and Raman, Arvind, "Higher-order eigenmodes of qPlus sensors for high resolution dynamic atomic force microscopy" (2010). Birck and NCN Publications. Paper 675.
http://dx.doi.org/10.1063/1.3407511
Comments
Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics 107, 104508 (2010) and may be found at http://dx.doi.org/10.1063/1.3407511. The following article has been submitted to/accepted by Journal of Applied Physics. Copyright (2010) Ryan C. Tung, Thorsten Wutscher, David Martinez-Martin, Ronald G. Reifenberger, Franz Giessibl, and Arvind Raman. This article is distributed under a Creative Commons Attribution 3.0 Unported License.