Higher-order eigenmodes of qPlus sensors for high resolution dynamic atomic force microscopy

Ryan C. Tung, Purdue University - Main Campus
Thorsten Wutscher, Univ Regensburg
David Martinez-Martin, Univ Autonoma Madrid
R. Reifenberger, Birck Nanotechnology Center, Purdue University
Franz Giessibl, Univ Regensburg
Arvind Raman, Birck Nanotechnology Center, Purdue University

Date of this Version



Journal of Applied Physics 107, 104508 (2010)

This document has been peer-reviewed.



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.


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.


Engineering | Nanoscience and Nanotechnology