Calibration of quartz tuning fork spring constants for non-contact atomic force microscopy: direct mechanical measurements and simulations.
Quartz tuning forks are being increasingly employed as sensors in non-contact atomic force microscopy especially in the "qPlus" design. In this study a new and easily applicable setup has been used to determine the static spring constant at several positions along the prong of the tuning fork. The results show a significant deviation from values calculated with the beam formula. In order to understand this discrepancy the complete sensor set-up has been digitally rebuilt and analyzed by using finite element method simulations. These simulations provide a detailed view of the strain/stress distribution inside the tuning fork. The simulations show quantitative agreement with the beam formula if the beam origin is shifted to the position of zero stress onset inside the tuning fork base and torsional effects are also included. We further found significant discrepancies between experimental calibration values and predictions from the shifted beam formula, which are related to a large variance in tip misalignment during the tuning fork assembling process.
Center for Nanotechnology (CeNTech) and Institute of Physics, University of Münster (WWU), Heisenbergstrasse 1, 48149 Münster, Germany ; Institute of Applied Physics (IAP), Justus-Liebig-University Gießen, Germany.
Jens
J
Falter
Center for Nanotechnology (CeNTech) and Institute of Physics, University of Münster (WWU), Heisenbergstrasse 1, 48149 Münster, Germany ; Institute of Applied Physics (IAP), Justus-Liebig-University Gießen, Germany.
Marvin
M
Stiefermann
Center for Nanotechnology (CeNTech) and Institute of Physics, University of Münster (WWU), Heisenbergstrasse 1, 48149 Münster, Germany.
Gernot
G
Langewisch
Institute of Applied Physics (IAP), Justus-Liebig-University Gießen, Germany.
Philipp
P
Schurig
Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz Platz 1, 76344 Eggenstein-Leopoldshafen, Germany.
Hendrik
H
Hölscher
Center for Nanotechnology (CeNTech) and Institute of Physics, University of Münster (WWU), Heisenbergstrasse 1, 48149 Münster, Germany ; Institute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz Platz 1, 76344 Eggenstein-Leopoldshafen, Germany.
Harald
H
Fuchs
Institute of Applied Physics (IAP), Justus-Liebig-University Gießen, Germany.
André
A
Schirmeisen
atomic force microscopy; calibration; instrumentation