Calibration of quartz tuning fork spring constants for non-contact atomic force microscopy: direct mechanical measurements and simulations

Jens Falter,André Schirmeisen,Philipp Schurig,Harald Fuchs,Hendrik Hölscher,Marvin Stiefermann,Gernot Langewisch

doi:10.3762/bjnano.5.59

Abstract

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.

Highlights

Atomic force microscopy (AFM) allows the imaging of surfaces with true atomic resolution and the resolution of intra-molecular structures of molecules [1]
These tuning forks are microfabricated from piezoelectric quartz, which is electrically contacted by gold electrodes placed onto the quartz substrate
The experimental results are compared to the beam formula and finite element method (FEM)-simulations revealing the limits of the commonly used models for the determination of “qPlus” sensor stiffness

Summary

Introduction

Atomic force microscopy (AFM) allows the imaging of surfaces with true atomic resolution and the resolution of intra-molecular structures of molecules [1]. These values are estimated from the geometric dimensions of the free prong of the tuning fork and the Young’s modulus of quartz by using the beam formula according to Equation 1 [16].

Results

Conclusion