Spring constant of a tuning-fork sensor for dynamic force microscopy.

Dennis Van Vörden,Manfred Lange,Merlin Schmuck,Rolf Möller,Nico Schmidt

doi:10.3762/bjnano.3.90

Abstract

We present an overview of experimental and numerical methods to determine the spring constant of a quartz tuning fork in qPlus configuration. The simple calculation for a rectangular cantilever is compared to the values obtained by the analysis of the thermal excitation and by the direct mechanical measurement of the force versus displacement. To elucidate the difference, numerical simulations were performed taking account of the real geometry including the glue that is used to mount the tuning fork.

Highlights

Quartz tuning forks provide excellent self-sensing probes in scanning probe microscopy, offering several advantages compared to the standard microfabricated silicon-based cantilevers [1,2]
In the present paper we compare the results for the determination of the spring constant of tuning fork sensors in the qPlus configuration [1,2] based on the following methods: a simple calculation for a cantilever beam; the measured deflection as a function of the applied force; the thermal noise; and a numerical simulation by the finite-element method
Beam deflection as function of applied force To a good approximation, the force F exerted by the tuning fork (TF) in the qPlus configuration is given by Hooke’s law F = −kz, with the spring constant k and the deflection z

Summary

Introduction

Quartz tuning forks provide excellent self-sensing probes in scanning probe microscopy, offering several advantages compared to the standard microfabricated silicon-based cantilevers [1,2]. While the resonance frequency may be measured accurately in the experiment, it is more difficult to evaluate the spring constant k The latter is required to evaluate the force gradient and other physical quantities, e.g., the energy dissipated due to the interaction between tip and sample. By comparing the images for the loaded and unloaded TF, the deflection at the end of the prong is determined, using WSxM [26] and Corel Draw X5 (Corel Corporation, Ottawa, Canada). In the present paper we compare the results for the determination of the spring constant of tuning fork sensors in the qPlus configuration [1,2] based on the following methods: a simple calculation for a cantilever beam; the measured deflection as a function of the applied force; the thermal noise; and a numerical simulation by the finite-element method

Result and Discussion

Conclusion