Dynamics of quartz tuning fork force sensors used in scanning probe microscopy

Abstract

We have performed an experimental characterization of the dynamics of oscillating quartztuning forks which are being increasingly used in scanning probe microscopy asforce sensors. We show that tuning forks can be described as a system of coupledoscillators. Nevertheless, this description requires knowledge of the elastic couplingconstant between the prongs of the tuning fork, which has not yet been measured.Therefore, tuning forks have usually been described within the single oscillator or theweakly coupled oscillators approximation that neglects the coupling between theprongs. We propose three different procedures to measure the elastic couplingconstant: an opto-mechanical method, a variation of the Cleveland method anda thermal noise based method. We find that the coupling between the quartztuning fork prongs has a strong influence on the dynamics and the measuredmotion is in remarkable agreement with a simple model of coupled harmonicoscillators. The precise determination of the elastic coupling between the prongs of atuning fork allows us to obtain a quantitative relation between the resonancefrequency shift and the force gradient acting at the free end of a tuning fork prong.