Simulation of steady-state response of tip-sample interaction for a torsional cantilever in tapping mode atomic force microscopy for material characterization in nanoscale

Abstract

Dynamic atomic force microscopy (AFM) techniques involving multifrequency excitation or detection schemes offer improved compositional sensitivity and quantitative material property imaging. A correct interpretation of cantilever vibrations in multifrequency excitation and detection schemes demands an improved understanding of the effects of enhanced high frequency vibrations on the steady-state dynamics of the cantilever and in particular, on the tip-sample interaction force. In this thesis, a simulation background is developed with proper modelling of tip-sample ensemble for accurate simulation of tip-sample interaction when multifrequency excitation and detection schemes are utilized. The simulation results are analyzed and used for material characterization. The tip-sample ensemble is modelled as a multiple degree of freedom system that includes torsional mode and higher order flexural modes of the cantilever. The nonlinear behavior of sample surface is also included in the model. This mechanical model is transformed into an electrical circuit and an electrical circuit simulator is used to find steady-state of the circuit. Thereby, a simulation of steady-state dynamics of multifrequency imaging schemes is achieved.Using the developed simulation tool, the effect of torsional vibrations and higher order flexural vibrations on steady-state of tip-sample interaction is investigated. The tip trajectory and tip-sample interaction force are calculated for torsional harmonic cantilevers. The potential of torsional harmonic cantilevers in reconstruction of tip-sample interaction force for the quantitative estimation of material properties is verified. Change in amplitude of torsional harmonics with respect to elastic modulus (sensitivity) is investigated. It is shown that sensitivity of a particular torsional harmonic changes with sample stiffness and higher harmonics are more sensitive to change in stiffness. Additionally, a noise analysis of torsional harmonic cantilevers is made and included in the simulations. The tip-sample interaction force is recovered from the simulated torsional vibration signal and the effective elastic modulus of the sample is estimated. It is observed that accuracy of the estimation is affected by number of torsional harmonics used in the recovery of interaction force.