Scanning Probe Microscopy Force Reconstruction from Non-Equilibrium Dynamics

Abstract

Atomic Force Spectroscopy generates a voltage time trace which contains physical information of the sample under study. This information is hidden in the trace and a central challenge is the recovery of a force vs. separation curve, which characterizes the physical and chemical properties of the sample. Often theoretical approaches approximate the motion of the AFM cantilever as a mass-spring system. These models assume that the motion of the cantilever is either quasi-static or dominated by a single mode. However, under relevant realistic measuring conditions, the cantilever is likely to accelerate appreciably and its motion may become a sum of many modes. Furthermore, these models (and others that go beyond a single mode) require that the voltage be related to deflection when, in reality, the voltage relates to the slope of the cantilever end. In this paper we explore beyond these constrains by considering the dynamics of a flexible cantilever satisfying the Euler-Bernoulli equation including an appropriate boundary condition that interprets the voltage as a slope. With this explicit boundary condition in conjunction with standard boundary conditions we are able to calculate the force in the snap-tocontact region. The snap-to-contact approach may contain high velocities and acceleration events. To the best of our understanding, the model and solutions we propose here are based on a physically sound basis. A central result of this thesis is the assessment of the accuracy of previous and current models. We show that the accuracy is related to a single constant α which characterizes the curvature of the snap-to-contact in relation to the frequency of the slowest mode of oscillations.