Detection of electrostatic forces with an atomic force microscope: Analytical and experimental dynamic force curves in the nonlinear regime

Dynamic force curves of an atomic force microscope in the presence of attractive van der Waals and electrostatic forces are analytically treated using a variational method taking into account nonlinear tip-sample coupling. This approach allows describing and understanding the motion of a voltage-biased tip observed in experimental approach-retract curves in dynamic mode. The solutions predict a hysteretic behavior in the force curves for both amplitude and phase of oscillation. This hysteresis diminishes and disappears with increasing tip-sample voltage. The tip-surface system is modeled as a plane capacitor with an effective area of interaction. The analytical solution clearly accounts for the apparent height measured in topographical scanning due to the presence of charges on the sample. It also furnishes an estimation of the quantity of excess charges on the sample surface measured in the experiment. There, an estimated 360 electrons were injected into a SiO2 surface. Additionally, at the onset of electrostatic coupling, an abrupt transition from intermittent contact to noncontact regime is experimentally evidenced by a jump of the phase from one branch of solution to the other. This phase contrast represents an easy way to distinguish and to choose between intermittent contact and noncontact regime.