Van der Pol type self-excited micro-cantilever probe of atomic force microscopy

Abstract

For usage of noncontact atomic force microscopy (NC-AFM) in a liquid environment, we propose a “van der Pol”-type self-excited cantilever probe whose steady state amplitude can be controlled to be sufficiently small so as not to damage the surface of the observation object. The self-exciting technique for the micro cantilever probe has become a powerful tool for obtaining atomically resolved images in environments where the cantilever has a very low quality factor Q. It is important to maintain the steady state amplitude of the cantilever to prevent damage to the surface, to reduce the contact force with the sample surface, and to avoid destruction of a soft material having an irregular surface such as biomolecules. In contrast to external excitation, the response amplitude of a self-excited oscillator is generally determined by the amount of nonlinearity of the system. The greater the nonlinearity, the smaller the steady state amplitude. We apply nonlinear feedback control in addition to linear feedback control to increase inherent nonlinearity in the system. Thereby, the cantilever probe has nonlinear characteristics that are equivalent to a van der Pol oscillator. It is shown analytically via an asymptotic perturbation approach that the self-excited oscillation has small steady state amplitude. Experiments are performed using a micro cantilever that is fabricated from a Pt/Ti/PZT/Pt/Ti/SiO2/SOI multi-layered structure. The validity and advantage of the proposed control method are confirmed to realize the stable self-excited oscillation with as small an amplitude as possible for the NC-AFM for a liquid environment.