Amplitude Control in van der Pol Type Self-excited Micro Cantilever for AFM

Abstract

Usage of self-excitation as an excitation method for cantilever-probe in atomic force microscopy (AFM) has been proposed in order to improve the low quality factor Q in liquid environments. For realization of non-contact mode AFM, it is necessary to reduce the amplitude of the self-excited cantilever-probe. In this study, the self-excited oscillation of the cantilever-probe is generated by the angular velocity feedback. In addition, the small steady state amplitude is achieved by nonlinear feedback proportional to the squared deflection angle and the angular velocity. Regarding the micro cantilever-probe as a micro cantilever beam, we show the equation of motion in which the geometrical nonlinear effect is taken into account. Averaged equation is derived by applying the method of multiple scales and the bifurcation diagram is theoretically described. Then, it is clarified that the amplitude of the cantilever-probe can be reduced by increasing the nonlinear feedback gain. By using our own making AFM, we demonstrate the nonlinear dynamics of a “van der Pol” type self-excited cantilever. Steady state amplitude of self-excited oscillation is reduced to 8 nm.