Analysis of the constant-excitation mode in frequency-modulation atomic force microscopy with active Q-Control applied in ambient conditions and liquids

摘要

The constant-excitation mode of the frequency modulation technique can be used to perform atomic force microscopy experiments in vacuum, air, and liquids. Adding an additional Q-Control feedback to the cantilever driving the effective Q-factor of the cantilever can be increased. This is especially useful for applications in air and liquids where the cantilever is damped by the surrounding medium. Here, we present an experimental and theoretical analysis of this technique. Based on the analytical solution of the equation of motion, we give an explicit formula for the tip-sample indentation for a Hertzian tip-sample force. In addition, we studied the imaging capabilities of the new operation mode in liquids, which revealed a significantly smaller tip-sample indentation for increased effective Q-factors. Furthermore, we measured the tip-sample interaction force between a silicon tip and a graphite(0001) surface in water with and without Q-Control.