Mathematical model of tip oscillations: Influence on image quality

Abstract

The scanning probe microscopy method is based on the probe response to the tip–surface interaction with nanometer resolution. From the accuracy point of view, the disadvantage of this method is that it is not sufficiently precise and reliable owing to the non-equilibrium state of the SWCNT tip and the phase lag between the surface and the tip. Typically, the tip voibrates together with the cantilever. However, the tip has its own oscillations, and the frequency of these oscillations differs from those of the cantilever. We consider the displacements from the equilibrium position of the SWCNT tip as those of a mathematical pendulum. The relationships between the tip oscillation, topography, and structural properties of the tip as an atomic layer were determined. By examining these relations, the equations of the motion of the tip were analyzed. We propose to implement the tip oscillation compensation in the “tip atom–surface atom” system by discriminating the misalignment between the center of the tip and the center of the surface segment under the tip in the XY–plane. This approach can prevent the impact of the tip vibrations on the degradation of the AFM image quality and will provide a high degree of precision.