Numerical simulation of the atomic force microscope

Abstract

The convolution of the tip and the motion of the cantilever in the scanning probe microscope, especially atomic force microscope of tapping mode, are surveyed. The tip convolution is described in terms of the dilation, which is one subject of mathematical morphology. The dilation is to find the maximum of possible values and we provide the simulation program. The motion of the tip interacting with a surface takes into account the nonlinear harmonic oscillation, the attractive van der Waals force and the repulsive indentation. It includes several parameters sensitive to the tip-surface interactions. Hence we provide the graphical user interface to analyze and visualize the motion of the tip. To solve the governing equation numerically and approximate its solution analytically, we use the 4th-order Runge-Kutta method and fast Fourier transform method, respectively. This work will be the basis of further studies, which cover the transverse motion considering the resonance shift, its additional artifacts, and other applications such as carbon nanotube probing.