An analytical solution for nonlinear dynamics of one kind of scanning probe microscopes

TL;DR

This paper derives an analytical solution for the nonlinear dynamics of AFM, considering nonlinear forces and sample vibrations, revealing how these factors influence the system's resonant frequency.

Contribution

It presents an analytical approach to model AFM nonlinear dynamics with polynomial force approximation, including effects of sample vibration.

Findings

Resonant frequency is insensitive to tip mass.

Sample vibration significantly affects resonant frequency.

Nonlinear forces impact AFM dynamic behavior.

Abstract

The dynamic behavior of AFM is studied taking into account the nonlinear interaction forces between probe and sample. The exerted forces on the free end of micro-beam are simulated with the third degree polynomial. The effect of some parameters on the dynamics of AFM is studied. The results show that the frequency response of AFM is not sensitive to the tip mass in the case of both the sample and cantilever vibration. The effect of sample vibration is studied in the case of in-phase and anti-phase vibration. The results show that although the vibration amplitude of sample is very small compared to the amplitude of cantilever, it has great effect on the resonant frequency of the cantilever.