Frequency Response of Carbon Nanotube Probes during Tapping Mode of Atomic Force Microscopy

Abstract

The dynamic behaviors of carbon nanotube probes applied in Atomic Force Microscope measurement are of interest in advanced nanoscalar topography. In this paper, we developed the characteristic equations and applied the model analysis to solve the eigenvalues of the microcantilever and the carbon nanotube. The eigenvalues were then used in the tapping mode system to predict the frequency responses against the tip-sample separations. It was found that the frequency drop steeply if the separation was less than certain distances. This instability of frequency is deduced from the jump of microcantilever or the jump of the carbon nanotube. Various lengths and binding angles of the carbon nanotube were considered, and the results indicated that the binding angle dominated the frequency responses and jumps.