Design and analysis of higher harmonic cantilever based on finite element analysis

Abstract

Recently, the developing multi-frequency atomic force microscopy, not only can characterize more physical properties of samples with a remarkable spatial resolution, but also detect non-linear force with time-resolved. Its basic principle is that multiple vibrating frequencies of micro cantilever probe is motivated and detected, which is closely related to higher harmonics or eigenmodes of micro cantilever. In order to realize this new technology, it is very important and necessary to design special micro cantilever. Generally, silicon cantilever and quartz cantilever are widely used in traditional AFM. For rectangular silicon cantilever, the ratio of the second order eigenmode and basic frequency is 6.27, and for quartz tuning micro-cantilever, it also isn’t an integral value, so it is almost impossible to study the MF-AFM using the conventional cantilevers directly. Based on the resonant amplification effect, in this article, we discussed the corresponding eigenvibration of traditional rectangular silicon micro-cantilever and quartz tuning micro-cantilever by the method of changing the mass distribution of micro cantilever, namely changing its geometric size and shape. Finally we designed some special cantilevers, which the ratio of second mode frequency and basic frequency are all integer times by theoretical calculation and Finite Element Analysis, including some discussions between flexural resonant and basic frequency.