Sensitivity of an Atomic Force Microscope Cantilever with a Crack

The atomic force microscope (AFM) has become an essential tool for the measurement of surface characteristics of diverse materials on a microand nanoscale level [1]. The resolution of measurements for the AFM cantilever is related to its vibration sensitivity. Many researchers have much interest in studying the resonant frequency and sensitivity analysis of AFM cantilevers [2 4]. Cracks may be induced in an AFM cantilever during the fabrication process [5]. Cracks will affect the sensitivity of AFM cantilevers during scanning. However, there are very few literature reports on the crack effect of AFM cantilevers. In this article, we analyze the sensitivity of AFM cantilever using the modified couple stress theory [6]. Unlike the classical continuum theory, the modified couple stress theory includes one additional material length scale parameter revealing the micro-scale effect on the response of structures to estimate the size-dependent behaviours. Here the effects of the length scale parameter and crack parameter on the sensitivity of a cracked AFM cantilever are investigated. An AFM probe is considered as a cantilever beam which have the density ρ, Poisson’s ratio μ, uniform cross-section A, thickness h, and length L. Assume the probe has a crack at a distance D from the fixed end as shown in Fig. 1. Therefore, the cantilever will be divided into two segments by the crack. A rigidity of the rotational spring simulated the cracked section to connect the two segments of the cantilever. The governing equations of transverse vibration of the cantilever with a crack can be expressed as [3]