Effects of the Casimir Force and Surface Elasticity on the Natural Frequencies of Cantilever AFM Probes

Natural frequencies of cantilever probes are one of the most significant parameters in optimizing the performance of an atomic force microscope (AFM). In this article, a theoretical model based on a continuum mechanics approach is presented towards investigation of the natural frequencies for transverse vibration of a cantilever beam when taking the Casimir force and surface properties into account. The characteristic equation is derived. The effects of surface elasticity, residual surface tension and Casimir force on the natural frequencies of cantilever beams are examined. Obtained results might be helpful for the design of cantilever probes in AFM.