Effect of non-ideal clamping shape on the resonance frequencies of silicon nanocantilevers

In this paper, we investigate the effects of non-ideal clamping shapes on the dynamic behavior of silicon nanocantilevers. We fabricated silicon nanocantilevers using silicon on insulator (SOI) wafers by employing stepper ultraviolet (UV) lithography, which permits a resolution of under 100 nm. The nanocantilevers were driven by electrostatic force inside a scanning electron microscope (SEM). Both lateral and out-of-plane resonance frequencies were visually detected with the SEM. Next, we discuss overhanging of the cantilever support and curvature at the clamping point in the silicon nanocantilevers, which generally arises in the fabrication process. We found that the fundamental out-of-plane frequency of a realistically clamped cantilever is always lower than that for a perfectly clamped cantilever, and depends on the cantilever width and the geometry of the clamping point structure. Using simulation with the finite-elements method, we demonstrate that this discrepancy is attributed to the particular geometry of the clamping point (non-zero joining curvatures and a flexible overhanging) that is obtained in the fabrication process. The influence of the material orthotropy is also investigated and is shown to be negligible.