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

机译：非理想夹持形状对硅纳米悬臂梁共振频率的影响

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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 100nm. 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.
机译：在本文中，我们研究了非理想夹持形状对硅纳米悬臂梁动力学行为的影响。我们通过采用步进紫外（UV）光刻技术，使用绝缘体上硅（SOI）晶圆制造了硅纳米悬臂，其分辨率低于100nm。纳米悬臂由扫描电子显微镜（SEM）内的静电力驱动。用SEM可以同时观察到横向和平面外共振频率。接下来，我们讨论在硅纳米悬臂的夹紧点处悬臂支撑的悬垂和弯曲，这通常在制造过程中出现。我们发现，实际夹紧的悬臂的基本面外频率始终低于完全夹紧的悬臂的平面外频率，并且取决于悬臂的宽度和夹紧点结构的几何形状。通过使用有限元方法进行仿真，我们证明了这种差异归因于在制造过程中获得的特定的夹紧点几何形状（非零接合曲率和柔性悬伸）。还研究了材料正交性的影响，并显示可以忽略不计。

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