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An analytical model for calculating the pull-in voltage of micro cantilever beams subjected to tilted and curled effects

机译：用于计算微悬臂梁在倾斜和弯曲作用下的引入电压的解析模型

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摘要

Pull-in is a fundamental phenomenon in electrostatic micro devices. In previous studies on modeling the pull-in voltage of suspended micro cantilever beam subject to residual stress, only curled deformation was considered. This study proposed a modified deformation function, which considered both curled and tilted deformations caused by gradient stress and mean stress, to calculate the pull-in voltage of the suspended cantilever beam with residual deformations. In order to verify the proposed analytical model, suspended poly-silicon cantilever beams with three different lengths, 260 μm, 295 μm and 330 μm, are fabricated through surface micromachining process. It is shown that the residual deformations include both curled and tilted deformations, where the tilted angle and radius of curvature can be identified by white light interferometer (WLI). By comparing the analytical results with measurement results on pull-in voltages, it is found that while only considering curled effect, the average error of calculated pull-in voltage is 10.5%. On the other hand, when both tilted and curled effects are considered, the average error is reduced to 3.2%, which verifies the accuracy improvement of the proposed analytical model.
机译：引入是静电微器件中的基本现象。在先前的建模中，对承受残余应力的悬臂微悬臂梁的引入电压进行建模时，仅考虑了卷曲变形。这项研究提出了一种修正的变形函数，该函数考虑了由梯度应力和平均应力引起的卷曲和倾斜变形，以计算具有残余变形的悬臂梁的引入电压。为了验证所提出的分析模型，通过表面微加工工艺制造了三种长度分别为260μm，295μm和330μm的悬置多晶硅悬臂梁。结果表明，残余变形包括卷曲变形和倾斜变形，其中倾斜角度和曲率半径可以通过白光干涉仪（WLI）识别。通过将分析结果与输入电压的测量结果进行比较，可以发现，仅考虑卷曲效应，计算出的输入电压的平均误差为10.5％。另一方面，当同时考虑倾斜和卷曲效应时，平均误差降低到3.2％，这证明了所提出的分析模型的准确性有所提高。

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  • 来源
    《Microelectronic Engineering》 |2014年第8期|73-77|共5页
  • 作者

    Yuan-Te Huang; He-Ling Chen; Wensyang Hsu;

  • 作者单位

    Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan;

    Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan;

    Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Cantilever beam; Curled deformation; Tilted deformation; Pull-in voltage; Deformation function;

    机译：悬臂梁弯曲变形;倾斜变形;吸合电压变形功能;

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