This paper presents the analytical modeling, simulation and experimental validation of sensitivity, temperature variation and active controllability of MEMS geometric anti-spring (GAS) devices. Two models, the elasticity model and the thermal drift model, were proposed and analyzed, based on the study of asymmetrical and symmetrical geometric anti-spring structures. With the elasticity model, structural optimization led to analytical frequency-prestress design formula and a dedicated MEMS structure. An independent pre-stress and frequency shift effect is the result of thermal changes, so a thermal drift analytical model was built for the geometric anti-spring device, showing thermal sensitivities of and for the 3-spring and 4-spring devices, respectively. The analytical model was validated by both finite element analyses and experimental measurements. The designed devices (3-springs and 4-springs) were tested afterward in a dedicated setup, for both positive and negative electrostatically induced pre-stresses. Without electrical compensation, the thermal drift of the symmetrical 4-spring GAS device, for temperatures in the range to , is about 2138ppm, and it is reduced to only 8.35ppm when the electrostatic temperature compensation is active. Similarly, the asymmetrical structure has an uncompensated thermal sensitivity of its resonant frequency of 2254ppm in the temperature operation range, and it is reduced to 51.5ppm with electrical compensation within the easily controlled range of the temperature span, from to . As a result, although the benefits of the asymmetrical structure would lead to a higher sensitivity, trade-offs related to thermally-induced drift behavior and controllability also should be taken into consideration in the selection of the structural topology and application environment.

中文翻译：

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基于几何抗弹簧的MEMS器件频率特性及热补偿

本文介绍了 MEMS 几何抗弹簧 (GAS) 设备的灵敏度、温度变化和主动可控性的分析建模、仿真和实验验证。基于对非对称和对称几何抗弹簧结构的研究，提出并分析了弹性模型和热漂移模型两种模型。使用弹性模型，结构优化导致分析频率-预应力设计公式和专用 MEMS 结构。独立的预应力和频移效应是热变化的结果，因此建立了几何抗弹簧装置的热漂移分析模型，分别显示了 3 弹簧和 4 弹簧装置的热敏性。分析模型通过有限元分析和实验测量得到验证。设计的设备（3 弹簧和 4 弹簧）随后在专用设置中针对正负静电感应预应力进行了测试。在没有电气补偿的情况下，对称 4 弹簧 GAS 设备的热漂移，对于 范围内的温度，约为 2138ppm，而当静电温度补偿处于活动状态时，热漂移降至仅 8.35ppm。同样，非对称结构在温度工作范围内其谐振频率的未补偿热灵敏度为 2254ppm，在易于控制的温度跨度范围内通过电气补偿降低到 51.5ppm，从 到 。因此，