Micro Electro Mechanical Systems (MEMS) membranes are utilized as both transmitter and receiver in acoustic and ultrasound applications. Their operating frequency ranges are determined by their resonance frequencies. Thus, the resonance frequency estimation is one of the most critical part of the membrane design. In this study, two perforated circular MEMS membranes are designed, microfabricated and characterized to get proper operation under residual stress since this stress might cause buckling of the membrane. Finite element methods (FEM) are applied and optical measurements are taken to extract the resonance frequencies. For the fundamental mode, The FEM results deviate 5.5% and 6.7% from the experimental work. 33.4% stress relaxation is achieved for the proposed perforated membranes. Furthermore, six different circular membranes are simulated and compared with the analytical solutions. The minimum and maximum average percentage errors are acquired as 0.5% and 3.3% for the fundamental mode. The electrical characterizations are carried out with the impedance analyzer and results are supported by FEM. Stress was successfully managed with the help of the perforation, as verified by the experimental works and simulations.

中文翻译：

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残余应力下抗屈曲穿孔 MEMS 膜的设计和表征

微机电系统 (MEMS) 膜在声学和超声应用中用作发射器和接收器。它们的工作频率范围由它们的共振频率决定。因此，共振频率估计是膜设计中最关键的部分之一。在这项研究中，设计、微制造和表征了两个穿孔圆形 MEMS 膜，以便在残余应力下正常运行，因为这种应力可能导致膜弯曲。应用有限元方法 (FEM) 并进行光学测量以提取共振频率。对于基模，FEM 结果与实验工作偏差 5.5% 和 6.7%。所提出的穿孔膜实现了 33.4% 的应力松弛。此外，模拟了六种不同的圆形膜并与解析解进行了比较。基本模式的最小和最大平均百分比误差分别为 0.5% 和 3.3%。使用阻抗分析仪进行电气特性分析，结果得到 FEM 的支持。正如实验工作和模拟所证实的那样，在穿孔的帮助下成功地控制了应力。