Electrostatic mechanism has been widely used for actuating and sensing in Micro-Electro-Mechanical Systems (MEMS). However, the instability of pull-in often limits the operations of MEMS electrostatic devices. This dissertation proposed analytical methods for studying such pull-in behaviors, based on the energy method and the equivalent circuit models. In addition, finite element method (FEM) simulations and experiments were conducted for verifications. MEMS electromechanical behaviors such as static displacements, hysteresis, and dynamic responses were also analyzed.
This dissertation first investigated the electromechanical hysteresis of electrostatic MEMS. Such hysteresis formed by pull-in/contact/pull-out behaviors was employed for material properties extractions using micro-cantilevers and micro-bridges. The results showed that the Young’s modulus of <100> silicon in SOI wafers was from 112 GPa to 130 GPa. The residual stress was found to be from 7.8 MPa to 14 MPa. Then, the side instability of comb-finger electrode was reported and studied. It was observed that four outermost comb-finger were deflected by the transversal electrostatic forces. The first and last comb-fingers easily tended to lose their stabilities and led to the side pull-ins. The stabilizing method by using five times wider first and last comb-fingers for suppressing the instability was suggested, and it was confirmed by equivalent circuit model and experiment. Finally, the pull-in happening in the nano-scale gap between electrodes was reported. An excessive electrostatic force, formed in the narrow electrode gap due to the charging effect, caused the pull-in of RF switches. The nano-scale pull-in induced the spontaneous oscillations at tens of kHz in RF MEMS switch. This phenomenon was characterized under in-situ TEM observations and studied by equivalent circuit model. The lifetime of MEMS switches may be reduced because of the electrode surface degradation after cyclical contacts in oscillations. The results and analytical methods obtained in this dissertation can be used in material properties extractions, pull-in failure predictions, and system-level analyses for MEMS.

微機電靜電式元件具有製程穩定、材料選擇多樣化、結構可靠度較佳、與積體電路整合容易，不易受環境影響及容易控制的特性。然而，靜電式元件容易受非線性靜電力影響而出現電極吸附現象，導致元件短路而造成失效。本文針對此吸附現象分析與探討，透過能量法與等效電路法方式，建立微機電元件靜電吸附現象之理論模型，並以有現單元分析軟體與實驗進行驗證。
本論文首先分析微懸臂樑結構與微橋樑結構之靜電遲滯現象並提出其相關之理數學模型。藉由本文之模型，提出利用遲滯現象萃取材料性質的方法，透過推算吸附電壓、回復電壓與材料係數之關係，成功地量測微機電元件之材料楊氏係數與殘餘應力。量測結果顯示，SOI晶圓之矽楊氏係數為112 GPa至130 GPa，殘餘應力則為7.8 MPa至14 MPa。另外，本論文觀察到微機電梳狀電極由於靜電場之不對稱分佈，造成最外側之四根梳狀電極側向變形。尤其是第一與最末梳狀電極受靜電力影響而出現極大的側向位移，這兩根電極容易與其相鄰電極相互吸附造成電極短路，導致側向不穩定現象。本研究以能量法推導梳狀電極之理論模型，並利用電路分析軟體建立等效電路模型，用以分析靜電場的對稱性與結構穩定之關係，且實際製作微結構進行量測，與理論模型和電路模型驗證。此研究建議透過增加最外側電極寬度五倍的方式來抑制側向不穩定現象發生，此方法於實驗獲得證實。本論文最後一章節觀察並量測到射頻微開關元件在運作時之非線性震盪行為。由於電荷累積，當電極之間距縮短至數十奈米的距離時，電極之間形成過大的靜電力驅動可動電極而導致吸附現象發生，本文透過等效電路模型分析此奈米等級之吸附現象，並在實驗中發現電極不斷吸附、碰撞後出現表面磨耗，並進而影響射頻微開關元件之可靠度。本文所提出分析微機電元件吸附現象之理論模型，等效電路模型及其相關之研究成果，將可使用於半導體元件之材料性質量測，靜電式微元件之失效分析，或是應用至微機電系統層級分析。

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