本論文在於探討如何以靜電彈簧軟化效應(electrostatic spring-softening effect)將兩微機電振盪器的振動頻率達到一致，此研究的延伸可進一步應用於陀螺儀上來達到頻率匹配(mode-matching)的操作，提供高感測靈敏度。本論文利用CMOS-MEMS整合技術將電容式的MEMS共振器結構與鎖相迴路(phase-looked-loop, 以下簡稱PLL)整合在單一顆晶片上。我們以鎖相迴路的輸出訊號回授驅動MEMS共振器結構，透過鎖相迴路相位差90度的補償，能夠維持整個迴路的穩定振盪，並直接在鎖相迴路的輸出端得知振盪器的共振頻率。以此共振頻率為目標，我們另外在其他MEMS振盪器結構上設計指狀軟化電極，利用靜電彈簧軟化效應，以鎖相迴路控制方式以電壓變化造成振盪結構的共振頻率變化，來達成與目標頻率匹配的目的。
本論文晶片使用TSMC 2P4M 0.35μm CMOS製程，單一晶片內整合了MEMS振盪器結構、感測電路與鎖相迴路，整顆晶片總面積為2.8mm×2.8mm。在鎖相迴路方面，我們使用全類比式的設計做為此次的迴路架構，主要由相位偵測器(phase detector)、電壓控制震盪器(voltage-controlled oscillator)以及迴路濾波器(loop filter)所組成，內容包含迴路的模擬以及量測等等。
而在MEMS共振器方面，為了要做共振頻率匹配，本論文總共設計六個MEMS微結構原始振頻接近170 kHz，因為後製程和環境等因素共振頻率會有飄移而造成微結構彼此間共振頻率不同，本論文目標為以較高頻率的微結構和較低頻率的微結構達成頻率匹配，成功的將兩結構原本頻率差250 Hz拉近至頻率相差40 Hz，我們使用Allan variance來檢測震盪器的穩定性，發現在時間積分約1秒有最佳值為0.62 Hz，最後提出分析並針對結果進行討論。

In this work, the electrostatic spring-softening effect is used to achieve matched resonant frequencies between two MEMS resonators. Matched-mode operation is important for a MEMS vibratory gyroscope to achieve high sensitivity. Both the capacitive micro-resonators and the phase-locked-loop (PLL) driving circuit are monolithically integrated on the same CMOS chip. In the oscillator loop, PLL provides a driving signal to the target resonator with a 90-degree phase compensation at the resonant frequency. Based on this frequency, the resonant frequency of the second micro-resonator is adjusted for mode-matching by the spring-softening electrode, whose input is provided by a PLL-based control loop.
The chip containing MEMS structures, sensing circuit and PLL is fabricated by using the TSMC two-polysilicon four-metal 0.35-μm standard CMOS process. This chip area size is 2.8x2.8 mm2. The analog PLL contains a phase detector (PD), a voltage-controlled oscillator (VCO) and a loop filter. The chip contains six MEMS structures whose resonant frequencies vary due to manufacturing tolerance. Experimental results show that the frequency difference of the two MEMS resonators can be reduced from the original 250 Hz to 40 Hz with the proposed control method. The measured Allan variance provides as an efficient method to quantify frequency stability. We found the best frequency resolution was 0.62 Hz over an average time of 1 second.

致謝 I
摘要 II
Abstract III
目錄 IV
圖目錄 VI
表目錄 IX
第1章 緒論 1
1-1 研究動機 1
1-2 互補式金氧半導體微機電系統(CMOS-MEMS) 1
1-3 陀螺儀與頻率匹配(Mode-Matching) 3
1-4 文獻回顧 5
1-5 論文架構 7
第2章 理論分析 8
2-1 整體系統架構 8
2-2 機械結構動態模型 9
2-3 MEMS振盪器設計與參數規格 10
2-4 電容式致動與感測 15
2-5 靜電彈簧軟化效應 18
2-6 結構的製程 20
2-7 電路模型架構 23
2-8 感測電路設計與模擬 23
2-9 鎖相迴路介紹與設計 28
2-9-1 前級寬頻鎖相迴路 28
2-9-2 鎖相迴路工作原理 30
2-9-3 相位偵測器設計 31
2-9-4 迴路濾波器設計 34
2-9-5 鎖相迴路的迴路模型 36
2-10 外接電路圖以及外接電路元件參數 37
2-11 晶片布局圖 38
第3章 實驗及量測結果 39
3-1 微結構後製程結果 39
3-2 量測環境 42
3-3 感測電路量測 44
3-4 MEMS結構共振頻量測 45
3-5 MEMS共振器彈簧軟化效應量測 47
3-6 使用鎖相迴路驅動MEMS結構量測 51
3-7 相位偵測器模擬與量測 54
3-8 主動式低通濾波器模擬與量測 56
3-9 迴路模擬與量測 56
3-10 系統頻率匹配量測 62
3-11 Allan variance量測 63
第4章 結論 66
4-1 結果與討論 66
4-2 未來規劃 66
參考文獻 67

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