本文實現具有自我偏壓機制的電容式微機械振盪器，其組成之共振器具備50奈米傳導間隙，且為一真空封裝之單晶矽Lamè-mode微機械振盪器。我們能有效利用設計電路的輸入與輸出端之直流偏壓電位，使共振器元件的致動與感測電極分別具有電性，這種方式足夠使Lamè-mode微機械振盪器產生自我振盪。
除此之外，為了探討降低微機械振盪器相位雜訊的方法，本論文利用商用IC與微機械共振器的整合，實現兩種不同的Lamè-mode微機械振盪器架構:分別為全差動式(Differential-In-Differential-Out, DIDO)與單端輸入雙端輸出(Single-In-Differential-Out, SIDO)。我們能透過全差動式的架構，有效減少第二諧波對於振盪器相位雜訊的影響，由本文實驗結果得知DIDO相較於SIDO架構，在close-to-carrier至少改善多達25dB的相位雜訊。因此全差動式的架構，能使電容式微機械振盪器具有良好的相位雜訊表現。
此微機械振盪器工作頻率為17.6MHz，於1KHz頻率偏移的相位雜訊表現為-127dBc/Hz，且於far-from-carrier的相位雜訊達到-132dBc/Hz。此振盪器的相位雜訊表現，在現今電容式微機械振盪器中極具競爭力，且與至今發表的MEMS振盪器比較，本研究具有最低之極化電壓。

In this work, we realize the low-polarization-voltage (Vp) capacitive MEMS oscillators implementing vacuum packaged 50nm-gap Lamè-mode silicon micromechanical resonators and investigate their phase noise performance. Single-crystal-silicon square-plate microresonators were fabricated by a foundry-oriented SOI-MEMS plus a poly-Si refill process. The devices were hermetically encapsulated at wafer-level using a eutectic bonding technique, which reduces air damping and enables high Q. The frequency of the resonators are around 17.6MHz and the extracted Q is about 20,000 while the motional impedance is around 6.7kΩ (Vp = 3V).
We also report the design and characterization of high gain-bandwidth TIA (transimpedance voltage amplifier) which is composed of two stages: the inverter-based I-to-V stage and voltage gain amplifier. The tunable-gain TIA circuit is fabricated using 2P4M 0.35µm CMOS technology and has been demonstrated with the maximum gain of 80dBΩ, 3-dB bandwidth of 134MHZ. The fully-differential oscillators based on 0.35µm TIA achieve a phase noise of –92dBc/Hz at 1kHz offset and -117dBc/Hz far-from-carrier phase noise performance.
In order to reduce the phase noise, we study the different oscillator configurations which are composed of commercial IC; these are here referred to as differential-in-differential-out (DIDO) and single-in-differential-out (SIDO). Clear disparities in their respective phase noise profiles could be observed. The DIDO outperforms the SIDO with an improved close-to-carrier phase noise by more than -127dBc/Hz at 1kHz offset and -132dBc/Hz far-from-carrier phase noise performance, which is competitive with state-of-the-art capacitive MEMS oscillators but with lowest Vp in this work.

目錄
ABSTRACT ix
摘要 xi
致謝 xii
第一章 前言 1
1.1 射頻微機電簡介 1
1.2 研究動機與內容架構 2
1.3 MEMS振盪器研究動機 6
1.4 內容架構 9
第二章 原理與模擬 12
2.1 MEMS共振器結構設計 12
2.2 共振器運作原理分析與模擬 12
第三章 支撐電路與微機械振盪器設計 25
3.1 串聯諧振振盪器介紹 26
3.2 轉阻放大器回顧 29
3.3 振盪器電路設計 33
第四章 SOI-MEMS製程與結果 47
第五章 量測結果 52
5.1 Lamè模態共振器量測 52
5.2 支撐電路量測 57
5.3 MEMS振盪器量測 62
第六章 結論與未來研究 70
文獻參考 73

圖目錄
Figure 1-1：美國密西根大學的Prof. Nguyen團隊利用多晶矽製作梳狀結構共振器SEM圖。[7] 4
Figure 1-2：美國密西根大學的Prof. Nguyen團隊利用多晶矽製作酒杯式共振器SEM圖。[8] 4
Figure 1-3：喬治亞理工大學Prof. Farrokh Ayazi利用SOI製作具有高Q值與高頻率之MEMS振盪器。[9] 5
Figure 1-4：法國Minatec研究中心以SOI製程完成具有90奈米間隙之MEMS共振器。[10] 5
Figure 1-5：芬蘭VTT研團隊以square-extensional 模態微機械振盪器達成GSM標準。[11] 5
Figure 2-1：(a) Lamè模態共振器之結構圖，其中共振器主結構位於中央 ; 周圍的電極提供致動(Driving)與感測(Sensing)的功用。(b)機械振動學的等效MCK模型。(c)共振器的等效RLC電路模型。 19
Figure 2-2：共振器的等效RLC電路模型。 20
Figure 2-3：方型板邊界條件與座標說明作示意圖。 20
Figure 2-4：ADS (Advanced Design System)模擬共振器等效RLC電路。(a) S21的Amplitude，單位為dB。(b) S21的Phase。 21
Figure 2-5：Comsol Multiphysics模擬Lamè模態共振器因蝕刻孔洞對頻率漂移的影響。(a) 蝕刻孔洞大小為2µm，共振器振盪頻率為18.4 MHz。(b) 蝕刻孔洞大小為3µm，共振器振盪頻率為17.7 MHz。 22
Figure 3-1：MEMS串聯諧振振盪器說明圖。 27
Figure 3-2：MEMS串聯諧振振盪器說明圖:(a) 180°與(b) 0°相位偏移情形。 28
Figure 3-3：喬治亞理工大學Prof. Farrokh Ayazi團隊提出具有頻寬150MHz以上，增益為80dBΩ的二級電路架構。[9] 32
Figure 3-4：加拿大Unuversite du Québee áMontréal團隊提出具有112 dBΩ增益與74 MHz頻寬的轉阻放大器架構。[24] 32
Figure 3-5：美國史丹佛團隊提出可調且極高增益的轉阻放大器架構。[25] 33
Figure 3-6：本論文設計之支撐電路架構。 40
Figure 3-7：第一級電路架構: Inverter-based TIA。 40
Figure 3-8：第一級轉阻放大器的小訊號等效模型。 41
Figure 3-9：第一級轉阻放大器的小訊號等效模型。 41
Figure 3-10：第二級寬頻電壓放大器的等效半電路示意圖。 42
Figure 3-11：第二級寬頻電壓放大器的小訊號等效模型。 42
Figure 3-12：本論文設計電路CMOS T18製程之低阻抗輸出級。 43
Figure 3-13：本論文設計電路CMOS D35製程之低阻抗輸出級。 43
Figure 3-14：(a) Hspice模擬T18整體電路增益結果。(b) Hspice模擬T18整體電路增益與相位關係。 44
Figure 3-15：(a) Hspice模擬D35整體電路增益結果。(b) Hspice模擬D35整體電路增益與相位關係。 45
Figure 4-1：側視圖說明SOI-MEMS共振器的製程。(a) SOI Wafer側視圖。(b)定義共振器幾何結構。(c)犧牲氧化矽層生成。(d)定義共振器周圍電極。(e)利用光阻定義金屬與蝕刻孔洞位置。(f)乾式蝕刻以移除二氧化矽而釋放共振器結構。 49
Figure 4-2：方形板共振器的SEM全景圖，包括電容致動器與電極板。 50
Figure 4-3：方形板共振器表面蝕刻孔洞局部放大SEM圖。 50
Figure 4-4：具微小50奈米傳導間隙的方形板共振器與多晶矽側電極。 51
Figure 5-1：Lamè模態共振器的雙埠(Two-Port)量測實驗儀器架設。 55
Figure 5-2：Lamè模態共振器在不同極化電壓下的量測結果。 55
Figure 5-3：Lamè模態共振器功率負載能力量測結果，訊號強度為-20dBm至0dBm。 56
Figure 5-4：具有微小間隙的Lamè模態共振器量測結果，其中虛線為當輸入較大交流訊號時共振器共振響應結果。 56
Figure 5-5：應用於振盪器之後端支撐電路OM圖: (a) CMOS 0.18µm製程。(b) CMOS 0.35µm製程。 58
Figure 5-6支撐電路增益變化圖: (a) CMOS 0.18µm製程。(b) CMOS 0.35µm製程。 59
Figure 5-7：微機械振盪器架構: (a) 單端輸入雙端輸出微機械振盪器(SIDO)。(b) 全差動式微機械振盪器(SIDO)。 61
Figure 5-8：應用於SIDO振盪器架構的商用電路AD8015與Ths4131的增益與相位量測結果。 61
Figure 5-9:印刷電路板裝載設計電路與共振器(利用wire bonding整合)的陶瓷板。 66
Figure 5-10: Lamè模態微機械振盪器相位雜訊表現(電路為CMOS 0.35μm製程)。 66
Figure 5-11: Lamè模態微機械振盪器時域輸出訊號(電路為CMOS 0.35μm製程)。 67
Figure 5-12: De-embedded振盪器開迴路量測：(a) SIDO；(b) DIDO架構(各圖中的小圖分別為沒經過De-embedding的振盪器開迴路量測)。 67
Figure 5-13：振盪器的基頻(~17.63 MHz)頻譜量測圖：(a) SIDO (VP=2.2V, Span=10 kHz)；(b) DIDO (VP=3.2V, Span=1 kHz)(各圖中的小圖分別為輸出訊號的時域波形)。 68
Figure 5-14：振盪器的相位雜訊量測圖：(a) SIDO；(b) DIDO。 69

表目錄
Table 1-1：電容式與壓電式制動的比較。 11
Table 2-1：機械參數與電路參數轉換關係。 20
Table 2-2：方型板共振器尺寸規格表。 24
Table 3-1：設計之電路與文獻的比較。 33
Table 3-2：支撐電路post-sim模擬與量測結果。 46
Table 5-1：本論文設計之轉阻放大器模擬與量測統整表。 60
Table 6-1：本論文設計之Lamè模態振盪器與現今商品化產品比較表。 72

[1] C. T.-C. Nguyen,"MEMS technology for timing and frequecny control,"IEEE Trans. Ultrason., Ferrolect., Freq. Contr.,vol. 54, no. 2, pp. 251-270, Feb. 2007.
[2] J. B. Muldavin and G. M. Rebeiz, "High-isolation CPW MEMS shunt switchesPart 2: Design," IEEE Trans. Microw., Tech., vol. 48, pp. 1053, 2000.
[3] S.-S. Li, Y.-W. Lin, Y. Xie, Z. Ren, and T.-C. Nguyen," Microelectromechanical Hollow-Disk Ring Resonators,"Proceedings, 17th Int. IEEE Micro Electro Mechanical Systems Conf., Maastricht, The Netherlands, Jan. 25-29, 2004, pp.821-824
[4] G. Piazza, P.J. Stephanou, J.P. Black, R.M. White, A. P. Pisano, "Single-Chip Multiple-Frequency RF Microresonators based on Contour-Mode and FBAR Technologies," 2005 IEEE Ultrasonic Symposium, Rotterdam,pp. 1187-1190, 2005.
[5] R Abdolvand, H. Mirilavasani, G.K. Ho and F. Ayazi, "Thin-Film Piezoelectric-on-Silicon Resonators for High-Frequency Reference Oscillator Application,"IEEE Trans. Ultrason., Ferrolect., Freq. Contr.,vol. 55, Issue 12, pp. 2596-2606, Dec. 2008.
[6] A. Kaajakari, et al., "Square-extensional mode single-crystal silicon micromechanical resonator for low-phase-noise oscillator applications," IEEE Electron Devices Letters , vol. 25, no. 4, pp. 173-175, April 2004.
[7] Y. W. Lin, S. S. Li, Z. Ren, T.-C. Nguyen, "Low phase noise array-composite micromechanical wine-glass disk oscillators," in 2005 IEEE International Electron Devices Meeting (IEDM),Dec. 2005, pp. 287-290.
[8] T.-C. Nguyen and Howe R T,"An integrated CMOS micromechanical resonator high-Q oscillator,"IEEE J.Solid-State Circuit 34 440-55.
[9] H. M. Lavasani, A. K. Samarao, H. Casinovi, and F. Ayazi, "A 145MHz low phase-noise capacitive silicon micromechanical oscillator," IEDM2008, pp.675-678, Dec. 2008.
[10] Eric Colinet, Julien Arcamone, Antoine Niel, Emerick Lorent, Sèbastien Hentz, Eric Ollier, "100MHz oscillator based on a low polarization voltage capacitive Lamé-mode MEMS resonator,"FCS 2010 , pp. 174-178, June,2010.
[11] V. Kaajakari, Tomi Mattila, Aarne Oja, Jyrki Kiihamaki, Heikki Seppa, "Square-Extension mode single-Crystal silicon micromechanical resonator for low-phase-noise oscillator applications," IEEE Electron Device Letters, vol. 25, no. 4, pp. 173-175, April,2004.
[12] R. J. Matthys, Crystal Oscillator Circuits. New York: John Wiley & Sons, 1983.
[13] Discera, Inc., http://www.discera.com/
[14] SitTime, Inc., http://www.sitime.com/
[15] Y. W. Lin, S. Lee, Z. Ren, T.-C. Nguyen, "Series-resonant micromechanical resonator oscillator phase noise," Technical Digest, 2003 IEEE International Electron Devices Meeting, Washington, DC, Dec. 8-10,2003, pp. 341-349.
[16] S. Lee and T.-C. Nguyen, "Influence of automatic level control on micromechanical resonator oscillator phase noise,"Proceedings, 2003 IEEE Int. Frequency Control Symposium, Tampa Florida, May 5-8, 2003, pp. 341-349.
[17] S. Lee and T.-C. Nguyen, "Mechanically-coupled micromechanical arrays for improved phase noise,"Proceedings, IEEE Int. Ultrason., Ferrolect., Freq. Control 50th Anniv. Joint Conf., Montreal, Canada, Aug. 24-27, 2004, pp.280-286.
[18] W. A. Brantley, "Calculated elastic constants for stress problems associated with semiconductor devices, "Journal of Applied Physics, Vol. 44, no. 1, pp.534-535, Jan 1973.
[19] J. J. Wortman and R. A. Evans, "Youngs, modulus, shear modulus and poisson,s ratio in silicon and germanium, " Journal of Applied Physics, Vol. 36, no. 1, pp.153-156, Jan 1965.
[20] S. D. Senturia, Microsystem design, Kluwer Academic Publishers, 2001.
[21] W. W. Jr, S. P. Timpshenko, and D. H. Young, Vibration problems in engineering, 5th ed. John Wiley & Sons, 1990.
[22] C. T.-C. Nguyen and R. T. Howe, "An integrated CMOS micromechanical resonator high-Q oscillator," IEEE J. Solid-State Circuits, vol. 34,no.4,pp. 440-455, April 1999..
[23] H. M. Lavasani et al.,“A 76dBΩ 1.7GHz 0.18μm CMOS tunable TIA Using Broadband Pre-Amplifier for High Frequency Lateral MEMS oscillators,” IEEE J. Solid-State Circuits, vol. 46, no. 1, pp. 224-235, Jan. 2011.
[24] F. Nabki et al., “A highly integrated 1.8 GHz frequency synthesizer based on a MEMS resonator,” IEEE J. Solid-State Circuits, vol. 44, pp. 2154–2168, Mar. 2009.
[25] James Salvia et al.,“A 56MΩ CMOS TIA for MEMS Applications,” Tech. Dig., IEEE Custom Integrated Circuits Conference (CICC), 2009 pp. 198-202