本論文利用標準CMOS 0.35 µm製程中之Poly-2層蝕刻以及Contact陣列結構設計製作出一具有微小等效換能間隙之微機械共振器陣列，並搭配全差動式轉阻放大器實現單晶片CMOS-MEMS振盪器電路架構。文中亦探討了高剛性驅動機制對本研究所設計共振器之最大功率負載的影響。
由於一般使用CMOS製程製作的電容式微機械共振器的運動阻抗(Rm)大約在0.1~10 MΩ的等級，使得將其應用於振盪器的設計變得非常困難，同時也降低了相位雜訊的表現。本論文嘗試在CMOS 0.35 µm製程中製作具有微小等效換能間隙之微機械共振器，其低運動阻抗的特性有利於振盪器電路的設計。我們同時也採用了「陣列結構」與「高剛性驅動」設計，在進一步降低運動阻抗的同時盡可能地提高其最大功率負載能力。另外在振盪器製作方面，我們設計一全差動式轉阻放大器並配合另一個「虛設」共振器(Dummy Resonator)用以在振盪器迴路中實現「Feedthrough Cancellation」的技巧。
本研究所設計之微機械共振器在真空環境的量測結果可以發現，在給定直流偏壓(VP)為30 V的條件下其Q值約為1,000，共振頻率為4.15 MHz，Rm經粗略計算為11 kΩ左右。我們同時也進行了高剛性與低剛性驅動機制的特性量測，並觀察到在兩種狀況下對於共振器之最大功率負載的明顯差異。而振盪器閉迴路的量測結果顯示了其工作頻率為4.22 MHz，且於1-kHz頻率偏移下的相位雜訊表現為-90 dBc/Hz，1-MHz頻率偏移下的相位雜訊為-121 dBc/Hz。

This work reports the design of a monolithic oscillator based on a low motional impedance (Rm) CMOS-MEMS resonator array with high-stiffness driving scheme in a standard 0.35 μm CMOS. Combined with polysilicon release process and the proposed “contact-array-assisted” gap spacing design, a tiny equivalent transducer’s gap (deff) of only 190 nm is successfully attained. We also discussed the effectiveness of the high-stiffness driving scheme to the proposed MEMS resonator.
Traditional capacitive CMOS-MEMS resonators often exhibit high motional impedance (Rm) in a range of 0.1 to 10 MΩ owing to their large gap spacing and insufficient transduction areas. Such a high Rm not only makes oscillator design very difficult, but also introduces additional thermal-mechanical noise in the oscillation spectrum. This work attempted to fabricate a MEMS resonator with deep-submicron gaps in the CMOS process, and the feature of the small motional impedance of the resonator makes the implementation of the oscillator easier. To address the nonlinearity issue for the narrow-gap resonators, the designed resonator is formed by multiple high-velocity coupled clamped-clamped beams with a high-stiffness driving scheme, thus greatly improving power handling and reducing motional impedance of the resonator. The dummy resonator and fully-differential transimpedance amplifier (FD-TIA) are also employed for active feedthrough cancellation.
Based on this feature, a low Rm of 10 kΩ is achieved under a medium bias voltage (VP) of only 30 V for a 4.15-MHz resonator in vacuum with the measured Q of 1,000. The combination of the mechanically coupled array and high-stiffness driving scheme significantly enhances oscillator performance. The 4.22-MHz single-chip CMOS-MEMS oscillator exhibits the phase noise of -90 dBc/Hz at 1-kHz offset and -121 dBc/Hz at 1-MHz offset, respectively.

[1] R. J. Matthys, Crystal Oscillator Circuits. New York: John Wiley & Sons, 1983.
[2] Discera, Inc., http://www.discera.com/
[3] SiTime, Inc., http://www.sitime.com/
[4] Y. W. Lin, S. S. Li, Z. Ren, T.-C. Nguyen, “Low phase noise array-composite micromechanical wine-glass disk oscillators,” Proceedings, 2005 IEEE International Electron Devices Meeting, pp. 287-290, Dec. 2005.
[5] C. T.-C. Nguyen and R. T. Howe, “An integrated CMOS micromechanical resonator high-Q oscillator,” IEEE J. Solid-State Circuit, vol. 34, pp. 440-55, 1999.
[6] H. M. Lavasani, A. K. Samarao, H. Casinovi, and F. Ayazi, “A 145-MHz low phase-noise capacitive silicon micromechanical oscillator,” Proceedings, 2008 IEEE International Electron Devices Meeting, pp.675-678, Dec. 2008.
[7] E. Colinet, J. Arcamone, A. Niel, E. Lorent, S. Hentz, and E. Ollier, “100-MHz oscillator based on a low polarization voltage capacitive Lamé-mode MEMS resonator,” Proceedings, 2010 Joint Conf. of the IEEE Int. Frequency Control Symp.(IFCS’10), pp. 174-178, June,2010.
[8] V. Kaajakari, T. Mattila, A. Oja, J. Kiihamaki, and H. 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.
[9] J. Verd, A. Uranga, J. Segura, and N. Barniol, “A 3 V CMOS-MEMS oscillator in 0.35 μm CMOS technology,” in Proceedings, 17th Int. Conf. Solid-State Sens., Actuators, Microsyst., Barcelona, Spain, pp. 806–809, Jun. 2013.
[10] M.-H. Li, C.-Y. Chen, C.-S. Li, C.-H. Chin, and S.-S. Li, “A monolithic CMOS-MEMS oscillator based on an ultra-low-power ovenized micromechanical resonator,” IEEE/ASME J. Microelectromech. Syst. (JMEMS), vol. 24, no. 2 pp. 360-372, April 2015.
[11] F. D. Bannon III, J. R. Clark, and C. T.-C. Nguyen, “High-Q HF microelectromechanical filters,” IEEE J. Solid-State Circuits, vol. 35, no. 4, pp. 512-526, April 2000.
[12] M.-H. Li, W.-C. Chen, and S.-S. Li, “Mechanically-coupled CMOS-MEMS free-free beam resonator arrays with enhanced power handling capability,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control (T-UFFC), vol. 59, no. 3, pp. 346-357, March 2012.
[13] S.-S. Li, “CMOS-MEMS resonators and their applications,” Proceedings, 2013 IEEE UFFC Joint Symposia, pp. 915-921, July 2013.
[14] M.-H. Li, W.-C. Chen, and S.-S. Li, “Mechanically-coupled CMOS-MEMS free-free beam resonator arrays with two-port configuration,” Proceedings, 2011 Joint Conf. of the IEEE Int. Frequency Control Symp.(IFCS’11), San Francisco, pp. 1-4, May 2-5, 2011.
[15] L.-J. Hou and S.-S. Li, “High-stiffness-driven micromechanical resonator oscillator with enhanced phase noise performance,” Applied Physics Letters (APL), vol. 100, no. 13, pp. 131908, 2012.
[16] K.-L. Chen, H. Chandrahalim, A. Graham, S. A. Bhave, R. T. Howe and T. W. Kenny, “Epitaxial silicon microshell vacuum-encapsulated CMOS-compatible 200 MHz bulk-mode resonator,” Proceedings, 2009 IEEE 22nd International Conference on Micro Electro Mechanical Systems (MEMS’09), Sorrento, Italy, pp. 23-26, Jan. 25-29, 2009.
[17] Y. Xu, J. E.-Y. Lee, “Single-Device and On-Chip Feedthrough Cancellation for Hybrid MEMS Resonators,” IEEE Transactions on Industrial Electronics, vol. 59, no. 12, pp. 4930-4937, Dec. 2012.
[18] Kun Wang, Ark-Chew Wong and Clark T.-C. Nguyen, “VHF Free–Free Beam High-Q Micromechanical Resonators,” IEEE/ASME J. Microelectromech. Syst. (JMEMS), vol. 9, no. 3 pp. 347-360, Sep. 2000.
[19] C.-H. Chin, C.-S. Li, M.-H. Li, Y.-L. Wang, S.-S. Li, “Fabrication and characterization of a charge-biased CMOS-MEMS resonant gate field effect transistor,” J. Micromech. Microeng. (JMM), vol.24, no.9, pp. 095005, 2014.
[20] 陳昭瑜，“機械耦合式CMOS-MEMS濾波器之設計與特性探討”，國立清華大學奈米工程與微系統研究所碩士論文，中華民國102年。
[21] Y. Lin, et al., “A resonance dynamical approach to faster, more reliable micromechanical switches,” Proceedings, 2008 Joint Conf. of the IEEE Int. Frequency Control Symp.(IFCS’08), pp. 640-645, May. 2008.
[22] J. Verd, A. Uranga, G. Abadal, J. L. Teva, F. Torres, J. LÓpez, F. PÉrez-Murano, J. Esteve, and N. Barniol, “Monolithic CMOS MEMS oscillator circuit for sensing in the attogram range,” IEEE Electron Device Letters, vol. 29, no. 2, pp. 146-148, Feb. 2008.
[23] F. Nabki, K. Allidina, F. Ahmad, P.-V. Cicek, and M. N. El-Gamal, “A highly integrated 1.8 GHz frequency synthesizer based on a MEMS resonator,” IEEE J. Solid-State Circuits, vol. 44, no. 8, pp. 2154-2168, Aug. 2009.
[24] V. Petrescu, J. Pettine, D. M. Karabacak, M. Vandecasteele, M. C. Calama, and C. Van Hoof, “Power-efficient readout circuit for miniaturized electronic nose,” Proceedings, 2012 IEEE International Solid-State Circuits Conference, pp. 318-320, 2012.
[25] 蔡明翰，“新型CMOS MEMS全差動Z軸加速度計”，國立清華大學奈米工程與微系統研究所碩士論文，中華民國96年。