本研究將針對機械耦合式CMOS-MEMS濾波器進行設計及特性探討。為了於頻譜上實現訊號濾波功能，文中所使用的共振器皆以雙端自由樑來實現，並以特殊設計之機械耦合樑，將一對共振器單元組成雙自由度系統，其中耦合樑之幾何形狀與座落位置將決定濾波通帶之頻寬大小。
建立在上述基礎下，我們利用CMOS結構中現有之金屬堆疊層進行濾波器製作，過程中為了使電容式元件具備較低的運動阻抗值，將使用陣列式結構設計以及間隙縮減技術，藉此獲得大範圍之感測面積與次微米換能間隙。量測上將使用De-Embedding技術去除外界寄生效應的干擾，並搭配適當端點阻抗，使平坦之濾波通帶順利於頻譜上實現。值得一提的是，於量測過程中，亦發現使用複合材料將有效提升系統共振頻之溫度穩定度。
而文中亦提出利用氧化物複合結構所開發的濾波元件，相較於上述之金屬複合結構，雖說元件後製作過程相對複雜，但理想上可獲得較為優異之機電轉換係數與品質因數表現。此外，鑑於傳統雙埠量測架設將為元件帶來可觀的寄生效應，因此，本研究使用差分驅動架構進行濾波元件的操作，在不使用De-Embedding技巧下，成功移除雜散電容對濾波頻帶所帶來的影響。
本文採用標準CMOS製程來實現中頻機械耦合式帶通濾波器，希冀能藉由其高度電路整合特性，進一步改善傳統應用於無線收發系統內之離散式或高功率消耗之濾波元件。

This work reports on the design and characterization of a mechanically-coupled CMOS-MEMS filter centered at several MHz with a narrow bandwidth and reasonable insertion loss after filter termination performed in a 4-port network analyzer. To implement a bandpass filter, the proposed filter structure produces two physical resonance modes, therefore forming a filter passband with a desired bandwidth by the use of the mechanical coupler at proper coupling locations.
By the use of a conventional filter design, the metal stacking layers in a foundry-oriented CMOS platform were used to fabricate the device structures, making great progress aligned with existing fabrication lines. To further reduce the motional impedance, the high-velocity coupled array and gap-reduction mechanism were adopted to create larger transduction areas and tiny gap spacing for capacitive transducers, respectively. However, due to the existence of undesired parasitics from a typical two-port configuration, the resonance response would be dwarfed and masked by the background feedthrough floor. Furthermore, the matching condition is also limited by shunt capacitance at the I/O ports for filter transmission, that significantly barricades the proper filter termination. To solve this issue, a pure motional response of the proposed filter can be extracted once the de-embedding scheme is carried out.
To attain the lower material loss, the silicon dioxide structure was developed in this work as well. Ideally, the SiO2 can provide better electromechanical coupling and higher quality factor as compared with the metal stacking counterparts. Based on the electrical isolation of the oxide structure, the filter devices can be operated in differential configuration via the balun function on the network analyzer. With that, the feedthrough parasitic can be evidently alleviated without any post-data processing, thus creating 30dB noise-floor improvement in filter performance.

目錄
第一章 前言 1
1-1 研究動機 1
1-2 文獻回顧 5
1-3 文章架構 9
第二章 理論分析及元件模擬 11
2-1 理論模型的建立 11
2-1-1 機械系統 12
2-1-2 等效電路 13
2-1-3 雙端自由樑 (free-free beam) 共振器 16
2-2 機械濾波器模型 21
2-2-1 機械耦合樑模型 22
2-2-2 Termination考量 27
第三章 金屬複合結構 30
3-1元件設計與模擬 31
3-1-1 增加感應面積 32
3-1-2 縮減運動間隙 34
3-1-3 參數設計及模擬 36
3-2 元件製程與製作結果 38
3-2-1 CMOS-MEMS後製程 39
3-2-2製程結果檢視 41
3-3 量測設置及結果 44
3-3-1 元件寄生效應去除(De-Embedding)技術 44
3-3-2 共振器量測 46
3-3-3 溫度特性量測 49
3-3-4 濾波器量測 51
第四章 氧化物複合結構 60
4-1元件設計及模擬 61
4-2元件製程與製作結果 65
4-2-1 CMOS-MEMS後製程 65
4-2-2製程結果檢視 69
4-3 量測設置及結果 71
4-3-1 濾波器雙埠量測 72
4-3-2差分驅動式濾波器量測 77
第五章 結論與未來研究 82
5-1 結論 82
5-2 未來研究 84
第六章 參考文獻 86

圖目錄
Figure 1.1: 超外插(Superheterodyne)接收器架構示意圖 2
Figure 1.2: 直接降頻(Direct-Conversion)收發器架構示意圖 3
Figure 1.3: Low-IF接收器架構示意圖 4
Figure 1.4: Avago Tx/Rx 雙工器系統 7
Figure 1.5: CMOS-MEMS濾波器相關範例 8
Figure 2.1: 樑型共振元件及其二階系統等效模型 11
Figure 2.2: 電容式共振元件模型及其驅動方式 12
Figure 2.3: 自由樑截面示意圖 16
Figure 2.4: 共振器工作頻率藉由直流偏壓調變 20
Figure 2.5: 計入寄生效應之共振器等效電路 20
Figure 2.6: 雜散電容對於頻率響應之影響 20
Figure 2.7: 濾波器之機械模型與其頻率響應 21
Figure 2.8: 機械耦合樑示意圖及其T-shaped等效模型 22
Figure 2.9: 濾波器等效電路模型 25
Figure 2.10: 耦合樑長度與剛性之對應關係(Al, ws=hs=1um, fo=8MHz) 26
Figure 2.11: 耦合樑長度與頻寬之對應關係(Al, ws=hs=1um, fo=8MHz) 26
Figure 2.12: 濾波器Termination過程(CP = 0pF) 29
Figure 2.13: 濾波器Termination過程(CP = 1pF) 29
Figure 3.1: 金屬複合結構之濾波器元件示意圖 32
Figure 3.2: CMOS-MEMS自由樑濾波器之有限元素模態模擬 32
Figure 3.3: 陣列式設計示意圖 34
Figure 3.4: 吸附效應(Pull-In)示意圖 35
Figure 3.5: 基於金屬複合結構之濾波器響應模擬 36
Figure 3.6: TSMC 0.35um CMOS 2P4M 標準製程剖面圖 39
Figure 3.7: CMOS-MEMS元件後製作過程之前後比較 40
Figure 3.8: 雙端自由樑陣列式共振器之SEM全景圖 42
Figure 3.9: Pull-in外框與Meander Spring之SEM放大圖 42
Figure 3.10: 雙端自由樑陣列式濾波器之SEM全景圖 43
Figure 3.11: 機械耦合樑(Coupler) 之SEM放大圖 43
Figure 3.12: 共振器(a)開啟與(b)關閉之等效電路模型 46
Figure 3.13: 陣列式共振器單埠(One-Port)量測架設圖 47
Figure 3.14: 自由樑陣列式共振器之量測結果 48
Figure 3.15: 對應不同元件材料之TCf量測結果 50
Figure 3.16: 對應不同陣列數之TCf量測結果 51
Figure 3.17: 陣列式濾波器雙埠(Two-Port)量測架設圖 52
Figure 3.18: 陣列式濾波器雙埠(two-port)架構量測結果 52
Figure 3.19: 濾波器頻寬調變能力 53
Figure 3.20: De-Embedding與Termination技術示意圖 56
Figure 3.21: 濾波頻帶使用De-Embedding技術之響應結果 56
Figure 3.22: 濾波頻帶進行阻抗匹配後之響應結果 57
Figure 4.1: 基於蝕刻Metal1所達成之等效運動間隙 61
Figure 4.2: 基於蝕刻Poly2所達成之等效運動間隙 61
Figure 4.3: 氧化物複合結構之濾波器元件示意圖 63
Figure 4.4: 基於氧化物複合結構之濾波器響應模擬 63
Figure 4.5: 以Metal1空間作為運動間隙之元件後製作過程 66
Figure 4.6: 以Poly2空間作為運動間隙之元件後製作過程 68
Figure 4.7: 雙端自由樑陣列式濾波器之SEM全景圖 69
Figure 4.8: 機械耦合樑(Coupler) 之SEM放大圖 70
Figure 4.9: 以Metal1空間作為運動間隙之結構剖面 70
Figure 4.10: 以Poly2空間作為運動間隙之結構剖面 71
Figure 4.11: 陣列式濾波器雙埠(Two-Port) 量測架構 72
Figure 4.12: 濾波器量測結果─以M1空間作為感測間隙 74
Figure 4.13: 濾波器量測結果─以Poly2空間作為感測間隙 75
Figure 4.14: 濾波頻帶進行阻抗匹配後之響應結果 75
Figure 4.15: 陣列式濾波器差分驅動式量測架構 78
Figure 4.16: 濾波元件於差動與雙埠量測架構之響應比較 79
Figure 4.17: 濾波元件於差動架構下之阻抗匹配過程 80
Figure 4.18: 濾波頻帶進行阻抗匹配後之響應結果 80
 
表目錄
Table 1.1: 中頻帶通濾波器規格表 4
Table 3.1: 單石式整合製程比較表 30
Table 3.2: 基於金屬堆疊之陣列式共振器設計參數 37
Table 3.3: 基於金屬堆疊之陣列式共振器規格 58
Table 3.4: 基於金屬堆疊之陣列式濾波器規格 59
Table 4.1: 基於氧化物複合材料之陣列式濾波器設計參數 64
Table 4.2: 雙埠架構下氧化物複合材料之陣列式濾波器規格 76
Table 4.3: 差動架構下氧化物複合材料之陣列式濾波器規格 81
Table 5.1: CMOS-MEMS濾波器比較 85
Table 5.2: 機械與電路式濾波器比較 85

[1]J. Adut, J. Silva-Martinez, M. Rocha-Perez, “A 10.7-MHz sixth-order SC ladder filter,” IEEE Transactions on Circuits and Systems, vol. 53, no. 8, Aug., 2006, pp. 1625-1635.
[2]H. A. Alzaher, M. K. Alghamdi, “A CMOS bandpass filter for low-IF bluetooth receivers,” IEEE Transactions on Circuits and Systems, vol. 53, no. 8, Aug., 2006, pp. 1636-1647.
[3]Ceramic Filters CERAFIL® /Ceramic Discriminators for Communications Equipment, Murata Manufacturing Co., Ltd., http://www.murata.com/products/catalog/pdf/p05e.pdf
[4]H. C. Nathanson, W. E. Newell, R. A. Wickstrom, J. R. Davis, “The Resonant Gate Transistor,” IEEE Transactions on Electron Devices, vol. ED-14, no. 3, Mar., 1967, pp. 117-133.
[5]L. Lin, C. T.-C. Nguyen, R. T. Howe, and A. P. Pisano, “Micro electromechanical filters for signal processing,” Proceeingsd, Int. IEEE Micro Electro mechanical Systems (MEMS1992), Travemunde, Germany, Feb. 4-7, 1992, pp. 226-231.
[6]K. Wang and C. T.-C. Nguyen, “High-order medium frequency micromechanical electronic filters,” Journal of Microelectromechanical System, vol. 8, no. 4, Dec. 1999, pp. 534-557.
[7]S.-S. Li, Y.-W. Lin, Z. Ren, and C. T.-C. Nguyen, “An MSI micromechanical differential disk-array filter,” Tech. Digest, the 14th Int. Conf. on Solid-State Sensors & Actuators (Transducers’07), Lyon, France, June 11-14, 2007, pp. 307-311.
[8]W. Pan, V. A. Thakar, M. Rais-Zadeh, and F. Ayazi, “Acoustically coupled thickness-mode AlN-on-Si band-pass filters—part I: principle and devices,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 59, no. 10, Oct. 2012, pp. 2262-2269.
[9]M. Rinaldi, C. Zuniga, C. Zuo, and G. Piazza, “Ultra-thin super high frequency two-port ALN contour-mode resonators and filters,” the 15th Int. Conf. on Solid-State Sensors, Actuators and Microsystems (Transducers’09), Denver, Colorado, USA, June 21-25, 2009, pp. 577-580.
[10]E. Hwang, T. A. Gosavi, S. A. Bhave, “Cascaded channel-select filter array architecture using high-K transducers for spectrum analysis,” 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum, May 2-5, 2011, pp.1-6.
[11]R. Ruby, M. Small, F. Bi, D. Lee, L. Callaghan, R. Parker, S. Ortiz, “Positioning FBAR technology in the frequency and. timing domain,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 59, no. 3, Mar. 2012, pp. 334-345.
[12]F. Chen, J. Brotz, U. Arslan, C.-C. Lo; T. Mukherjee, G. K. Fedder, “CMOS-MEMS resonant RF mixer-filters,” Proceedings, 18th IEEE Int. Conf. on IEEE Micro Electro Mechanical Systems (MEMS’05), Jan. 30 - Feb. 3, 2005, pp. 24–27.
[13]J. L. Lopez, J. Verd, J. Giner, A. Uranga, G. Murillo, E. Marigo, F. Torres, G. Abadal and N. Barniol, “High Q CMOS-MEMS resonators and its applications as RF tunable band-pass filters,” the 15th Int. Conf. on Solid-State Sensors, Actuators and Microsystems (Transducers’09), Denver, Colorado, USA, June 21-25, 2009, pp. 557-560.
[14]J. Giner, A. Uranga, F. Torres, E. Marigo, J. L. Muñoz Gamarra and N. Barniol, “A CMOS-MEMS filter using a V-coupler and electrical phase inversion,” 2010 IEEE International Frequency Control Symposium (IFCS), June 1-4 2010, pp.344-348.
[15]F. D. Bannon, J. R. Clark and C. T.-C. Nguyen, “High-Q HF microelectromechanical filters,” IEEE Journal of Solid-State Circuits, vol.35, no.4, April, 2000, pp. 512-526.
[16]R. Ludwig and G. Bogdanov., RF Circuit Design: Theory and Applications, international editions, Pearson Prentice Hall, 2006.
[17]S. S. Rao, Mechanical Vibrations, 4th ed., Upper Saddle River, NJ: Pearson Prentice Hall, 2004.
[18]A. I. Zverev, Handbook of Filter Synthesis. New York: Wiley, 1967.
[19]M. Konno and H. Nakamura, “Equivalent electrical network for the transversely vibrating uniform bar,” Journal of the Acoustical Society of America, vol. 38, no.4, Oct. 1965, pp.614–622.
[20]C. Zuo, N. Sinha, G. Piazza, “Very high frequency channel-select MEMS filters based on self-coupled piezoelectric AlN contour-mode resonators”, Sensors and Actuators A: Physical, vol. 160, no. 1-2, May 2010, pp. 132-140.
[21]G. K. Fedder, R. T. Howe, T.-J. King Liu, E. P. Quevy, “Technologies for cofabricating MEMS and electronics”, Proceedings of the IEEE, vol.96, no. 2, Feb. 2008, pp. 306-322.
[22]M. Demirci and C. T.-C. Nguyen, “Mechanically corner-coupled square microresonator array for reduced series motional resistance,” IEEE Journal of Microelectromech. Systems, vol. 15, no. 6, Dec. 2006, pp. 1419-1436.
[23]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, vol. 59, no. 3, Mar. 2012, pp. 346-357.
[24]W.-C. Chen, M.-H. Li, W. Fang and S.-S. Li, “Realizing deep-submicron gap spacing for CMOS-MEMS resonators with frequency tuning capability via modulated boundary conditions,” Proceedings, 2010 IEEE 23rd Int. Conf. on IEEE Micro Electro Mechanical Systems (MEMS’10), Hong Kong, 2010, pp. 735-738.
[25]M.-H. Li, W.-C. Chen, and S.-S. Li, “CMOS-MEMS transverse-mode square plate resonator with high Q and low motional impedance,” Proceedings, 16th Int. Conf. on Solid-State Sensors & Actuators (Transducers’11), Beijing, China, June 5-9, 2011, pp.1500-1503.
[26]D. Galayko, A. Kaiser, B. Legrand, D. Collard, L. Buchaillot and C. Combi, “High-frequency high-Q micro-mechanical resonators in thick epipoly technology with post-process gap adjustment,” Proceedings, 2002 IEEE 15th Int. Conf. on IEEE Micro Electro Mechanical Systems (MEMS’02), Las Vegas, NV, USA, 2002, pp. 665-668.
[27]M.-H. Cho, G.-W. Huang, C.-S. Chiu, K.-M. Chen, A.-S. Peng, and Y.-M. Teng, “A cascade open short thru COST de-embedding method for microwave on-wafer characterization and automatic measurement,” IEICE Transactions on Electronics, E88-C (5), 845-850, 2005.
[28]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, Jan. 25-29, 2009, pp. 23-26.
[29]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, Dec. 2012, pp. 4930 - 4937.
[30]W.-C. Chen, M.-H. Li, W. Fang, and S.-S. Li, “High-Q integrated CMOS-MEMS resonators with deep-submicron gaps,” Tech. Digest, 64th IEEE International Frequency Control Symposium (IFCS’10), Newport Beach, California, USA, June 1-4, 2010, pp.340-343.
[31]Chiung-Cheng Lo, “CMOS-MEMS Resonators for Mixer-Filter Application,” PhD Dissertation, Carnegie Mellon University, July, 2008.
[32]W.-C. Chen, C.-S. Chen, K.-A. Wen, L.-S. Fan, W. Fang and S.-S. Li, “A generalized foundry CMOS platform for capacitively-transduced resonators monolithically integrated with amplifiers,” Proceedings, 2010 IEEE 23rd Int. Conf. on IEEE Micro Electro Mechanical Systems (MEMS’10), Hong Kong, 2010, pp. 204-207.
[33]W.-L. Huang, “Fully monolithic CMOS nickel micromechanical resonator oscillator for wireless communications,” Ph.D. dissertation, Dept. of Electrical Engineering and Computer Science, University of Michigan at Ann Arbor, 2008.
[34]Y.-C. Liu, M.-H. Tsai, W.-C. Chen, S.-S. Li, and W. Fang, “High-Q, large-stopband-rejection integrated CMOS-MEMS oxide resonators with embedded metal electrodes,” Tech. Digest, the 16th Int. Conf. on Solid-State Sensors & Actuators (Transducers’11), Beijing, China, June 5-9, 2011, pp. 934-937.
[35]C.-H. Chin, M.-H. Li, and S.-S. Li, “A CMOS-MEMS resonant-gate transistor,” the 17th Int. Conf. on Solid-State Sensors & Actuators (Transducers’13), Barcelona. Spain, June 16-20, 2013.
[36]F. Nabki, K. Allidina, F. Ahmad, P.-V. Cicek, M. N. El-Gamal, “A highly integrated 1.8 GHz frequency synthesizer based on a MEMS resonator,” IEEE Journal of Solid-State Circuits, vol.44, no.8, Aug. 2009, pp. 2154-2168.
[37]H. M. Lavasani, W. Pan, and F. Ayazi, “An electronically temperature-compensated 427MHz low phase-noise AlN-on-Si micromechanical reference oscillator,” Proceedings, 2010 IEEE Radio Frequency Integrated Circuits Symposium (RFIC), Anaheim, CA, May 23-25, 2010, pp.329-332.
[38]Janet Stillman, “CMOS-MEMS Resonant Mixer-Filters,” Master Dissertation, Carnegie Mellon University, July, 2003.