進行微機電元件開發時，微機電元件結構與整體封裝型式的可靠度分析是相當重要的一環。本研究以有限單元模型對CMOS-MEMS具繞折式彈簧電容式微機電麥克風進行可靠度分析，模擬微機電麥克風在運作時受到聲壓、振動、衝擊等外力負載時之應力與變形，並以振動與掉落實驗驗證模擬結果。
為分析具繞折式彈簧結構微機電麥克風之可靠度，本文首先探討單一麥克風元件結構，分析麥克風結構在運作時受到外界負載聲壓、振動、衝擊與兩電極板間靜電力，多種負載耦合下之變形與受力之靜、動態行為。文中也以靜電力關係式簡化靜電與結構的複雜負載耦合問題。結果可知當振膜受到靜電力、聲壓與衝擊負載後，振膜最大主應力比只受到衝擊負載提升1.89倍;而以多晶矽(Polysilicon)作為微機電麥克風振膜之材料可減低最大主應力23.1%，減低最大位移61.6%；也發現考慮製程誤差時，麥克風可能發生吸附現象無法運作。另外進行模態分析時，發現整體模型之共振頻率遠小於麥克風元件結構之頻率，顯示整體模型更容易發生共振現象。從微機電麥克風陣列模型受衝擊負載之結果可知，當麥克風受衝擊負載時，在彈簧轉角處、彈簧與固定端連接處轉角、彈簧與振膜連接處及矽基板中央皆為應力集中和結構脆弱處且與掉落實驗麥克風破裂位置相似。最後在封裝可靠度分析上以板級模型進行分析，結果顯示板級模型受衝擊負載時黏膠層應力值已超出其鍵結強度，可能因黏膠層脫層或破裂而發生失效；也發現使用剛性較低之黏膠可有效降低應力。本文中對微機電麥克風結構與整體封裝型式的可靠度分析結果，可給予設計者參考。

The reliability analysis of MEMS (Micro Electro Mechanical System) components is an important issue when developing the novel MEMS sensor. In this study, finite element models are used to analyze the reliability of CMOS-MEMS capacitive microphone with serpentine spring under sound pressure, vibration, shock and electrostatic force. The simulation results were verified by vibration and drop test experiments.
The deformation and stress distribution of single MEMS microphone diaphragm under multiple loads, including sound pressure, vibration, shock and electrostatic force were analyzed to obtain the static and transient behavior of MEMS microphone. The equilibrium equation of multiple loads was used to simplify the loading coupling problem. The results show that the maximum 1st principal stress of MEMS microphone under sound pressure, shock loading and electrostatic force is 1.89 times higher than that of MEMS microphone under shock loading only. Replacing the diaphragm material of MEMS microphone from silicon dioxide to polysilicon can reduce 23.1 % of maximum stress and 61.6% of maximum displacement of MEMS microphone. The pull-in effect of MEMS microphone may occur due to possible imperfection in manufacturing process. Additionally, the fundamental frequency of MEMS microphone packaging model with printed circuit board is much smaller than that of single MEMS microphone and is more likely to resonate. The stress concentration regions are found at the corner of spring, the connection of spring and fixed end, the connection of spring and diaphragm and the center of silicon substrate in the MEMS microphone array and are consistent with those found from drop test experiment. Finally, the reliability of MEMS microphone packaging was evaluated by board level drop test simulation. The results show that the maximum von Mises stress of adhesive layer under shock loading exceeds the adhesive bond strength and the adhesive may fail possibly. And using an adhesive with a smaller stiffness can effectively reduce its stress. The results presented in this study can give valuable suggestions for the MEMS capacitive microphone designers.

1. M. Fuldner, A. Dehe and R. Lerch, “Analytical analysis and finite element simulation of advanced membranes for silicon microphones,” IEEE Sensor Journal, Vol. 5, pp. 857-863, 2005.
2. A. Dehe, “Silicon microphone development and application,” Sensor and Actuator A: Physical, Vol. 133, pp. 283-287, 2007.
3. J. Li, T. Mattila and V. Vuorinen, Handbook of silicon based MEMS materials and technologies, second edition, William Andrew, Norwich, NY, Chapter 41, pp. 744-763, 2015.
4. 呂如梅，微機電麥克風技術簡介，國家奈米元件實驗室奈米通訊，20卷，21-27頁，2013。
5. W. Chuang, H. Lee, P. Chang and Y. Hu, “Review on the modeling of electrostatic MEMS,” Sensor, vol. 10, pp. 6149-6171, 2010.
6. 莊婉君，胡毓忠，微機電元件之電彈性質研究現況介紹，2008。
7. P. Osterberg, H. Yie, X. Cai, J. White, and S. Senturia, “Self-Consistent simulation and modeling of electrostatically deformed diaphragms,”Proceedings IEEE Electro Mechanical Systems An Investigation of Micro Structures, Sensors, Actuators, Machines and Robotic Systems, Oiso, Japan, pp. 28-32, 1994.
8. J. Lardies, M. Berthillier, “A methodology for the pull-in voltage of clamped diaphragm,” 2011 Symposium on Design, Test, Integration & Packaging of MEMS/MOEMS (DTIP), Aix-en-Provence, France, 2011.
9. C. Maj, W. Zabierowski and A. Napieralski, “Parameterized model of MEMS microphone in comsol multiphysics,” The 14th International Conference The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), Lviv, Ukraine, 2017.
10. A. Saeedivahdat, F. Abdolkarimzadeh, A. Feyzi, G. Rezazadeh and S. Tarverdilo, “Effect of thermal stresses on stability and frequency response of a capacitive microphone,” Microelectronics Journal, vol. 41, pp. 865-873, 2010.
11. S. Talebian, G, Rezazadeh, M. Fathalilou and B. Toosi, “Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate,” Mechatronics, Vol. 20, Issue 6, pp. 666-673, 2010.
12. Knowles SPU0410LR5H MEMS Microphone cross section, http://www.system plus.fr/wp-content/uploads/2011/11/SP11073-Knowles-SPU0410LR5H-MEMS-Microphone_sample.pdf, retrieved on June 22, 2018.
13. Akustica AKU230 MEMS Microphone cross section, http://www.systemplus.fr/ wp-content/uploads/2011/11/SP11070-Akustica-AKU230-MEMS-Microphone-_sample.pdf, retrieved on June 22, 2018.
14. Analog Devices ADMP421 MEMS Microphone cross section, http://www.Syst emplus.fr/wp-content/uploads/2011/11/SP11066-ADI-ADMP421-MEMS-Microphone_sample.pdf, retrieved on June 22, 2018.
15. EPCOS T4060 MEMS Microphone cross section, http://www.systemplus.fr/wp-content/uploads/2013/05/Micromachine_2012_S+C_MEMS_Teardown.pdf, retrieved on June 22, 2018..
16. O. Rusanen and A. Torkkeli, “Adhesive as a thermomechanical stress source-comparing silicones to epoxies,” Proceedings of the IEEE 3rd International Conference on Adhesive Joining and Coating Technology in Electronics Manufacturing, pp. 288-294, 1998.
17. M. Yew, C. Huang, W. Lin, C. Wang and P. Chang, “A study of residual stress effects on CMOS-MEMS microphone technology,” The 4th International Microsystems, Packaging, Assembly and Circuits Technology conference, pp. 323-326, 2009.
18. M. Fuldner, A. Dehe and R. Lerch, “Analytical analysis and finite element simulation of advanced membranes for silicon microphone,” IEEE Sensors Journal, Vol. 5, Issue 5, pp. 857-863, 2005.
19. F. Wenxiao and H. Qinwen, “A study of the mechanical reliability of a MEMS microphone,” The 20th IEEE International Symposium on the Physical and Failure Analysis of Integrated Circuits (IPFA), pp. 716-719, 2013.
20. J. Li, J. Makkonen, M. Broas, J. Hokka, T. Mattila and M. Paulasto-Krockel, “Reliability Assessment of a MEMS microphone under shock impact loading,” The 14th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), pp. 1-6, 2013.
21. J. Meng, S. Douglas and A. Dasgupta. “MEMS packaging reliability in board-level drop tests under severe shock and impact loading conditions—part I: experiment,” IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 6, pp. 1595-1603, 2016.
22. W. Wang, D. Robbins and C.Glancey. “Simulation model to predict failure cycles in board level drop test,”2016 IEEE 66th Electronic Components and Technology Conference, pp. 1886-1891, 2016.
23. Y. Chen, C. Wang and Y. Yang. “Combining vibration test with finite element analysis for the fatigue life estimation of PBGA components,” Microelectronics Reliability, Vol. 48, pp. 638-644, 2008.
24. 毛威智，具繞折式彈簧結構之CMOS-MEMS電容式麥克風的設計與實現，碩士論文，國立清華大學奈米工程與微系統研究所，2016。
25. ANSYS Release 12.1, ANSYS, Inc., PA, 2009.
26. R. D. Cook, D. S. Malkus, M. E. Plesha and R. J. Witt, Concepts and Application of Finite Element Analysis, 4th ed., Wiley, New York, 2002.
27. ANSYS User’s Manual, ANSYS, Inc.
28. 康淵，陳信吉，ANSYS入門，全華科技圖書，新北市，台灣，2005。
29. 王柏村，振動學，全華科技圖書，新北市，台灣，2014。
30. J. Dolbow and M. Gosz, “Effect of out-of-plane properties of a polyimide film on the stress field in microelectronic structures,” Mechanics of Materials, Vol. 23, Issue 4, pp. 311-321, 1996.
31. J. F. Shackelford and W. Alexander, CRC Materials Science and Engineering Handbook, 3th ed., CRC press, New York, 2001.
32. B. Halg, “On a nonvolatile memory cell based on Micro-electro-mechanics,” IEEE Proceedings on Micro Electro Mechanical Systems, An Investigation of Micro Structures, Sensor, Actuators, Machines and Robots, pp.172-176, 1990.
33. Siliver epoxy material property, http://www.matweb.com/search/datasheet.aspx? matguid=d40d54dbea2e400f972fdc44f7360cbd, retrieved on June 22, 2018.
34. 呂俊麟，三維異質整合微系統晶片之可靠度分析，碩士論文，國立清華大學動力機械工程學系，新竹，2010。
35. 王顗涵，內嵌壓力感測器之微加速度計受振動負載之有限單元分析，碩士論文，國立清華大學動力機械工程學系，新竹，2017。
36. H. Kahn, S. Stemmer, K. Nanadakumar, A. H. Heuer, R. L. Mullen, R. Ballarini and M. A. Huff, “Mechanical properties of thock, surface micromachined polysilicon films,” IEEE Proceedings on Micro Electro Mechanical Systems, An Investigation of Micro Structures, Sensor, Actuators, Machines and Systems, the 9th annual international workshop, pp. 343-348, San Diego, USA ,1996.
37. JESD22 B111, Board level drop test method of components for handheld electronic products, JEDEC Standard, 2003.
38. JESD22 B103B, Vibration, Variable Frequency, JEDEC Standard, 2006.
39. JESD22 B110B, Mechanical Shock-Component and Subassembly, JEDEC Standard, 2009.
40. L. B. Tan, C. W. Ang, C. T. Lim, V. B. C. Tan and X. Zhang, “Modal and impact analysis of morden portable eletronic products,” Electronic Components and Technology Conference, pp. 645-653, 2005.
41. C. L. Yeh, Y. S. Lai and C. L. Kao, “Evaluation of board-level reliability of electronic packages under consecutive drops,” Microelectronics. Reliability, vol. 46, pp. 1172-1182, 2006.
42. C. L. Coq, A. Tougui, M. P. Stempin and L. Barreau, “Optimization for simulation of WL-CSP subjected to drop-test plasticity behavior,” Microelectronics. Reliability, vol. 51, pp. 1060-1068, 2011.
43. M. L. Wu and J. S. Lan, “Reliability and failure analysis of SAC 105 and SAC 1025N lead-free solder alloys during drop test events,” Microelectronics. Reliability, vol. 80, pp. 213-222, 2018.
44. C. L. Yeh and Y. S. Lai, “Support excitation scheme for transient analysis of JEDEC board-level drop test,” Microelectronics Reliability, vol. 46, pp. 626-636, 2006.
45. C. L. Yeh, Y. S. Lai and C. L. Kao, “Evaluation of board-level reliability of electronic packages under consecutive drops,” Microelectronics Reliability, vol. 46, pp. 1172-1182, 2006.
46. M.K. Yeh, T. H. Huang, “Drop test and finite element analysis of test board,” Procedia Engineering, vol. 79, pp. 238-243, 2014.