臺灣博碩士論文加值系統

目前MEMS在有關提升元件表現良率的研究，大多是以改善製程方法來提升良率，鮮少以穩健設計的方法來改善。如果只以改善製程方法來提升MEMS元件表現的一致性，往往需要提高製造成本。為了不提高製造成本而又能提升元件的表現一致性，本研究利用穩健設計方法來設計MEMS元件的尺寸。研究方法首先先推導目標函數，此目標函數是元件尺寸及MEMS元件的表現的函數。接著將此目標函數利用Lagrange乘數法或田口實驗法來探討MEMS元件的表現和製程誤差之關係，以找出使元件表現一致性的最佳元件尺寸。本研究找出製程誤差影響共振頻率一致性最小的微懸臂樑或掃描面鏡的尺寸。為了驗證，分別將微懸臂樑與掃描面鏡以設計的最佳尺寸及其相近尺寸製造出來，並量測不同尺寸頻率之一致性以證明設計結果是最佳的。為了更增加穩健性，本研究尚將一個晶圓分成三個區域以討論分區設計之可行性。

目 錄 I
圖目錄 IV
表目錄 IX
第一章 緒論 1
1-1 前言 1
1-2 研究動機 1
1-3 文獻回顧 2
1-4 研究目標 9
第二章 穩健設計的元件 21
2-1 懸臂樑 21
2-1.1 懸臂樑共振頻率與模態 21
2-1.2 微懸臂樑的製作流程 23
2-2 微掃描面鏡 24
2-2.1 微掃描面鏡共振頻率與模態 24
2-2.2 微掃描面鏡的製作流程 25
第三章 微懸臂樑共振頻率的穩健設計 32
3-1 微懸臂樑共振頻率的穩健設計方法 32
3-1.1 標準差與公差 32
3-1.2 Lagrange乘數法 34
3-1.3 Lagrange乘數法穩健設計的過程 35
3-2 微懸臂樑共振頻率的穩健設計流程 36
3-2.1 目標函數 36
3-2.2 製程標準差量測 37
3-2.3 穩健設計尺寸方程式 37
3-2.4 穩健設計尺寸計算 39
3-2.5 穩健設計尺寸的驗證 40
第四章 微掃描面鏡扭轉共振頻率的穩健設計 50
4-1 微掃描面鏡扭轉共振頻率的穩健設計方法 50
4-1.1 田口實驗法 50
4-1.2 靈敏度分析 52
4-2 單軸微掃描面鏡扭轉共振頻率的穩健設計流程 52
4-2.1 製程標準差量測 53
4-2.2 標準差方程式 54
4-2.3 靈敏度分析結果 55
4-2.4 穩健設計 56
4-2.5 穩健設計的驗證 58
4-3 雙軸微掃描面鏡扭轉共振頻率的穩健設計流程 60
4-3.1 標準差方程式 60
4-3.2 穩健設計 61
4-3.3 穩健設計的驗證 62
第五章 結論 81
5-1 研究成果 81
5-2 未來工作 82
參考文獻 84
附錄 89

[1] R.E. Devor, T.H. Chang, and J.W. Sutherland, Statistical Quality Design and Control.2th Ed. New Jersey, Pearson Prentic Hall, 2007.
[2] http：//ares.ee.ncu.edu.tw/wiki3/index.php/
[3] S. S. Rao, Reliability-Based Design, 1th Ed., New York, NY： McGraw-Hill, 2002.
[4] 李輝煌, "田口方法－品質設計的原理與實務", 第三版, 台北, 高立出版, 民國98年
[5] 林振邦, "微機械麥克風之最佳化設計及其陣列於 3D 聲場重建之實現", 國立交通大學碩士論文, 2004.
[6] 周鵬程, "遺傳演算法原理與應用-活用Matlab", 第二版, 台北, 全華, 2005
[7] J.K. Coultate, C.H.J. Fox, S. McWilliam, and A. R. Malvern, ”Application of optimal and robust design methods to a MEMS accelerometer,” Sensors and Actuators A, 142, pp 88-96, 2008.
[8] S.P. Vudathu, D. Boning, R. Laur, “A design method for the yield enhancement of MEMS design with respect to process induced variation,” Electronic Components and Technology Conference, Reno, NV, May, 2007, pp 1947-1952.
[9] S.P. Vudathu, D. Boning, and R. Laur, “A critical enhancement in the yield analysis of Microsystems,” Reliability Physics Symposium, Phoenix, AZ, April, 2007, pp 422-428.
[10] F.M. Battiston, J.-P. Ramseyera, H.P. Langa, M.K. Ballera, C. Gerberb, J.K. Gimzewskib, E. Meyera and H.-J. G?刡therodt, “ A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sensors and Actuators B, 77, pp 122-131, 2001.
[11] M. Villarroyaa, J. Verda, J. Tevaa, G. Abadala, E. Forsenc, F.P. Muranob, A. Urangaa, E. Figuerasb, J. Montserratb, J. Esteveb, A. Boisenc and N. Barniol, “System on chip mass sensor based on polysilicon cantilevers arrays for multiple detection,” Sensors and Actuators A, 132, pp 154-164, 2006.
[12] M. Narducci, E. Figueras, M.J. Lopez, I. Gr?趓ia, L. Fonseca, J. Santander, and C. Can?? “A high sensitivity silicon microcantilever based mass sensor,” IEEE Sensors, Lecce, Italy, October, 2008, pp 1127 - 1130.
[13] M. Calleja, M. Nordstr?卌, M. ?柝varez, J. Tamayo, L.M. Lechuga, and A. Boisen, “Highly sensitive polymer based cantilever sensors for DNA detection, “ Ultramicroscopy, 105, pp 215-222, 2005.
[14] F.M. Battiston, J.-P. Ramseyer, H.P. Lang, M.K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer and H.-J. G?刡therodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sensors and Actuators B, 77, pp 122-131, 2001
[15] S.M. Yang, T.I. Yin and C. Chang, “A biosensor chip by CMOS process for surface stress measurement in bioanalyte,” Sensors and Actuators B, 123, pp 707-714, 2007.
[16] W.-C. Wang, M. Fauver, J. Ho, E.J. Seibel, P.G. Reinhall, “Micromachined optical waveguide cantilever as a resonant optical scanner,” Sensors and Actuators A, 102, pp 165-175, 2002.
[17] D. Shen, J.-H. Park, J.H. Noh, S.-Y, Choe, S.-H. Kimc, H. C. Wikle III, and D. –J. Kim, “Micromachined PZT cantilever based on SOI structure for low frequency vibration energy harvesting,” Sensors and Actuators A, 154, pp 103-108, 2009.
[18] J. Teva, G. Abadala, Z.J. Davisb, J. Verda, X. Borris?繁, A. Boisenb, F. P?臆ez-Muranoc and N. Barniol, “On the electromechanical modelling of a resonating nano-cantilever-based transducer,” Ultramicroscopy, 100, pp 225-232, 2004.
[19] L. Jianga, R. Cheunga, J. Hedleyb, M. Hassanc, A.J. Harrisc, J.S. Burdessb, M. Mehreganyd and C.A. Zorman, “SiC cantilever resonators with electrothermal actuation,” Sensors and Actuators A, 128, pp. 376-386, 2006.
[20] K.E. Petersen, “Silicon torsional scanning mirror,” IBM J. Res., 24, pp 631-637, 1980.
[21] P. B. Chu, S.-S. Lee, S. Park, M. J. Tsai, I. Brener, D. Peale, R. A. Doran, and C. Pu, “MOEMS-enabling technologies for large optical cross-connects,” Proceedings of the SPIE, 4561, pp 55-65, 2001.
[22] V.A. Aksyuk, F.Pardo, C.A. Bolle, C.R. Giles, and D.J. Bishop,“Lucent MicrostarTM micromirror array technology for large optical crossconnects,” Proceedings of SPIE, 4178, pp 320-324, 2000.
[23] V.A. Aksyuk, F. Pardo, and D.J. Bishop, “Stress-induced curvature engineering in surface-micromachined devices,” Proceedings of the SPIE, 3680, pp 984-993, 1999.
[24] V.A. Aksyuk, F. Pardo, D. Carr, D. Greywall, H. B. Chan, M. E. Simon, A. Gasparyan, H. Shea, V. Lifton, C. Bolle, S. Arney, R. Frahm, M. Paczkowski, M. Haueis, Ronald Ryf, David T. Neilson, J. Kim, C. Randy Giles, D. Bishop, “Beam-Steering micromirrors for large optical cross-connects,” Journal of Lightwave Technology, 21, pp 634-642, 2003.
[25] N. Asada, H. Matsuki, K. Minami and M. Essashi, “Silicon micromachined two-dimensional alvano optical scanner, ” IEEE Transactions on Magnetics, 30, pp 4647–4649, 1994.
[26] L.O.S. Ferreira and S. Moehlecke, “A silicon micromechanical galvanometric scanner,” Sensors and Actuators A, 73, pp 252–260, 1999.
[27] H.A. Yang and W. Fang, “A Novel Coil-less Lorentz Force 2D Scanning Mirror Using Eddy Current,” IEEE MEMS International Conference, Istanbul, Turkey, Jan, 2006, pp 774-777.
[28] J.W. Judy, “Magnetic microactuators with polysilicon flexures,” Masters Thesis, Department of EECS, University of California, Berkeley, 1994.
[29] J.W. Judy, and R.S. Muller, “Magnetic microactuation of torsional polysilicon structures,” International Conference on Solid-State Sensors and Actuators, Stockholm, Sweden, June, 1995, pp 332-335.
[30] J.W. Judy, R.S. Muller, and H.H. Zappe, “Magnetic microactuation of polysilicon flexure structures,” Journal of Microelectromechanical Systems, 4, pp 162-169, 1995.
[31] J. W. Judy, Member, and R. S. Muller, “Magnetically actuated, addressable microstructures”, Journal of Microelectromechanical Systems, 6, pp 249-256 , 1997.
[32] H.-J. Cho, J.-Y. Stephen, T. Kowel, F.R. Beyette, Jr. and C. H. Aim , “Scanning silicon micromirror using a bi-directionally movable magnetic microactuator”, MOEMS and Miniaturized Systems, 4178, pp 106-115, 2000.
[33] A.D. Yalcinkaya, H. Urey, and S.Holmstrom, “NiFe plated biaxial MEMS scanner for 2-D imaging,” IEEE Photonics Technology Leters, 19, pp 330-332, 2007.
[34] L, Meirovith, Element of Vibration Analysis, 2th Ed., New York, NY： McGraw-Hill, pp 220–227, 1986.
[35] 湯宗霖, "利用靜磁力與勞侖茲力驅動雙軸循序掃描面鏡", 國立清華大學碩士論文, 2007.
[36] R.J. Roark, Formulas for Stress and Strain, 4th Ed., New York, NY： McGraw-Hill, 1965.
[37] D.G. Ullma, The Mechanical Design Process, 3th Ed., New York, NY： McGraw-Hill, 2003.
[38] http：//en.wikipedia.org/wiki/Normal_distribution
[39] http：//episte.math.ntu.edu.tw/entries/en_lagrange_mul/index.html
[40] J. Shigley and C. Mischke, Mechanical Engineering Design, 6th Ed., New York, NY： McGraw-Hill , 2001.