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研究生:林孟儒
研究生(外文):Meng-Ju Lin
論文名稱:微結構中平板吸附力及殘餘應力與擠壓薄膜現象研究
論文名稱(外文):Study of Adhesion, Residual Stress, and Squeeze Film Effect in Plates of Microstructures
指導教授:陳榮順陳榮順引用關係
指導教授(外文):Rongshun Chen
學位類別:博士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:114
中文關鍵詞:吸附現象殘餘應力擠壓薄膜毛細力中央固定圓形平板轉變頻率大變動理論微機電系統
外文關鍵詞:sticking effectresidual stresssqueezed film effectcapillary forcecenter-anchored circular platecut off frequencycatastrophe theoryMEMS
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近年來微機電系統的發展突飛猛進,已經成為重要的發展方向之一。微機電系統具有薄、精、短、小的優點,可以利用半導體製程批量製造,而且應用非常廣泛,因此受到各界重視。然而因為尺寸的減小,在微小尺度下,原本在大尺度下可以忽略的一些物理現象變得很重要,必須要重新規範。而且這些物理現象,例如毛細力所造成的吸附現象、高溫製程所產生的殘餘應力所造成的熱變形、以及微小間隙中空氣薄膜的受到擠壓對動態的影響,都可能損及結構、減少良率,以及降低性能。而平板廣泛應用於微機電元件結構中,並且其物理性質將決定元件成功與否。因此,以平板作為結構時,平板與平板下方基板之間的物理性質特別需要探討。在一般的研究上,為了分析的簡單起見,常用樑的數學模型作為分析板的方法,然而板的力學性質遠比樑複雜,因此,利用樑的模型作為分析方法,將有一定程度的失真。因此,本論文利用板殼理論作為平板分析的理論依據。
本論文首先探討中央固定之圓形與扇形平板和下方基板間的吸附現象。然後,研究上述兩種平板受製程高溫所造成的殘餘應力。最後,擠壓薄膜現象對矩形平板力學與動態性質的影響亦被討論。
在中央固定之圓形平板受毛細力的吸附現象影響方面,本論文推導出兩個臨界間隙, 及 。當 ,平板將會被吸附在基板上;而 時,平板將免於吸附。這兩個臨界間隙會受下列參數影響:平板厚度、平板尺寸、液體表面張力、楊氏係數(Young’s modulus)、以及波松比(Poisson’s ratio)。本文更進而推導出一無因次參數 ,作為推算圓形平板是否被吸附或是回復原來位置的依據。理論上,當 時,結構將不會被吸附,但是當 時,結構會被吸附。實驗結果證實 = 1可做為圓形平板是否被吸附的初步判斷。同時由實驗結果,本研究更進一步找出另一無因次因數 ,來作為吸附與否的判斷準則。當 > 0.9903,結構不會被吸附,而當 < 0.9903時,結構會被吸附。實驗結果證實 = 0.9903時,理論與實驗之誤差約8.87%。
而在考量殘餘應力的影響下,本論文進一步探討扇形平板的吸附現象。利用板殼理論,殘餘應力的數學模型被推導出來。本文將殘餘應力的模型包含進來之後,推導出兩臨界間隙。利用此兩臨界間隙,可以依據元件不同的內外徑分成三個區域。在上方區(小內徑大外徑),結構將被吸附。在下方區(內外徑長度接近),結構會回復原來形狀。而兩個區域之間,則無法判定。利用面型微細加工製程,扇行平板結構被製造出來用以驗證理論分析。結果發現殘餘應力確實會對吸附現象產生明顯的影響。而殘餘應力所造成之影響,在扇形平板的扇面張角的尖端變形量將比沿扇形平面中心軸之最大變形量為大,而且角度越大變形量越大。
當金屬鍍膜到結構上的時候,因為熱膨脹係數的不同,會產生殘餘應力造成結構的變形。本文利用板殼理論推導出圓形平板和扇形平板鍍上金屬膜後之變形大小和元件尺寸與材料性質的關係式。並且以製程實驗來驗證此理論分析,此理論分析結果符合量測樹據。結果發現,平板越薄以及金屬薄膜越厚,變形越大。
當微結構做週期運動時,尤其隨間隙變小時,四周的空氣將明顯影響微結構的運動行為。擠壓薄膜現象會對微小間隙平板間的正向運動之響應非常重要。本文利用平行板間脈衝波運動流體(pulsating flow between parallel surfaces)模型之奈維也-史托克方程式(Navier-Stokes equation)做為新的模型探討大氣壓下,元件作動受擠壓薄膜現象的影響。尋找出間隙和空氣受擠壓薄膜現象所產生之彈簧力的關係式。實驗結果發現,此模型是可用的。

Microelectronmechanical systems (MEMS) become one of the most promising research areas, and have gradually earned the respect in industry, by the advantages of tiny mass and size, fast dynamic response, wide usage in many regimes, and batch fabrication. However, some physical phenomena ignored in macroscale such as adhesion, deformation caused by residual stress, and effect of squeezed gas film, may become very important in microscale. Plates have been widely used as the structure layer in MEMS. The physical properties of plates often determine the success of a sensor or an actuator. Therefore, if a plate is used as a structure layer, the physical properties between a plate and its underlying substrate should be most concerned.
In the analysis of plate deformation, theory of beams is frequently applied in the current literatures due to simplicity. However, the mechanical behavior of plates is much more complex than beam, in general. Consequently, if a beam is utilized to model a plate, the predicted errors may be significant. Therefore, in this thesis, the theory of plates-and-shells is introduced to estimate the deflection of the plate caused by capillary force or residual stress.
In this thesis, the adhesion, due to the capillary force, between a center-anchored plate, a circular plate or a sector plate, and its underlying substrate is investigated. Then the effect of residual stress caused by thermal treatment processes is studied for both plates considered above. Finally, the effect of squeezed gas film for a rectangular plate and the substrate is examined.
The adhesion affected by the factors: thickness of plate, surface tension of liquid, and two material properties: Young’s modulus and Poisson’s ratio, are thoroughly investigated for the considered plates. Two critical gaps, and , are derived for circular plates. When , the plate adheres to substrate, while , it is free from sticking. Furthermore, by using catastrophe theory, a nondimensional elastocapillary number is derived and is employed as the first approximation to determine if the circular plate will pin on the substrate or not. Theoretically, when , the center-anchored circular plate will restore to its desired position, while , it will attach to substrate. Moreover, by the experimental results, a novel criterion is defined to examine the adhesion effect for the proposed devices. For > 0.9903, the plate will be free, while for < 0.9903, it will stick to the substrate. The circular plates have been successfully fabricated through surface micromachining to examine the feasibility of the proposed nondimensional numbers. The experimental results showed that only 8.87% error if = 0.9903 is employed.
From theoretical analysis, two critical gaps are derived to judge the adhesion for center-anchored sector plates. However, residual stress is also included here. As in the center-anchored circular plates and by using these two critical gaps, three regions are located to decide the adhesive conditions between the sector plate and its underlying substrate. From theory of plates-and-shells, a mathematical model of residual stress is derived. Using surface micromachining, the sector plates are fabricated to verify the theoretical analysis. It is concluded that residual stress is one of the major factors in sticking. It is also demonstrated that deformation in the tip of the sector plate is larger than in the centerline, and the phenomenon is more obvious if the angles of sector increase.
In the deposition of metal, the mismatch of thermal expansion coefficients between the metal layer and structure layer will induce residual stress after release, and thus deform the structure layer and lower the yield ratio of the devices. By theory of plates-and-shells, the deformation caused by residual stress from thermal treatment is investigated. It is shown that the theoretical predictions agree with the measured results. In general, the thinner plate of structure layer and the thicker metal layer will cause larger deformation.
The surrounding gas due to the pumping action significantly influences the motion of microstructure, especially as the size of the microstructure is reduced. The effect of squeezed gas film is important in dynamic response when two plates or a plate and its underlying substrate with narrow gap, move normal to each other. A novel model is derived by using Navier-Stokes equation with pulsating flow between parallel surfaces to discuss the effect of squeezed gas film when devices are actuated in one atmosphere pressure. The relationship between spring force caused by squeezed film effect and gaps is found. By experiments, it is proved that the proposed model is fea

中文摘要 I
Abstract IV
誌謝 VII
目錄 IX
圖目錄 XI
表目錄 XVI
Chapter 1 Introduction 1
1.1 Background and Motivation 1
1.2 Literature Reviews 5
1.3 Organization of This Thesis 10
Chapter 2 Sticking Effect on Center-Anchored Circular Plates in Microstructures 12
2.1 Introduction 12
2.2 Force Balance 13
2.2.1 Capillary Force 13
2.2.2 Elastic Force 15
2.2.3 Energy Method 18
2.3 Effect on Critical Gaps 22
2.4 Summary 26
Chapter 3 Adhesion Criterion for Center-Anchored Circular Plates in Microstructures 27
3.1 Introduction 27
3.2 Sticking Model 28
3.2.1 Capillary Force 28
3.2.2 Elastic Force 29
3.2.3 Catastrophe Theory Method 30
3.3 Fabrication 38
3.4 Results and Discussion 39
3.5 Summary 47
Chapter 4 Sticking Effect for LPCVD Polisilicon Center-Anchored Sector Plates 48
4.1 Introduction 48
4.2 Sticking Model with Residual Stresses 48
4.2.1 Balance of Elastic Force and Capillary Force 48
4.2.2 Residual Stresses 51
4.2.3 Critical Gap 53
4.3 Fabrication 59
4.4 Results and Discussions 66
4.4.1 Results 66
4.5 Summary 71
Chapter 5 Deformation Caused by Residual Stresses 72
5.1 Introduction 72
5.2 Model of thermal stress in plate 73
5.3 Fabrication 75
5.4 Results and Discussions 77
5.5 Summary 86
Chapter 6 Effect of Squeezed Gas Film 87
6.1 Introduction 87
6.2 Model of Fluid Mechanics 88
6.3 Fabrication 94
6.4 Results and Discussions 96
6.5 Summary 101
Chapter7 Conclusions and Future Works 102
7.1 Conclusions 102
7.2 Future Work 103
Acknowledgement 105
Reference 106

[1] Osterberg, P.; Yie, H.; Cai, X.; White, J.; Senturia, S. “Self-consistent simulation and modelling of electrostatically deformed diaphragms “Micro Electro Mechanical Systems, 1994, MEMS '94, Proceedings, IEEE Workshop on, 1994, Page(s): 28 —32
[2] Bifano, T.G.; Perreault, J.; Krishnamoorthy Mali, R.; Horenstein, M.N.Selected “ Microelectromechanical deformable mirrors” Topics in Quantum Electronics, IEEE Journal on Volume: 5 1, Jan.-Feb. 1999, Page(s): 83 —89
[3] Chu, P.B.; Pister, S.J. “Analysis of closed-loop control of parallel-plate electrostatic microgrippers” Robotics and Automation, 1994. Proceedings, 1994 IEEE International Conference on, 1994, Page(s): 820 -825 vol.1
[4] Maboudian, R and Howe, R. T. “Critical review: Adhesion in surface micromechanical structures,” J. Vac. Sci. Technol. B, vol. 15, pp. 1-20, 1997.
[5] Tas, N. Sonnenberg,T. Jansen, H. legtenberg, R. and Elwenspoek, M. “Sticking in surface micromachining,” J. Micromech. Microeng., vol. 6, pp. 385-397, 1996;.
[6] Fearing, R.S.” Survey of sticking effects for micro parts handling “Intelligent Robots and Systems 95. 'Human Robot Interaction and Cooperative Robots', Proceedings. 1995 IEEE/RSJ International Conference on Volume: 2, 1995, Page(s): 212 -217
[7] Kucukkomurker A. And Garverick S. L. “ Optimized Step Controller for a Salient-Pole Micromotor” National Aerospace and Electronics Conference, 2000. NAECON 2000. Proceedings of the IEEE 2000, Page(s): 362 -366
[8] Mourlas N. J., Stark K.C., Mehregany M., and Phillips S. M. “ Exploring Polysilicon Micromotors for Data Storage Micro Disks” Micro Electro Mechanical Systems, 1996, MEMS '96, Proceedings. An Investigation of Micro Structures, Sensors, Actuators, Machines and Systems. IEEE, The Ninth Annual International Workshop on , 1996 Page(s): 198 -203
[9] Vivek, V.; Eun Sok Kim “Novel acoustic-wave micromixer ” Micro Electro Mechanical Systems, 2000. MEMS 2000. The Thirteenth Annual International Conference on , 2000 Page(s): 668 -673
[10] Yoshika E., Tsugai M., Hokikawa M., Otani H., and Hamada S. “Influence of RTA Parameters on Residual Stress and Stress Gradient of Multilayered LPCVD Polysilicon Film” Micro Electro Mechanical Systems, 2002. The Fifteenth IEEE International Conference on, 2002 Page(s): 451 —454.
[11] .Salbu, E. O. J “ Compressible Squeeze Films and Squeeze Bearings”, Transcation of ASME, J. of basic Engineering, 1964, pp. 355-366.
[12] Griffin, W.S.; Richardson, H.H.; and Yamanami, S.,” A Study of Fluid Squeeze-Film Damping”, Transcation of ASME, J. of basic Engineering, 1966, pp. 451-456.
[13] Langlois, W. E., “ Isothermal Squeeze Films”, Report RJ-192, International Business Machines Corporation, San Jose, Calif., 1961.
[14] Blech, J. J., “ On Isothermal Squeeze Films”, J. of Lubrication Technology, 1983, vol. 105, pp. 615-620.
[15] Arai, F.; Andou, D.; Fukuda, T.” Adhesion forces reduction for micro manipulation based on micro physics” Micro Electro Mechanical Systems, 1996, MEMS '96, Proceedings. An Investigation of Micro Structures, Sensors, Actuators, Machines and Systems. IEEE, The Ninth Annual International Workshop on , 1996 , Page(s): 354 —359
[16] Yee; Y., Chun; K., and Lee, J. D. “ Polysilicon Surface Modification Technique To Reduce Sticking Of Microstructures” Solid-State Sensors and Actuators, 1995 and Eurosensors IX.. Transducers '95. The 8th International Conference on Volume: 1 , Page(s): 206 —209
[17] Yee, Y. Park, M. and Chun, K.. “A Sticking Model of Suspended Polysilicon Microstructure Including Residual-Stress Gradient and Postrelease Temperature.” Journal of Microelectromechanical Systems, 1998, 7(3), 339-344.
[18] Lee; J. H., Lee; Y. I., Jang; W. I., Lee; C. S., and Yoo, H. J. “Gas-phase etching of sacrificial oxides using anhydrous HF and CH/sub 3/OH ” Micro Electro Mechanical Systems, 1997. MEMS ' 97, Proceedings, IEEE. Tenth Annual International Workshop on , 1997 , Page(s): 448 —453
[19] Ashurst, W.R.; Yau, C.; Carraro, C.; Maboudian, R.; Dugger, M.T. “Dichlorodimethylsilane as an anti-stiction monolayer for MEMS: a comparison to the octadecyltrichlorosilane self-assembled monolayer” Microelectromechanical Systems, Journal of , Volume: 10 Issue: 1 , March 2001 Page(s): 41 -49
[20] Kozlowski, F., Lindmair, N., Scheiter, T., Hierold , C., and W. Lang. “A Novel Method to Avoid Sticking of Surface-Micromachined Structures.” Sensors and Actuators, 1996, A(54), 659-662.
[21] Mani, S.S.; Fleming, J.G.; Walraven, J.A.; Sniegowski, J.J.; Beer, M.P.; Irwin, L.W.; Tanner, D.M.; LaVan, D.A.; Dugger, M.T.; Jakubczak, J.; and Miller, W.M. “Effect of W coating on microengine performance” Reliability Physics Symposium, 2000. Proceedings. 38th Annual 2000 IEEE International , 2000 Page(s): 146 -151
[22] Gogoi, Bishnu P. and. Mastrangelo, Carlos H “Adhesion Release and Yield Enhancement of Microstructures Using Pulsed Lozentz Forces” Journal of Microelectromechanical Systems, vol.4, No.4, 1995, pp. 185-192
[23] Lai, W. P. and Fang, W. L. “A Novel Antistiction Method Using Harmonic Excitation on the Microstructure” J. Vac. Sci. Technol. A 19(4), 2001 pp. 1224-1228
[24] Mastrangelo, C.H.; Hsu, C.H. ” Mechanical stability and adhesion of microstructures under capillary forces. I. Basic theory ” Microelectromechanical Systems, Journal of Volume: 2 1, March 1993, Page(s): 33 —43
[25] Mastrangelo, C.H.; Hsu, C.H.” Mechanical stability and adhesion of microstructures under capillary forces. II. Experiments” Microelectromechanical Systems, Journal of Volume: 2 1, March 1993, Page(s): 44 —55
[26] Yee, Y., Park, M., and Chun. K. “A Sticking Model of Suspended Polysilicon Microstructure Including Residual-Stress Gradient and Postrelease Temperature.” Journal of Microelectromechanical Systems, 1998, 7(3), 339-344.
[27] Yee; Y., Chun; K., and Lee, J. D.” Polysilicon Surface Modification Technique To Reduce Sticking Of Microstructures” Solid-State Sensors and Actuators, 1995 and Eurosensors IX.. Transducers '95. The 8th International Conference on , Volume: 1
Page(s): 206 -209
[28] Walker, J. K., Gabriel, K. J., and Mehregany, M. “Mechanical Integrity of Polysilicon Exposed to Hydrofluoric Acid Solutions.” Micro Electro Mechanical Systems, 1990. Proceedings, An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots. IEEE, 1990 56-60.
[29] Brown, R.B.; Ger, M.-L.; Nguyen, T.” Characterization of molybdenum thin films for micromechanical structures” Micro Electro Mechanical Systems, 1990. Proceedings, An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots. IEEE , 1990 , Page(s): 77 —81
[30] Fang, W.; Wickert, J.A.“ Post-buckling of micromachined beams“ Micro Electro Mechanical Systems, 1994, MEMS '94, Proceedings, IEEE Workshop on, 1994 , Page(s): 182 -187
[31] Zhang; X., Zhang; T. Y., Wong; M., and Zohar, Y. “Effects of high-temperature rapid thermal annealing on the residual stress of LPCVD-polysilicon thin films “ Micro Electro Mechanical Systems, 1997. MEMS ' 97, Proceedings, IEEE., Tenth Annual International Workshop on ,1997 , Page(s): 535 —540
[32] Abe, T.; Reed, M.L. “Low strain sputtered polysilicon for micromechanical structures” Micro Electro Mechanical Systems, 1996, MEMS '96, Proceedings. An Investigation of Micro Structures, Sensors, Actuators, Machines and Systems. IEEE, The Ninth Annual International Workshop on , 1996 , Page(s): 258 —262
[33] Ye, X.Y.; Zhang, J.H.; Zhou, Z.Y.; Yang, Y.” Measurement of Young's modulus and residual stress of Micromembranes” Micro Machine and Human Science, 1996., Proceedings of the Seventh International Symposium , 1996 , Page(s): 125 —129
[34] Fan, L.-S.; Howe, R.T.; Muller, R.S." Microstructures for fracture toughness characterization of brittle thin films” Micro Electro Mechanical Systems, 1989, Proceedings, An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots. IEEE, 1989, Page(s): 40 —41
[35] Kahn, H.; Stemmer, S.; Nandakumar, K.; Heuer, A.H.; Mullen, R.L.; Ballarini, R.; Huff, M.A. “Mechanical properties of thick, surface micromachined polysilicon films” Micro Electro Mechanical Systems, 1996, MEMS '96,Proceedings. An Investigation of Micro Structures, Sensors, Actuators, Machines and Systems. IEEE, The Ninth Annual International Workshop on , 1996 , Page(s): 343 —348
[36] Tai, Y.-C.; Muller, R.S.” Measurement of Young's modulus on microfabricated structures using a surface profiler” Micro Electro Mechanical Systems, 1990. Proceedings, An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots. IEEE, 1990, Page(s): 147 —152
[37] Fan, L.-S.; Lane, L.H.; Robertson, N.; Crawforth, L.; Moser, M.A.; Reiley, T.C.; Imaino, W. “Batch-fabricated milli-actuators “ Micro Electro Mechanical Systems, 1993, MEMS '93, Proceedings An Investigation of Micro Structures, Sensors, Actuators, Machines and Systems. IEEE. , 1993, Page(s): 179 —183
[38] Yen, H., Lee, C., Chen, R. and Lin, M. J. "Analysis and Fabrication of Deformable Focusing Micromirrors," Proceedings of 2001 ASME International Mechanical Engineering Congress Exposition, Nov. 11-16, 2001, New York, NY, U. S. A.
[39] Minami, K.; Matsunaga, T.; Esashi, M.” Simple modeling and simulation of the squeeze film effect and transient response of the MEMS device“Micro Electro Mechanical Systems, 1999. MEMS '99. Twelfth IEEE International Conference on , Page(s): 338 —343
[40] Hung, E.S.; Yao-Joe Yang; Senturia, S.D. “Low-order models for fast dynamical simulation of MEMS microstructures “Solid State Sensors and Actuators, 1997. TRANSDUCERS '97 Chicago., 1997 International Conference on Volume: 2 , 1997 , Page(s): 1101 -1104 vol.2
[41] Kim; E., S. Cho; Y. H., and Kim, M. U. “Effect of holes and edges on the squeeze film damping of perforated micromechanical structures" Micro Electro Mechanical Systems, 1999. MEMS '99. Twelfth IEEE International Conference on , Page(s): 296 —301
[42] Rabinovich, V.L.; Gupta, R.K.; Senturia, S.D.“ The Effect of Release-etch holes on the electromechanical behaviour of MEMS structures” Solid State Sensors and Actuators, 1997. TRANSDUCERS '97 Chicago., 1997 International Conference on Volume: 2 , 1997 , Page(s): 1125 -1128 vol.2
[43] Andrews, M., Harris, I., and Turner, G. “ A Comparison of Squeeze-film Theory with Measurements on a Microstructure “Sensors and Actuators A,36(1993) pp.79-87
[44] Veijola, T., Kuisma, H., Lahdenpera, J. and Ryhanen, T. “ Equivalent-circuit Model of the Squeezed Gas Film in a Silicon Accelerometer “ Sensors and Actuators A 48 (1995) pp.239-248
[45] Mehner, J.; Kurth, S.; Billep, D.; Kaufmann, C.; Kehr, K.; Dotzel, W.” Simulation of gas damping in microstructures with nontrivial geometries” Micro Electro Mechanical Systems, 1998. MEMS 98. Proceedings., The Eleventh Annual International Workshop on , 1998 , Page(s): 172 —177
[46] Yang; Y. J., Gretillat, M.-A.; and Senturia, S.D.” Effect of air damping on the dynamics of nonuniform deformations of microstructures “Solid State Sensors and Actuators, 1997. TRANSDUCERS '97 Chicago., 1997 International Conference on Volume: 2 , 1997 , Page(s): 1093 -1096 vol.2
[47] Uchida, N.; Uchimaru, K.; Yonezawa, M.; Sekimura, M. “Damping of micro electrostatic torsion mirror caused by air-film viscosity” Micro Electro Mechanical Systems, 2000. MEMS 2000. The Thirteenth Annual International Conference on, 2000
Page(s): 449 —454
[48] M. K. Andrews, G. C. Turner, P.D. Harris and I. M. Harris “A Resonant Pressure Sensor Based on a Squeezed Film of Gas “ Sensors and Actuators A, 36 (1993) 219-226
[49] Gupta, R.K.; and Senturia, S.D.” Pull-in time dynamics as a measure of absolute pressure “Micro Electro Mechanical Systems, 1997. MEMS ' 97, Proceedings, IEEE., Tenth Annual International Workshop on , 1997 , Page(s): 290 —294
[50] Andrews, M., Harris, I. and Turner, G. “A Comparison of Squeeze-film Theory with Measurements on a Microstructure” Sensors and Actuators A., 36, 1993, pp. 79-87.
[51] Fowkes, F. M. “Contact Angle, Wtttabilit and Adhension,” pp.57-58, Washington: American Chemical Society, 1964.
[52] Ugural, A. C. “ Stresses in Plates and Shells ”The McGraw-Hill Companies, Inc., 1981
[53] Sze, S. M. “Semiconductor Sensors,” pp.535, New York: John Wiley and Sons, Inc., 1994.
[54] Arnold, V. I. “Catastrophe theory”, Springer-Verlag, New York, 1986
[55] Arnold, V. I., et. al. “Bifurcation Theory and Catastrophe Theory”, Springer-Verlag, New York, 1994.
[56] Poston, T. and Stewart, I. “Catastrophe Theory and its Applications”, Pitman, London, 1978.
[57] Spiegel, M. R. “Mathematical Handbook”, pp. 32-33, McGraw-Hill, New York, 1981.
[58] Kovacs, G. T. A. “Micromachined Transducers Sourcebook.” pp. 201, McGraw-Hill, New York,1998.
[59] Ye, X. Y., Zhang, J. H., Zhou, Z. Y., and Yang, Y. “Measurement of Young's modulus and residual stress of micromembranes”, Micro Machine and Human Science, 1996, Proceedings of the Seventh International Symposium, 1996, 125 —129
[60] Timoshenko S. P. and Woinowsky-Krieger S. “Theory of Plates and Shells” McGraw-Hill International Editions, 1959
[61] Carrier G. F. “ The Bending of the Clamped Sectorial Plate ” J. Appl. Mech., 11, 1944, pp. A.134-139
[62] Holman, J. P. “ Heat Transfer ” McGraw-Hill, 1968.
[63] Currie, I. G. “Fundamental mechanics of fluids “ The McGraw-Hill Companies Inc., 1974.
[64] David K.Cheng “ Field and Wave Electromagnetics “ Addison-Wesley Publish Company,Inc., 1989
[65] Gere and Timoshenko “ Mechanics of Materials “4th edition, PWS Publish Company, 1990
[66] Oscar Pinkus, and Beno Sternlight “ Theory of Hydrodynamic Lubrication”, 1972

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