本論文分二部分：（一）寬度對微小製造雙層懸臂樑彎曲之影響，（二）厚度對微小製造雙層圓板變形產生之影響，二部份均包含理論分析與工程應用。
論文的第一部份，證明了寬度會影響微機電系統雙層懸臂樑的彎曲曲率（第二章），並發現寬度的影響會在寬度大於一臨界值後消失。結論應用於量測殘餘應力之雙層樑法（第三章），加大寬度超過臨界值，避免寬度影響，得到比從前更可靠的結果。另外，超寬樑模型包含波生比訊息，藉此已成功發展出少有的波生比量測法（第四章）。

論文的第二部份，探討上下厚度比對微機電系統雙層圓板變形產生之影響，在比值接近零或無限大時，圓盤之彎曲曲率皆為零。若比值由零變化至無限大，曲率會先增後減，其中出現一個最大值；若結構維持穩定，圓盤會被彎成碗狀（第五章）。應用此結論，已成功成功製作出可聚焦之微小凹面鏡（第六章）。

Today a fast growing interest in microsystems exists both in the academic research world and in commercial industrial products. One reason for this evolution is the sophisticated processing techniques and production methods associated with silicon technology. Silicon micromachining offers the possibility of low-cost highly miniaturized sensors, actuators and systems. However, the planar nature of the photolithography technique used in micromechanics makes it not easy to realize three-dimensional (3-D) structures. Batch and mass fabrication of true 3-D silicon structures is a key step in future micromachining technology that can enrich the world with new 3-D sensors, actuators and systems. Such devices have broad applications from medical, military and household equipment to pure research tools.
One category of common 3-D structures used in MEMS is bilayer microstructures, such as micromachined bilayer cantilevers and micromachined bilayer plates. Although this type of 3-D microstructures has been widely integrated in various microsystems, a lot of mechanical behaviors of these microstructures are still unknown. The motivation for this work is to deeply understand the geometric effects on 3-D structures fabricated using bilayer method. The final goal is to implement the new knowledge to obtain better performance of microsystems.

This dissertation presents the effect of width on the stress-induced bending of the micromachined bilayer cantilever. Following the foregoing study, a modified method for measuring the residual stress and a novel method for measuring the Poisson’s ratio have been demonstrated. This dissertation also presents the effect of thickness on the stress-induced bending of the micromachined bilayer plate. Following the conclusions, a novel focusing micromirror has been designed and fabricated. Extensive discussion on symmetry has been made to characterize the new bilayer microstructures.

[1] Petersen K E 1982 Silicon as a mechanical material Proc. IEEE 70 420-457
[2] Eloy J-C 1997 Market analysis for microsystems – an interim report from the NEXUS task force Proc. of the 11th European Conference on Solid-State Transducers (EUROSENSORS XI) 519-526
[3] Hyer M W 1981 Some observations on the cured shape of thin unsymmetric laminates J. Compos. Mater. 15 175-194
[4] Hyer M W 1981 Calculation of the room-temperature shapes of unsymmetric laminates J. Compos. Mater. 15 296-310
[5] Hyer M W 1982 The room-temperature shape of four-layer unsymmetric cross-ply laminates J. Compos. Mater. 16 318-340
[6] Dano M L and Hyer M W 1998 Thermally-induced deformation behavior of unsymmetric laminates Int. J. Solids Structures 17 2101–2120
[7] Fahnline D E, Masters C B and Salamon N J 1991 Thin film stress from nonspherical substrate bending measurements J. Vac. Sci. Technol. A 9 2483-2487
[8] Masters C B and Salamon N J 1993 Geometrically nonlinear stress-deflection relations for thin film/substrate systems Int. J. Engng. Sci. 31 915-925
[9] Finot M and Suresh S 1996 Small and large deformation of thick and thin film multilayers: Effects of layer geometry, plasticity and compositional gradients J. Mech. Phys. Solids 44 683-721
[10] Finot M, Blech I A, Suresh S and Fujimoto H 1997 Large deformation and geometric instability of substrates with thin film deposits J. Appl. Phys. 81 3457-3464
[11] Freund L B 1993 The stress distribution and curvature of a general compositionally graded semiconductor layer J. Crystal Growth 132 341-344
[12] Freund L B 1996 Some elementary connections between curvature and mismatch strain in compositionally graded thin films J. Mech. Phys. Solids 44 723-736
[13] Freund L B 1997 The mechanics of a free-standing strained film / compliant substrate system Thin Films: Stresses and Mechanical Properties VI 436 Mater. Res. Soc. Proc. 393-404
[14] Freund L B, Floro J A and Chason E 1999 Extension of the stoney formula for substrate curvature to configurations with thin substrate or large deformations Applied Physics Letters 74 1987-1989
[15] Freund L B 2000 Substrate curvature due to thin film mismatch strain in the nonlinear deformation range J. Mech. Phys. Solids 48 1159-1174
[16] Masters C B and Salamon N J 1994 Geometrically nonlinear stress-deflection relations for thin film / substrate systems with a finite element comparison J. Appl. Mech. 61 872-878
[17] Salamon N J and Masters C B 1995 Bifurcation in isotropic thin film / substrate plates Int. J. Solids Structures 32 473-481
[18] Yasuda T, Shimoyama I and Miura H 1995 Electrostatically driven micro elastic joints Proc. IEEE MEMS 242-245
[19] Greitmann G and Buser R A 1996 Tactile microgripper for automated handling of microparts Sensors and Actuators A 53 410-415
[20] Schweizer S, Calmes S, Laudon M and Renaud Ph 1999 Thermally actuated optical microscanner with large angle and low consumption Sensors and Actuators A 76 470-477
[21] Zhang Y, Zhang Y and Marcus R B 1999 Thermally actuated microprobes for a new wafer probe card J. Microelectromech. Syst. 8 43-49
[22] Chen R T, Nguyen H and Wu M C 1999 A low voltage micromachined optical switch by stress-induced bending Proc. IEEE MEMS 424-428
[23] Chang C and Chang P 2000 Innovative micromachined microwave switch with very low insertion loss Sensors and Actuators A 79 71-75
[24] Miller D C, Zhang W and Bright V M 2000 Microrelay packaging technology using flip-chip assembly Proc. IEEE MEMS 265-270
[25] Liu Y, Li X, Abe T, Haga Y and Esashi M 2001 A thermomechanical relay with microspring contact array Proc. IEEE MEMS 220-223
[26] Lammel G, Schweizer S and Renaud P 2001 MEMS infrared gas spectrometer based on a porous silicon tunable filter Proc. IEEE MEMS 578-581
[27] Judy M W, Cho Y, Howe R T and Pisano A P 1991 Self-adjusting microstructures (SAMS) Proc. IEEE MEMS 51-56
[28] Smela E, Kallenbach M and Holdenried J 1999 Electrochemically driven polypyrrole bilayers for moving and positioning bulk micromachined silicon plates J. Microelectromech. Syst. 8 373-383
[29] Fang W, Tsai H and Lo C 1999 Determining thermal expansion coefficients of thin films using micromachined cantilevers Sensors and Actuators A 77 21-27
[30] Fang W and Wickert J A 1995 Comments on measuring thin-film stresses using bi-layer micromachined beams J. Micromech. Microeng. 5 276-281
[31] Min Y and Kim Y 2000 In situ measurement of residual stress in micromachined thin films using a specimen with composite-bilayer cantilevers J. Micromech. Microeng. 10 314-321
[32] Timoshenko S 1925 Analysis of bi-metal thermostats J. Optical Society of America 11 233-256
[33] Chu W-H, Mehregany M and Mullen R L 1993 Analysis of tip deflection and force of a bimetallic cantilever microactuator J. Micromech. Microeng. 3 4-7
[34] Pionke C D and Wempner G 1991 The various approximations of the bimetallic thermostatic strip J. Appl. Mech. 58 1015-1020
[35] Timoshenko S P and Goodier J N 1970 Theory of Elasticity Ch 2 15-17 (New York: McGraw-Hill)
[36] Schneider D and Tucker M D 1996 Non-destructive characterization and evaluation of thin films by laser-induced ultrasonic surface waves Thin solid films 290-291 309
[37] Kahn H, Stemmer S, Nandakumar K, Heuer A H, Mullen R L, Ballarini R and Huff M A 1996 Mechanical properties of thick, surface micromachined polysilicon films Proc. IEEE MEMS 347
[38] Stoney G G 1909 The tension of metallic films deposited by electrolysis Proc. R. Soc. 9 172-5
[39] Mehregany M, Howe R and Senturia S 1987 Novel microstructures for the in situ measurement of the mechanical properties of thin films J. Appl. Phys. 62 3579-84
[40] Zavracky P M, Adams G G and Aquilino P D 1995 Strain analysis of silicon-on-insulator films produced by zone melting recrystallization J. Microelectromech. Syst. 4 42-8
[41] Gianchandani Y and Najafi K 1996 Bent-beam strain sensors J. Microelectromech. Syst. 5 52-8
[42] Ericson F, Greek S, Söderkvist J and Schweitz J-Å 1997 High-sensitivity surface micromachined structures for internal stress and stress gradient evaluation J. Micromech. Microeng. 7 30-6
[43] Guckel H, Randazzo T and Burns D W 1985 A simple technique for the determination of mechanical strain in thin films with applications to polysilicon J. Appl. Phys. 57 1671-5
[44] Guckel H, Burns D, Rutigliano C, Lovell E and Choi B 1992 Diagnostic microstructures for the measurement of intrinsic strain in thin films J. Micromech. Microeng. 2 86-95
[45] Tabata O, Kawahata K, Sugiyama S and Igarashi I 1989 Mechanical property measurements of thin film using load-deflection of composite rectangular membrane Proc. IEEE Microelectromech. Syst. pp 152-6
[46] Maier-Schneider D, Maibach J, Obermeier E and Schneider D 1995 Variations in Young’s modulus and intrinsic stress of LPCVD-polysilicon due to high-temperature annealing J. Micromech. Microeng. 5 121-4
[47] Zhang L M, Uttamchandani D and Clushaw B 1991 Measurement of the mechanical properties of silicon microresonators Sensors Actuators A 29 79-84
[48] Gianchandani Y and Najafi K 1992 A bulk silicon dissolved wafer process for microelectromechanical devices J. Microelectromech. Syst. 1 77-85
[49] Najafi K and Suzuki K 1989 A novel technique and structure for the measurement of intrinsic stress and Young’s modulus of thin films Proc. IEEE Microelectromech. Syst. pp 96-7
[50] Osterberg P M and Senturia S D 1997 M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures J. Microelectromech. Syst. 6 107-18
[51] Chen S, Baughn T V, Yao Z J, and Goldsmith C L 2002 A New In Situ Residual Stress Measurement Method for a MEMS Thin Fixed–Fixed Beam Structure J. Microelectromech. Syst. 11 309-16
[52] Baker M S, de Boer M P, Smith N F, Warne L K, and Sinclair M B 2002 Integrated Measurement-Modeling Approaches for Evaluating Residual Stress Using Micromachined Fixed–Fixed Beams J. Microelectromech. Syst. 11 743-53
[53] Hou M T-K and Chen R 2003 Effect of width on the stress-induced bending of micromachined bilayer cantilevers J. Micromech. Microeng. 13 141-8
[54] Ugural A C 1999 Stresses in Plates and Shells Ch 3 71-84 (New York: McGraw-Hill)
[55] Roark R J and Young W C 1975 Formulas for Stress and Strain Ch 10 377 (New York: McGraw-Hill)
[56] Dunn M L, Zhang Y and Bright V M 2002 Deformation and structural stability of layered plate IEEE J MEMS 11(4) 372-384
[57] Maier-Schneider D, Maibach J and Obermeier E 1995 A new analytical solution for the load-deflection of square membranes IEEE J MEMS 4(4) 238–41
[58] SharpeWN, Yuan B, Vaidyanathan R and Edwards RL 1997 Measurements of Young’s modulus, Poisson’s ratio, and tensile strength of polysilicon. Proc. 10th IEEE Int. Workshop on MEMS, Nagoya, Japan, 424-429
[59] Thornton J A and Hoffman D W 1989 Stress-related effects in thin film Thin Solid Films 171 5-31
[60] Vkassak J J and Nix W D 1992 A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films J Mater. Res. 7(12) 3242-3249
[61] Luo C, Schneider T W, White R C, Currie J and Paranjape M 2003 A simple deflection-testing method to determine Poisson’s ratio for MEMS applications J Micromech. Microeng. 13(1) 129-133
[62] Tsai H-C and Fang W 2003 Determining the Poisson’s ratio of thin film materials using resonant method. Sensors and Actuators A 103(3) 377-383
[63] Fang W 1999 Determination of the elastic modulus of thin film materials using self-deformed micromachined cantilevers J Micromech. Microeng. 9(3) 230-235
[64] Fang W and Wickert J A 1996 Determining mean and gradient residual stresses in thin films using micromachined cantilevers J. Micromech. Microeng. 6(3) 301-309
[65] Brand O, Baltes H and Baldenweg U 1992 Thermally excited silicon oxide bridge resonators in CMOS technology J. Micromech. Microeng. 2 208-210
[66] Brook A J, Bending S J , Pinto J, Oral A, Ritchie D, Beere H, Springthorpe A and Henini M 2003 Micromachined III-V cantilevers for AFM-tracking scanning Hall probe microscopy J. Micromech. Microeng. 13 124-128
[67] Van Kessel P F, Hornbeck L J, Meier R E and Douglass M R 1998 A MEMS-based projection display Proc. IEEE 86 1687-1704
[68] Lucent Technology, Bell Laboratories Physical Science Research, http://www.bell-labs.com/org/physicalsciences/projects/mems/mems3.html
[69] Lin L Y, Lee S S, Pister K S J and Wu M C 1994 Three-dimensional micro-Fresnel optical elements fabricated by micromachining technique Electronics Letters 30 448-449
[70] Tang W C, Nguyen T-C H and Howe R T 1989 Laterally driven polysilicon resonant microstructures Proc. IEEE MEMS (MEMS ‘89) 53 -59
[71] Hou M T-K, Liao K-M, Yeh H-Z, Hong P-Y and Chen R 2002 Design and fabrication of surface-micromachined spherical mirrors Conf. Digest 2002 IEEE/LEOS Int. Conf. on Optical MEMs 20-23
[72] Yen H, Lee C, Chen R and Lin M J 2001 Analysis and fabrication of deformable focusing micromirrors Proceedings of 2001 ASME International Mechanical Engineering Congress Exposition
[73] Saif M T A and MacDonald N C 1996 Planarity of large MEMS J. MEMS, 5 79-97
[74] Gan M C, Tan and Chan K W 1996 Flattening developable bi-parametric surfaces Computers & Structures 58 703-708
[75] ANSYS Inc. 2000, ANSYS 5.7 User’s Manual, Canonsburg, PA
[76] Lee C 1999 Design and Fabrication of Variable Focusing Micro Mirror Master Dissertation of National Tsing Hua University, TAIWAN
[77] Glaser I, Glaser R and Meshulam G 2002 Stationary pick-up head for very fast seek in optical disk drives Int. Symp. Optical Memory and Optical Data Storage Topical Meeting 335-337
[78] Hisanaga M, Koumura T and Hattori T 1993 Fabrication of 3-dimensionally shaped Si diaphragm dynamic focusing mirror Proc. IEEE MEMS 30-35
[79] Wang P K C and Hadaegh F Y 1996 Computation of static shapes and voltages for micromachined deformable mirrors with nonlinear electrostatic actuators J. Microelectromechanical Systems 5 205-220
[80] Burns D M and Bright V M 1998 Micro-electro-mechanical focusing mirrors Proc. IEEE MEMS. 460-465
[81] Mescher M J, Vladimer M L and Bernstein J J 2002 A novel high-speed piezoelectric deformable varifocal mirror for optical applications Proc. IEEE MEMS 511-515
[82] Focus Software, Inc. 2001 ZEMAX 10.0
[83] Jones R M 1999 Mechanics of Composite Materials: Taylor & Francis