微雙層材料之懸臂樑結構已經被廣泛地使用在微機電系統之研究。它可以作為很有用的元件以利於各種不同的應用（例如：光學微機電系統）。其中利用兩層不同薄膜組成之雙層材料懸臂樑結構經常被使用，當犧牲層被蝕刻完及鬆脫結構後，上層材料（通常為金屬）會呈現殘留應力現象使結構產生彎曲變形。本研究首先使用有限元素法模擬如此的彎曲變形並且和理論及實驗結果做對照。本文對於殘留應力彎曲之微雙層材料懸臂樑結構的形狀效應首先做一有系統的研究。

　　本研究亦成功地發展出許多微光學元件，包括光開關、光柵、凹面鏡及掃瞄鏡片等等。我們亦提出利用殘留應力彎曲之懸臂樑所做出的一高效能光交換器。此光交換器使用一扭轉軸及彎曲之蹺蹺板結構，基本上有較低的驅動電壓並且可提供多個切換功能，此外它的次毫秒切換時間及光插入損失（0.65dB）已被驗證。如此精細的元件使得它可理想地建構高密度的光交換器於一個晶片上以作為光通訊方面的應用。

　　最後，本研究整合發展出的微光學元件設計微型化系統於光學應用上，幾個微光學系統已被驗證包括：（1）使用三維鏡面及光柵之新型微光學干涉儀系統，（2）利用殘留應力彎曲凹面鏡之微光學聚焦系統，和（3）利用三色混光波導元件及微掃瞄鏡片之投影顯示器。結果顯示這些微光學元件可成功地整合成系統，最後冀望本研究對光學微機電領域能有所貢獻。

　Micromachined cantilevers are a common component in many MEMS (Micro-Electro-Mechanical-Systems) and MOEMS (Micro-Opto-Electro-Mechanical Systems) applications. One of the most frequently employed cantilevers has a bilayer structure composed of two different thin-film layers (i.e. a base layer and an additional layer). The sacrificial-layer etching and drying processes involved in the fabrication of bilayer cantilevers induce residual stresses in the additional layer (generally metal). These stresses cause the cantilever to become activated and to curl up. This study establishes a finite element model to analyze this deformation. The accuracy of this model is verified through experimental and theoretical analysis. Having established a theoretical model, this study performs a systematic investigation into the influences of the geometrical shape of the bilayer structure and the area of coating deposition on the stress-induced bending of micromachined bilayer structures.

　This study successfully develops several micro-optics components using the stress-induced cantilevers, including an optical switch, a grating mirror, a concave mirror, and a scanner. A high performance optical crossconnect device which operates by exploiting the stress-induced bending of a micromachined bilayer cantilever is also presented. The use of a curved polysilicon seesaw structure and a torsional beam lowers the electrostatic operating voltage of the optical switch substantially and provides a multi-switching function. Furthermore, the device demonstrates a sub-millisecond switching time and a low optical insertion loss (0.65 dB). The compact nature of the optical multi-switch element renders it an ideal candidate for the construction of optical crossconnects (OXCs) with a large number of ports on a chip for optical communication applications.

　Finally, the micro-optic MEMS components developed in this study are integrated to construct miniature systems suitable for optical applications. Several micro-systems are demonstrated, including: (1) a novel micro-optic interferometer system incorporating three-dimensional micromirrors and microgratings, (2) a three-dimensional optical focusing system based on the stress-induced bending of a concave micromirror, and (3) a projection display technique utilizing three-color-mixing waveguides and micro scanning devices. The results confirm the feasibility of the developed micro-optic systems and represent a significant contribution toward the further development of optical MEMS applications.

[1] M. C. Wu, “Micromachining for Optical and Optoelectronic Systems,” Proc. IEEE, vol. 85, no. 11, pp. 1833-1856, Nov. 1997.
[2] S. E. Miller, “Integrated optics: An introduction,” Bell Syst. Tech. J., vol. 48, pp. 2059-2068, 1969.
[3] K. E. Petersen, “Micromechanical light modulator array fabricated on silicon,” Appl. Phys. Let., vol. 31, pp. 521-523, 1977.
[4] L. J. Hornbeck, “128x 128 deformable mirror devices,” IEEE Trans. Electron Devices, vol. ED-30, pp. 539-545, 1983.
[5] H. Fujita, M. Harada, K. Sato, “An Integrated Micro Servosystem,” IEEE International Workshop on Intelligent Robots, pp. 15-20, Oct. 1988.
[6] O. Solgaard, F. S. A. Sandejas, D. M. Bloom, “Deformable grating optical modulator,” Optics Letters, vol. 17, no. 9, pp. 688-690, 1992.
[7] L. J. Hornbeck, “Digital light processing and MEMS: Timely convergence for a bright future” Proc. SPIE Symp. Micromachining and Microfabrication, Austin, TX, Oct. 1995.
[8] J. W. Judy and R. S. Muller, “Batch-fabricated, addressable, magnetically actuated micro-structure,” Proc. of the solid-state sensors and actuators workshop, pp. 3046-3064, Jun. 1996.
[9] R. A. Miller, G. W. Burr, Y. –C. Tai, D. Psaltis, C. H. Ho, and R. R. Katti, “Electromagnetic MEMS scanning mirrors for holographic data storage,” Proc. of the solid-state sensors and actuators workshop, pp. 89-92, Jun. 1996.
[10] R. S. Muller and K. Y. Lau, ” Surface-Micromachined Microoptical Elements and Systems,” Proc. IEEE, vol. 86, no. 8, pp. 1705-1720, Aug. 1998.
[11] M. W. Hyer, “Some observations on the cured shape of thin unsymmetric laminates,” J. Compos. Mater., vol. 15, pp. 175-194, 1981.
[12] M. W. Hyer, “Calculation of the room-temperature shapes of unsymmetric laminates,” J. Compos. Mater., vol. 15, pp. 296-310, 1981.
[13] M. W. Hyer, “The room-temperature shape of four-layer unsymmetric cross-ply laminates,” J. Compos. Mater., vol. 16, pp. 318-340, 1982.
[14] C. B. Masters and N. J. Salamon, “Geometrically nonlinear stress-deflection relations for thin film/substrate systems, ” Int. J. Engng. Sci., vol. 31, pp. 915-925, 1993.
[15] M. Finot and S. Suresh, “Small and large deformation of thick and thin film multilayers: effects of layer geometry, plasticity and compositional gradients,” J. Mech. Phys. Solids, vol. 44, pp. 683-721, 1996.
[16] M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, “Large deformation and geometric instability of substrates with thin film deposits,” J. Appl. Phys., vol. 81, pp. 3457-64, 1997.
[17] L. B. Freund, “Some elementary connections between curvature and mismatch strain in compositionally graded thin films,” J. Mech. Phys. Solids, vol. 44, pp. 723-736, 1996.
[18] L. B. Freund, “The mechanics of a free-standing strained film/compliant substrate system,” Thin Films: Stresses and Mechanical Properties Ⅵ, vol. 436, pp. 393-404, 1997.
[19] L. B. Freund, J. A. Floro, and E. Chason, “Extension of the stoney formula for substrate curvature to configurations with thin substrate or large deformations,” Appl. Phys. Let., vol. 74 pp. 1987-89, 1999.
[20] L. B. Freund, “Substrate curvature due to thin film mismatch strain in the nonlinear deformation range,” J. Mech. Phys. Solids, vol. 48, pp. 1159-74, 2000.
[21] S. Akamine, T. R. Albrecht, M. J. Zdeblick, and C. F. Quate, “A planar process for microfabrication of integrated scanning tunneling microscopes,” Sensors and Actuators, A21-A23, pp. 964-970, 1990.
[22] K. E. Petersen, “Silicon torsional scanning mirror,” IBM J. Res. Develop., vol. 24, pp. 631-637, 1980.
[23] M. Capanu, J. G. Ⅳ Boyd, and P. J. Hesketh, “Design, fabrication, and testing of a bistable electromagnetically actuated microvalve,” J. Microelectromech. Syst., vol. 9, pp. 181-189, 2000.
[24] J. N. Kuo, G. B. Lee, W. F. Pan, and H. H. Lee, “Shape and thermal effects of metal films on stress-induced bending of micromachined bilayer cantilever,” Japanese Journal of Applied Physics, vol. 44, no. 5A, pp. 3180-86, 2005.
[25] J. N. Kuo, G. B. Lee, and W. F. Pan, “A High-Speed Low-Voltage Double-Switch Optical Crossconnect Using Stress-Induced Bending Micromirrors,” IEEE Photonics Technology Letters, vol. 16, no. 9, pp. 2042-44, Sept. 2004.
[26] J. N. Kuo, G. B. Lee, and W. F. Pan, “Surface-Micromachined Optical Interferometry System Utilizing Three-Dimensional Micromirrors and Microgratings,” Japanese Journal of Applied Physics, vol. 44, no. 21, pp. L668-L671, 2005.
[27] J. N. Kuo, G. B. Lee, and W. F. Pan, “Projection Display Technique Utilizing Three-Color-Mixing Waveguides and Micro Scanning Devices,” IEEE Photonics Technology Letters, vol. 17, no. 1, pp. 217-219, Jan. 2005.
[28] G. Greitmann, and R. A. Buser, “Tactile microgripper for automated handling of microparts,” Sensors and Actuators A, vol. 53, pp. 410–15, 1996.
[29] S. Schweizer, S. Calmes, M. Laudon, and Ph. Renaud, “Thermally actuated optical microscanner with large angle and low consumption,” Sensors and Actuators A, vol. 76, pp. 470–77, 1999.
[30] Y. Zhang, and R. B. Marcus, “Thermally actuated microprobes for a new wafer probe card,” J. Microelectromech. Syst., vol. 8, pp. 43-49, 1999.
[31] R. T. Chen, H. Nguyen, and M. C. Wu, “A low voltage micromachined optical switch by stress-induced bending,” Proc. IEEE MEMS (MEMS’99), pp. 424-428, 1999.
[32] C. Chang, and P. Chang, “Innovative micromachined microwave switch with very low insertion loss,” Sensors and Actuators A, vol. 79, pp. 71-75, 2000.
[33] D. C. Miller, W. Zhang, and V. M. Bright, “Microrelay packaging technology using flip-chip assembly,” Proc. IEEE MEMS (MEMS’00), pp. 265–270, 2000.
[34] Y. Liu, X. Li, T. Abe, Y. Haga, and M. Esashi, “A thermomechanical relay with microspring contact array,” Proc. IEEE MEMS (MEMS’01), pp. 220-223, 2001.
[35] T. C. Hodge, S. A. Bidstrup-Allen and P. A. Kohl, “Stresses in thin film metallization,” IEEE Trans. Compon. Packaging Technol. A, vol. 20, pp. 241-250, 1997.
[36] W. Fang, and J. A. Wickert, “Comments on measuring thin-film stresses using bi-layer micromachined beams,” J. Micromech.Microeng., vol. 5, pp. 276-281, 1995.
[37] Y. Min, and Y. Kim, “In situ measurement of residual stress in micromachined thin films using a specimen with composite-bilayer cantilevers,” J. Micromech. Microeng., vol. 10, pp. 314–21, 2000.
[38] S. Timoshenko, “Analysis of bi-metal thermostats,” J. Opt. Soc. Am., vol. 11, pp. 233-255, 1925.
[39] M. W. Judy, Y. Cho, R. T. Howe, and A. P. Pisano, “Self-Adjusting Microstructures (SAMS),” Proc. IEEE MEMS (MEMS’91), pp. 51-56, 1991.
[40] W. Fang, H. Tsai, and C. Lo, “Determining thermal expansion coefficients of thin films using micromachined cantilevers,” Sensors and Actuators A, vol. 77, pp. 21-27, 1999.
[41] D. Koester, A. Cowen, R. Mahadevan, M. Stonefield and B. Hardy, “PolyMUMPs Design Handbook Revision 10.0,” MEMSCAP Inc., Triangle Research Park, NC, USA, 2003.
[42] V. M. Poladian, R. Muller, N. Mierlacioiu, “Modelling of residual stress in a multilayer micromachined cantilever,” Proc. IEEE Semiconductor Conf., pp. 499-502, 2000.
[43] M. T.-K. Hou and R. Chen, “Effect of width on the stress-induced bending of micromachined bilayer cantilevers,” J. Micromech. Microeng., vol. 13, pp. 141-148, 2003.
[44] H. D. Espinosa and B. C. Prorok, “Effects of film thickness on the yielding behavior of polycrystalline gold films,” Proc. Mat. Res. Soc. Symp., vol. 695, pp. 83-88, 2002.
[45] Y. Yee, M. Park, K. Chun, “A sticking model of suspended polysilicon microstructure including residual stress gradient and postrelease temperature,” J. Microelectromech. Syst., vol. 7, no. 3, pp. 339-344, 1998.
[46] X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron., vol. 8, pp. 26-32, 2002.
[47] C. S. Chang, T. S. Chu, L. S. Huang, C. Y. Chang, S. Y. Zeng, M. H. Wen, Y. K. Yen, “A novel addressable switching micro corner cube array for free-space optical applications,” Proc. IEEE MEMS (MEMS’03), pp. 279-282, 2003.
[48] A. Mokhtar, L. Benmohamed and M. Bortz, “OXC Port Dimensioning Strategies in Optical Networks-A Nodal Perspective,” IEEE Commun. Lett., vol. 8, pp. 283–285, 2004.
[49] Y. C. Lin, J. C. Chiou, W. T. Lin, Y. J. Lin, and S. D. Wu, “The Design and Assembly of Surface-Micromachined Optical Switch for Optical Add/Drop Multiplexer Application,” IEEE Trans. Adv. Packag., vol. 26, pp. 261–267, 2003.
[50] A. Q. Liu, X. M. Zhang, V. M. Murukeshan, Q. X. Zhang, Q. B. Zou, S. Uppili, “An optical crossconnect (OXC) using drawbridge micromirrors,” Sens. Actuator A, vol. 97-98, pp. 227–238, 2002.
[51] T. Xie, H. Xie, G. K. Fedder, Y. Pan, “ Endoscopic optical coherence tomography with new MEMS mirror,” Electron. Lett., vol. 39, pp. 1535–1536, 2003.
[52] L. Li, J. Zawadzka, D. Uttamchandani, “Integrated Self-Assembling and Holding Technique Applied to a 3-D MEMS Variable Optical Attenuator,” J. Microelectromech. Syst., vol. 13, pp. 83–90, 2004.
[53] R. T. Chen, H. Nguyen, and M. C. Wu, “A high-speed low-voltage stress-induced micromachined 2x2 optical switch,” IEEE Photon. Technol. Lett., vol. 11, pp. 1396–1398, 1999.
[54] F. Wang, C. Lu, Z. S. Liu, J. Li, A. Q. Liu, X. M. Zhang, “Finite element simulation and theoretical analysis of fiber-optical switches,” Sens. Actuator A, vol. 96, pp. 167-178, 2002.
[55] S. Pau, J. Yu, K. Kojima, N. Chand, and V. Swaminathan, “160-Gb/s All-Optical MEMS Time-Slot Switch for OTDM and WDM Applications,” IEEE Photon. Technol. Lett., vol. 14, pp. 1460–1462, 2002.
[56] S. Mechels, L. Muller, G. D. Morley, and D. Tillett, “1D MEMS-Based Wavelength Switching Subsystem,” IEEE Commun. Mag., vol. 41, pp. 88–94, 2003.
[57] P. D. Dobbelaere et al., “Digital MEMS for Optical Switching,” IEEE Commun. Mag., vol. 40, pp. 88–95, 2002.
[58] D. J. Bishop, C. R. Giles, and G. P. Austin, “The Lucent LambdaRouter: MEMS Technology of the Future Here Today,” IEEE Commun. Mag., vol. 40, pp. 75–79, 2002.
[59] P. B. Chu, S.-S. Lee, and S. Park, “MEMS: The Path to Large Optical Crossconnects,” IEEE Commun. Mag., vol. 40, pp. 80–87, 2002.
[60] S. S. Lee, L. Y. Lin, and M. C. Wu, “Surface-micromachined free-space micro-optical systems containing three-dimensional microgratings,” Appl. Phys. Lett., vol. 67, no. 15, pp. 2135-37, Oct. 1995.
[61] H. Sagberg, M. Lacolle, I.-R. Johansen, O. Løvhaugen, R. Belikov, O. Solgaard, and A. S. Sudbø, “Micromechanical Gratings for Visible and Near-Infrared Spectroscopy,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 3, pp. 604-613, June 2004.
[62] M. Hisanage, T. Koumura, and T. Hattori, “Fabrication of 3-dimensionally shaped Si diaphragm dynamic focusing mirror,” Proc. IEEE MEMS (MEMS’93), pp. 30-35, 1993.
[63] D. M. Burns, and V. M. Bright, “Micro-electro-mechanical focusing mirrors,” Proc. IEEE MEMS (MEMS’98), pp. 460-465, 1998.
[64] Y. Shao, D. L. Dickensheets, and P. Himmer, “3-D MOEMS Mirror for Laser Beam Pointing and Focus Control,” IEEE J. Sel. Top. Quantum Electron., vol. 10, pp. 528-535, 2004.
[65] G. Vdovin, S. Middelhoek, L. Sarro, “Deformable mirror display with continuous reflecting surface micromachined in silicon,” Proc. IEEE MEMS (MEMS’95), pp. 61-65, 1995.
[66] D. M. Burns, and V. M. Bright, “Designs to improve polysilicon micromirror surface topology,” Proc. SPIE, vol. 3008, pp. 100-110, 1997.
[67] M. T-K. Hou, K. M. Liao, H. Z. Yeh, P. Y. Hong, and R. Chen, “Design and fabrication of surface-micromachined spherical mirrors,” Optical MEMS Conf., pp. 20-23, 2002.
[68] H. Yen, C. Lee, R. Chen, and M. J. Lin, “Analysis and fabrication of deformable focusing micromirrors,” Proc. ASME International Mechanical Engineering Congress Exposition, 2001.
[69] M. T. A. Saif and N. C. MacDonald, “Planarity of large MEMS,” J. MEMS, vol. 5, pp. 79-97, 1996.
[70] M. L. Dunn, Y. Zhang, and V. M. Bright, “Deformation and structural stability of layered plate,” J. MEMS, vol. 11, no. 4, pp. 372-384, 2002.
[71] T. G. Bifano, H. T. Johnson, P. Bierden, and R. K. Mali, “Elimination of Stress-Induced Curvature in Thin-Film Structures,” J. Microelectromech. Syst., vol. 11, pp. 592-597, 2002.
[72] H. D. Espinosa, and B. C. Prorok, “Effects of film thickness on the yielding behavior of polycrystalline gold films,” Proc. Mat. Res. Soc. Symp., vol. 695, pp. 83-88, 2001.
[73] P. F. van Kessel, “Electronics for DLPTM technology based projection systems,” Symposium on VLSI Circuits Digest of Technical Papers, June 2001, pp. 91-94.
[74] K. Hoshino, K. Yamada, K. Matsumoto, I. Shimoyama, “A diffraction-limited-resolution full-color display with a 10-m-square visual field,” Proc. IEEE MEMS (MEMS’03), pp. 283-286, Jan. 2003.
[75] J. P. Ruske, M. Rottschalk, B. Zeitner, V. Grober, A. Rasch, “Integrated-optical three-colour-mixing device,” Electron. Lett., vol. 34, no. 4, pp. 363-364, 1998.
[76] R. F. Wolffenbuttel, ”State-of-the-Art in Integrated Optical Microspectrometers,” IEEE Trans. Instrum. Meas., vol. 53, no. 1, pp. 197-202, 2004.
[77] P. Rabiei, W. H. Steier, Cheng Zhang, L. R. Dalton, “Polymer micro-ring filters and modulators,” J. Lightwave Technol., vol. 20, no. 11, pp. 1968-75, 2002.
[78] A. Borreman, S. Musa, A.A.M. Kok, M. B. J. Diemeer, A. Driessen, “Fabrication of Polymeric Multimode Waveguides and Devices in SU-8 Photoresist Using Selective Polymerization,” Proc. Sym. IEEE/LEOS, 2002, pp. 83-86.
[79] J. S. Kim, J. W. Kang and J. J. Kim, “Simple and Low Cost Fabrication of Thermally Stable Polymeric Multimode Waveguides using a UV-curable Epoxy,” Jpn. J. Appl. Phys., vol. 42, pp. 1277-1279, 2003.
[80] Y. Ansel, F. Gindele, J. Scheurer, F. Schmitz, “Optical waveguide device realised using two SU-8 layers,” Optical MEMS Conf., 2002, pp. 123-124.
[81] B. Beche, N. Pelletier, E. Gaviot, J. Zyss, “Single-mode TE00-TM00 optical waveguides on SU-8 polymer,” Opt. Commun., vol. 230, pp. 91-94, 2004.