在本研究中，微無邊界樑的共振特性已經予以充分的探討，並且透過分析與實驗的方式，觀察懸吊彈簧與製程參數變異對其共振頻率及模態的影響。基於此設計與分析的基礎透過體型微加工技術實際製作出微無邊界樑結構，量測出其共振頻率並與分析結果比較。除此之外，在應用方面，本研究利用微無邊界樑的共振頻率成功的萃取出薄膜的機械特性，同時與微懸臂樑的萃取結果做比較，在體型微加工時，因為製程的關係，微懸臂樑浸於蝕刻液中懸浮時存在著不可避免的缺點，其邊界條件將受底切效應影響甚至隨著蝕刻的時間變化，而微無邊界樑成功的解決此問題。

簡言之，本研究成功的驗證出微無邊界樑在長蝕刻時間下是一較好的微機電測試鍵，同時，在決定楊氏係數值時微無邊界樑可提供一個上邊界值而微懸臂樑可提供一個下邊界值。此外，微無邊界樑製造容易，製程相容性高，同時數學與物理模型廣為大眾所知的微結構，故可用以彌補微懸臂樑在萃取機械特性測試鍵上的不足。

[1] K.E. Petersen, and C.R. Guarnieri, “Young’s modulus measurements of thin films using micromechanics,” Journal of Applied Physics, 50, pp 6761-6766, 1979.
[2] H.-C. Tsai, and W. Fang, “Determining the Poisson’s ratio of thin film materials using resonant method,” Sensors and Actuators A, 103, pp 377-383, 2003.
[3] L. Kiesewetter, J.-M. Zhang, D. Houdeau, and A. Steckenborn, “Determination of Young's moduli of micromechanical thin films using the resonance method,” Sensors and Actuators A, 35, pp 153-159, 1992
[4] L.M. Zhang, D. Uttamchandani, B. Culshaw, and P. Dobson, “Measurement of Young’s modulus and internal stress in silicon microresonators using a resonant frequency technique,” Measurement Science & Technology, 1, pp 1343-1346, 1990.
[5] H.-H. Hu, H.-Y. Lin, W. Fang, and B.C.S. Chou, “The diagnostic micromachined beams on (111) substrate,” Sensors and Actuators A, 93, pp 258-265, 2001
[6] ASTM standard, C623-92: Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and Glass-Ceramics by Resonance, ASTM International, West Conshohocken, PA, 2000.
[7] G. Stemme, “Resonant silicon sensors,” Journal of Micromechanics and Microengineering, 1, pp 113-125, 1991.
[8] M. Wu, C.-F. Lai, and W. Fang, "Integration of the DRIE, MUMPs, and bulk micromachining for superior micro-optical systems," IEEE Micro Electro Mechanical Systems, Maastricht, Netherlands, Jan. 2004, pp 97-100.
[9] P.R. Patterson, D. Hah, H. Nguyen, H. Toshiyoshi, R. Chao, and M.C. Wu, “A scanning micromirror with angular comb drive actuation,” IEEE Micro Electro Mechanical Systems, Las Vegas, NV, Jan. 2002, pp 544-547.
[10] R. Conant, J. Nee, K. Lau, and R. Muller, “A flat high-frequency scanning micromirror,” in Technical Digest Solid-State Sensor & Actuator Workshop, Hilton Head, SC, 2000, pp 6-9.
[11] H. Xie, Y. Pan, and G.K. Fedder, “A SCS CMOS micromirror for optical coherence tomographic imaging,” IEEE Micro Electro Mechanical Systems, Las Vegas, NV, Jan. 2002, pp 495-498.
[12] L. Zhou, M. Last, V. Milanovic, J.M. Kahn, and K.S.J. Pister, “Two-axis scanning mirror for free-space optical Communication between UAVs,” IEEE/LEOS Optical MEMS 2003, Hawaii, Aug. 2003.
[13] H. Urey, ”Optical MEMS scanner design for high-resolution display system,” Optical Scanning Ⅱ, Proceeding SPICE, Seattle, Washington, 2002, pp 27-37.
[14] J. Yan, S. Luanava, and V.Casasanta, ”Magnetic actuation for MEMS scanners for retinal scanning displays,” MOEMS Display and Imaging Systems, Proceeding SPIE , 4985, San Jose, CA, 2003.
[15] M. Freeman, “Miniature high-fidelity displays using a biaxial MEMS scanning mirror,” MOEMS Display and Imaging Systems, Proceeding SPIE , 4985, San Jose, CA, 2003.
[16] R.A. Miller, G.W. Burr, Y.C. Tai, D. Psaltis, C.M. Ho, and R. Katti, “Electromagnetic MEMS scanning mirrors for holographic data storage,” Proceeding of Solid-State Sensor and Actuator workshop, Hilton Head Island, SC, 1996, pp 183-186.
[17] B. Piekarski, D. DeVoe, M. Dubey, R. Kaul, and J. Conrad, “Surface micromachined piezoelectric resonant beam filters,” Sensors and Actuators A, 91, pp 313-320, 2001
[18] H.H. Kim, B.K. Ju, Y.H. Lee, S.H. Lee, J.K. Lee, and S.W. Kim, ”Fabrication of suspended thin film resonator for application of RF bandpass filter,” Microelectronics Reliability, 44, pp 237-243, 2004.
[19] C.K. Madsen, J.A. Walker, J.E. Ford, K.W. Goossen, T.N. Nielsen, and G. Lenz, ”A Tunable Dispersion Compensating MEMS All-Pass Filter,” IEEE Photonics Technology Letters, 12, pp 651-653, 2000.
[20] A.R. Brown, and G.M. Rebeiz, “A Varactor Tuned RF Filter,” IEEE Transactions on Microwave Theory & Techniques, Oct. 1999, pp 1-4.
[21] Y. Ishikawa, T. Nishikawa, T. Okada, S. Shinmura, Y. Kamado, F. Kanaya, and K. Wakino, “Mechanically tunable MSW bandpass filter with combined magnetic units,” Microwave Symposium Digest, IEEE MTT-S International, May 1990, pp 143–146.
[22] D. Pastor, J. Capmany, and B. Ortega, “Experimental Demonstration of Parallel Fiber-Optic-Based RF Filtering Using WDM Techniques,” IEEE Photonic Technology Letters, 12, pp 77-78, 2000.
[23] H. Luo, X. Zhu, H. Lakdawala, L.R. Carley and G.K. Fedder, ”A copper CMOS-MEMS z-axis gyroscope,” IEEE Micro Electro Mechanical Systems, Las Vegas, NV, Jan. 2002, pp 631-634.
[24] P. Greiff, B. Boxenhorn, T. King, and L. Niles, ”Silicon monolithic micromechanical gyroscope,” Digest International Conference on Solid-State Sensors and Actuators, Transducers ’91, San Francisco, CA, 1991, pp 966-968.
[25] M. Putty, and K. Najafi, “A micromachined vibrating ring gyroscope,” Technical Digest Solid-State Sensor & Actuator Workshop, Hilton Head Island, SC, 1994, pp 213-220.
[26] W.A. Clark, R.T. Howe, and R. Horowitz, ”Surface micromachined Z-axis vibration rate gyroscope,” Technical Digest Solid-State Sensor & Actuator Workshop, Hilton Head Island, SC, 1996, pp 283-287.
[27] H. Xie, and G.K. Fedder, "A CMOS-MEMS lateral-axis gyroscope," IEEE Micro Electro Mechanical Systems, Interlaken, Switzerland, Jan. 2001, pp 162-165.
[28] O. Bel, R. Bourquin, and A. Jeanroy, “Two axes quartz angular rate sensor,” IEEE International Frequency Control Symposium and PDA Exhibition, 2002, pp 214-219.
[29] M. Lutz, W. Golderer, J. Gerstenmeier, J. Marek, B. Maihofer, S. Mahler, H. Munzel, and U. Bischof, “Aprecision Yaw Rate Sensor in Silicon Micromachining,” Transducers’97, Chicago, IL, June 16-19, 1997, pp 847-850.
[30] J. Bernstein, S. Cho, A.T. King, A. Kourepenis, P. Maciel, and M. Weinberg, "A micromachined comb-drive tuning fork rate gyroscope," IEEE Micro Electro Mechanical Systems, Fort Lauderdale, FL, 1993, pp 143-148.
[31] M. Weinberg, J. Bernstein, S. Cho, A.T. King, A. Kourepenis, P. Ward, and J. Sohn, “A micromachined comb-drive tuning fork gyroscope for commercial applications,” Sensor Expo, 1994, pp 187-193.
[32] N. Yazdi, F. Ayazi, and K. Najafi, “Micromachined Inertial Sensors,” Invited paper, Proceedings of the IEEE, Aug. 1998, pp 1640-1659.
[33] F. Ayazi and K. Najafi, “High Aspect-Ratio Dry-Release Poly-Silicon MEMS Technology for Inertial Grade Microgyroscopes,” Proceeding IEEE Position Location and Navigation Symposium, San Diego, CA, Mar. 2000, pp 304-308.
[34] X. Li, M. Bao, H. Yang, S. Shen, and D. Lu, “A micromachined piezoresistive angular rate sensor with a composite beam structure,“ Sensors and Actuators A, 72, pp 217–223, 1999.
[35] K. Wang, Y. Yu, A.-C. Wong, and C.T.-C. Nguyen, “VHF free-free beam high-Q micromechanical resonators,” IEEE Micro Electro Mechanical Systems, Orlando, Florida, Jan. 1999, pp 453-458.
[36] M.J. Hill, R.W. Ziolkowski, and J. Papapolymerou, ”A high-Q reconfigurable planar EBG cavity resonator,” IEEE Microwave and Wireless components letters, 11, pp 255-257, 2001.
[37] B.E. Little, S.T. Chu, H.A. Haus, J. Foresi, and J.–P. Laine, “Microring Resonator Channel Drop Filter,” Journal of Lightwave Technology, 15, pp 998-1005, 1997.
[38] B.E. Little, S.T. Chu, W. Pan, and Y. Kokubun, “Microring Resonator Arrays for VLSI Photonics,” IEEE Photonics Technology Letters, 12, pp 323-325, 2000.
[39] C.K. Madsen, G. Lenz, A.J. Bruce, M.A. Cappuzzo, L.T. Gomez, T.N. Nielsen, L.E. Adams, and I. Brenner, “An All-Pass Filter Dispersion Compensator Using Planar Waveguide Ring Resonators,” Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communications, Piscataway, NJ, 1999, pp 99-101.
[40] M.W. Putty, S.-C. Chang, R.T. Howe, A.L. Robinson, and K.D. Wise, ”Modeling and characterization of one-port polysilicon resonant microstructures”, IEEE Micro Electromechanical Systems Workshop, Salt Lake City, Utah, Feb. 1989.
[41] N. Deb, S.V. Iyer, T. Mukherjee, and R.D. Blanton, ”MEMS resonator synthesis for defect reduction,” Journal of Modeling and Simulation of Microsystems, 2, pp 11-20, 2001.
[42] W.C. Tang, T.-C.H. Nguyen, M.W. Judy, and R.T. Howe, “Electrostatic Comb Drive of Lateral Polysilicon Resonators,” Sensors and Actuators A, 21, pp 328-331, 1990.
[43] T. Mukherjee, S. Iyer, and G.K. Fedder, “Optimization-based Synthesis of Microresonators,” Sensors and Actuators A, 70, pp 118-127, 1998.
[44] V. Kaajakari, T. Mattila, A. Oja, J. Kiihamaki, and H. Seppa, ”Square-extensional mode single-crystal silicon micromechanical resonator for low phase noise oscillator applications,” IEEE electron device letters, 25, pp 173-175, 2004.
[45] M. Spacek, K.B. Brown, Y. Ma, A.M. Robinson, R.P.W. Lawson, and W. Allegretto, “CMOS cantilever microstructures as thin film deposition monitors,” IEEE Canadian Conference on Electrical and Computer Engineering Shaw Conference Center, Edmonton, Alberta, Canada, 1999.
[46] M. Su, S. Li, and V.P. Dravid, “Microcantilever resonance-based DNA detection with nanoparticle probes,” Applied Physics Letters, 82, pp 3562-3564, 2003.
[47] D. Lange, C. Hagleitner, O. Brand, and H. Baltes, ”CMOS resonant beam gas sensing system with on-chip self excitation,” IEEE Micro Electro Mechanical Systems, Interlaken, Switzerland, Jan. 2001, pp 547-552.
[48] D. Strembicke, A.M. Robinson, F.E. Vermeulen, M. Seto, and K.B. Brown, ”Humidity measurement using resonating CMOS microcantilever structures,” IEEE Canadian Conference on Electrical and Computer Engineering Shaw Conference Center, Edmonton, Alberta, Canada, 1999.
[49] W.-T. Hsu, J.R. Clark, and C.T.-C. Nguyen, “Q-optimized lateral free-free beam micromechanical resonators,” Digest of Technical Papers, the 11th International Conference on Solid-State Sensors & Actuators Transducers’01, Munich, Germany, June 10-14, pp 1110-1113, 2001.
[50] X.M.H. Huang, M.K. Prakash, C.A. Zorman, M. Mehregany, and M.L. Roukes, ”Free-free beam beam silicon carbide nanomechanical resonators,” IEEE, Transducer’03,12th international Conference on Solid State Sensors, Actuators and Microsystems, Boston, MA, June 2003, pp 342-343.
[51] W.N. Sharpe, Jr., B. Yuan, and R.L. Edwards, “A new technique for measuring the mechanical properties of thin films,” Journal of Microelectromechanical Systems, 6, pp 193-199, 1997.
[52] C. Serre, P. Gorostiza, A. Perez-Rodriguez, F. Sanz, and J.R. Morante, “Measurement of micromechanical properties of polysilicon microstructures with an atomic force microscope,” Sensors and Actuators A, 57, pp 215-219, 1998.
[53] T. Chudoba, N. Schwarzera, F. Richtera, and Beck, “Determination of mechanical film properties of a bilayer system due to elastic indentation measurements with a spherical,” Thin Solid Films, 377, pp 366-372, 2000.
[54] J.J. Vlassak, and W.D. Nix, “A New Bulge Test Technique for the determination of Young’s modulus and Poisson’s ratio of thin films,” Journal of Materials Research, 7, pp 3242-3249, 1992.
[55] O. Tabata, K. Kawahata, S. Sugiyama, and I. Igaraashi, “Mechanical property measurements of thin films,” Sensors and Actuators A, 20, pp 135-141, 1989.
[56] O. Tabata, T. Tsuchiya, and N. Fujitsuka, “Poisson’s ratio evaluation of thin film for sensor application,” Technical Digest of the 12th Sensor Symposium, 1994, pp 19-22.
[57] K. Najafi, and K. Suzuki, “A novel technique and structure for the measurement of intrinsic stress and Young’s modulus of thin film,” IEEE Micro Electro Mechanical Systems, Salk Lake City, UT, Feb. 1989, pp 96-97.
[58] X.-Q. Sun, Z. Li, X. Zheng, and L. Lin, ”Study of fabrication process of a micro electrostatic switch and its application to a micromechanical V-F converter,” Sensors and Actuators A, 35, pp 189-192, 1993.
[59] P.M. Osterberg, and S.D. Senturia, “M-Test: a test chip for MEMS material property measurement using electrostatically actuated test structures,” Journal of Microelectromechanical systems, 6, pp 107-118, 1997.
[60] W.N. Sharpe, Jr., B. Yuan, R. Vaidyanathan, and R.L. Edwards, “Measurements of Young’s modulus, Poisson’ ratio, and tensile strength of polysilicon,” IEEE Micro Electro Mechanical Systems, Nagoya, Japan, 1997, pp 424-429.
[61] H. Ogawa, K. Suzuki, S. Kaneko, Y. Ishikawa, and T. Kitahara, “Measurements of mechanical properties of microfabricated thin films,” IEEE Micro Electro Mechanical Systems, Nagoya, Japan, 1997, pp 430-435.
[62] T. Tsuchiya, O. Tabata, J Sakata, and Y. Taga, “Specimen size effect on tensile strength of surface-micromachined polycrystalline silicon thin films,” Journal of Microelectromechanical Systems, 7, pp 106-113, 1998.
[63] C. Serre, A. Perez-Rodriguez, J.R. Morante, P. Gorostiza, and J. Esteve, “Determination of micromechanical properties of thin films by beam bending measurements with an Atomic Force Microscope,” Sensors and Actuators A, 74, pp 134-138, 1999.
[64] N.X. Randall, and R.A.J. Soden, “Characterization of the mechanical properties of MEMS devices using nanoscale techniques,” Proceeding of Material Research Society Symposium, 741, 2003, pp 231-239.
[65] L. Riester, P.J. Blau, E. Lara-Curzio, and K. Breder, “Nanoindentation with a Knoop indenter,” Thin Solid Films, 377, pp 635-639, 2000.
[66] S. Johansson, J.-A. Schweitz, L. Tenerz, and J. Tiren, “Fracture testing of silicon microelements in situ in a Scanning Electron Microscope,” Journal of Applied Physics, 66, pp 4799-4803, 1988.
[67] S.S. Rao, Mechanical Vibrations. 3rd Edition, Menlo Park, CA: Addision-Wesley, 1995.
[68] L. Meirovitch, Analytical Methods in Vibrations. New York, NY: Macmillan, 1967.
[69] W. Fang, and J.A. Wickert, “Determining mean and gradient residual stress in thin film using micromachined cantilevers,” Journal of Micromechanics and Microengineering, 6, pp 301-309, 1996.
[70] W.C. Oliver, and G.M. Pharr, “An improved technique for determing hardness and elastic modulus using load and displacement sensing indentation experiments,” Journal of Materials Research, 7, pp 1564-1583, 1992.
[71] 徐昌駿,“奈米壓痕系統於微懸臂樑彎矩測試之研究,”國立清華大學動力機械系碩士論文, 2004.