鑑於積體電路與微奈米機電系統技術迅速的進步，可靠度是一個微元件產品成功的重要因素。然而，可靠性在這些元件的運用，經常是取決於微結構的疲勞。微懸臂樑和多晶矽是常使用於微元件之結構與材料之一，因此，了解其機械疲勞特性是預測微元件壽命所需的指標。

本研究使用不同方法測試多晶矽微懸臂樑之彎曲疲勞壽命，包括微致動器，MTS Tytron250微拉力測試系統和壓電致動器。在微致動器測試方面，由於微致動器的位移振幅太小，無法產生足夠的應力，試件因而經過數百萬次而沒有產生破壞。依據MTS Tytron250微拉力測試系統與壓電致動器的實驗結果顯示，較大的應力會導致微結構的壽命減少，應力與壽命成反比。

為了更精準的預測多晶矽微懸臂樑彎曲疲勞壽命，本研究建立預測多晶矽微懸臂樑彎曲疲勞壽命之經驗關係式，並呈現了負載頻率對於疲勞壽命之影響。應力越高會使材料的疲勞壽命減少，而低頻率則增強這個影響。此外，本文也將現有的實驗數據與先前文獻對於多晶矽的疲勞數據合併製成應力-疲勞壽命曲線圖，其中包含不同的測試機制，如拉伸、彎曲、扭轉，可做為未來微元件設計人員或相關研究人員之重要參考。

In light of the rapid advancement in IC/MEMS/NEMS technology, the reliability is an essential factor for a successful microdevice product. However, the reliable application of these devices often depends on the fatigue of their microstructure. Microcantilever beam and polycrystalline silicon (polysilicon) are the most often used structure and material in microdevices, respectively. Therefore, their mechanical fatigue properties need to be characterized to predict the lifetime of the microdevices.
This study presents the fatigue life of polysilicon microcantilever beam in bending by various testing methods, including microactuator, MTS Tytron250 microforce testing system and piezoelectric actuator. During microactuator testing, the fatigue life persists up to millions of cycles without failure, because the amplitude of displacement is small. Based on the results of the MTS Tytron250 microforce testing system and the piezoelectric actuator, it can be concluded that large stress reduces the number of cycles, namely the fatigue life is inversely proportional to the stress.
In this study, an empirical correlation is established for predicting bending fatigue of polysilicon microcantilever beam. This correlation demonstrated the influence of applied frequency on fatigue life. The high stress reduced the fatigue life, and low frequencies enhanced this effect. Moreover, the collective plot of polysilicon by various testing mechanisms, such as tension, bending and torsion, will provide the microdevice designer and researcher with a good reference for various applications.

Alsem D. H., Pierron O. N., Stach E. A., Muhlstein C. L. and Ritchie R. O. “Mechanisms for fatigue of micron-scale silicon structural films”, Advanced Engineering Materials, vol. 9, No. 1-2, pp.15-30, 2007
Ando T., Shikida M. and Sato K., “Tensile-mode fatigue of silicon films as structural materials for MEMS”, Sens. Actuators A, vol. 93, pp. 70-75, 2001
ANSYS Manual, “ANSYS element reference-element library-solid 45”, Release 10.0
Bahgdahn J. and Sharpe Jr. W. N., “Fatigue of polycrystalline silicon under long-term cyclic loading”, Sens. Actuators A, vol. 103, pp. 9-15, 2003
Baumert E. K., Theillet P.-O. and Pierron O. N., “Investigation of the low-cycle fatigue mechanism for micron-scale monocrystalline silicon films”, Acta Mater., vol. 58, pp. 2854-2863, 2010
Bhalerao K., Soboyejo A. B. O., and Soboyejo W. O., “Modeling of fatigue in polysilicon MEMS structures”, J. Mater. Sci., vol. 38, pp. 4157-4161, 2003
Binnig G., Quate C. F. and Gerber Ch., “Atomic Force Microscope”, Phys. Rev. Lett., vol. 56, pp. 930-933, 1986.
Boroch R. E., Müller-Fiedler R., Bagdahn J. and Gumbsch P., “High-cycle fatigue and strengthening in polycrystalline silicon”, Scripta Mater., vol. 59, pp. 936-940, 2008
Budnitzki M. and Pierron O. N., “Highly localized surface oxide thickening on polycrystalline silicon thin films during cyclic loading in humid environments”, Acta Mater., vol. 57, pp. 2944-2955, 2009
Chasiotis I., “Mechanicals of thin films and microdevices”, IEEE Trans. Device Materials Reliability, vol. 4, pp. 176-188, 2004
Chen C. J., “ MEMS technology and application”, Precision Instrument Development Center, National science council, 2003
Chu P. B., Lee S. S., Park S., Tsai M. J., Brener I., Peale D., Doran R. and Pu C., “MOEMS-enabling technologies for large optical cross-connects”, in Proc. SPIE, vol. 4561, pp. 55-65, 2001
Comtois J. H., Michlicek M. A. and Barron C. C., “Characterization of electrothermal actuators and arrays fabricated in a four-level, planarized surface-micromachined polycrystalline silicon process”, Int. Conf. Solid State Sensors and Actuators, Transducers’ 97, pp.769-772, 1997
Erdogan, F. and Sih, G. C., “On the crack extension in plates under plane loading and transverse shear”, Trans. ASME. J. Basic Eng., vol. 85, pp. 519-527, 1963
Greek S., Ericson F., Johansson S., Fürtsch M. and Rump A., “Mechanical characterization of thick polysilicon films: Young's modulus and fracture strength evaluated with microstructures”, J. Micromech. Microeng., vol. 9, pp. 245-251, 1999
Haque M. A. and Saif M. T. A., “Microscale materials testing using MEMS actuators”, J. Microelectromech Sys., vol. 10, pp. 146-152, 2001
Haque M. A. and Saif M. T. A., “A review of MEMS-based microscale and nanoscale tensile and bending testing”, Exp. Mech., vol. 43, pp. 248-255, 2003
Hibbeler R. C., “Mechanical of materials”, 3rd ed., Prentice Hall, Inc., 1997
Hocheng H., Kao K. S. and Fang W., “Fatigue life of a microcantilever beam in bending”, J. Vac. Sci. Technol. B, vol. 22, pp. 3143-3146, 2004
Hocheng H., Hung J. N. and Guu Y. H., “Various fatigue testing of polycrystalline silicon microcantilever beam in bending”, Jpn. J. Appl. Phys., vol. 47, pp. 5256-5261, 2008
Hsu T. R., “MEMS & Microsystems Design and Manufacture”, McGraw-Hill, 2002
Hung J. N., “On the fabrication and performance analysis of an electro-thermal microactuator”, Master Thesis at Feng Chia University, 2004.
Hung J. N., Hocheng H. and Sato K., “Torsion fatigue testing of polycrystalline silicon cross-microbridge structures”, Jpn. J. Appl. Phys., vol. 50, 06GM07, 2011
Hung J. N., Lin M. J. and Hwan C. L, “Deformation and fatigue analysis of micro thermal-electrostatic actuator devices”, 7th Biennial ASME Conference Engineering Systems Design and Analysis, vol. 3, pp. 491-496, 2004
Johansson S., Schweitz J. Å., Tenerz L. and Tirén J., “Fracture testing of silicon microelements in situ in a scanning electron microscope”, J. Appl. Phys., vol. 63, pp. 4799-4803, 1988
Jones P. T., Johnson G. C. and Howe R. T., “Micromechanical structures for fracture testing of brittle thin films”, Proc. MEMS, DSC-Volume 59, ASME Int. Mechanical Engineering Congress and Exposition, Atlanta, GA, pp. 325-330, 1996.
Kahn H., Ballarini R., Mullen R. L. and Heuer A. H., “Electrostatically actuated failure of microfabricated polysilicon fracture mechanics specimens”, Proc. R. Soc. Lond. A, vol. 455, pp. 3807-3823, 1999
Kahn H., Ballarini R. and Heuer A. H., “Dynamic fatigue of silicon”, Curr. Opin. Solid State & Mater. Sci., vol. 8, pp. 71-76, 2004
Kahn H., Chen L., Ballarini R. and Heuer A. H., “Mechanical fatigue of polysilicon: Effects of mean stress and stress amplitude”, Acta Mater., vol. 54, pp. 667-678, 2006
Kamiya S., Amaki, T. Kawai, N. Honda, P. Ruther, J. Gaspar and O. Paul, “Seamless interpretation of the strength and fatigue lifetime of polycrystalline silicon thin films,” J. Micromech. Microeng., vol. 18, 095023, 2008
Kapels H., Aigner R. and Binder J., “Fracture strength and fatigue of polysilicon determined by a novel thermal actuator”, IEEE Trans. Electron Devices, vol. 47, pp. 1522-1528, 2000
Langfelder G., Longoni A., Zaraga F., Corigliano A., Ghisi A. and Merassi A., “A new on-chip test structure for real time fatigue analysis in polysilicon MEMS,” Microelectron. Relia., vol. 49, pp. 120-126, 2009
Li X., Kasai T., Nakao S., Tanaka H., Ando T., Shikida M. and Sato K., “Measurement for fracture toughness of single crystal silicon film with tensile test”, Sens. Actuators A, vol. 119, pp. 229-235, 2005
Lin Y. C., “Fatigue of an electrostatically driven microcantilever beam”, Master Thesis at National Tsing Hua University, 2004.
Lin Y. C, Hocheng H., Fang W. L. and Chen R., “Fabrication and fatigue testing of an electrostatically driven microcantilever beam”, Mater. Manuf. Process., vol. 21, pp. 75-80, 2006
Liu H. K., Lee B. J. and Liu P. P., “Low cycle fatigue of single crystal silicon thin films”, Sensors Actuators A, vol. 140, pp. 257-265, 2007
Madou M. J., “Fundamentals of Microfabrication”, CRC Press, 2nd ed., pp. 634, 2002
Miller R. A., Tai Y. C., Xu G., Bartha J. and Lin F. “An electromagnetic MEMS 2×2 fiber optic bypass switch”, Int. Conf. Solid State Sensors and Actuators, Transducers’ 97, pp. 89-92, 1997.
Muhlstein C. L., Brown S. B. and Ritchie R. O., “High-cycle fatigue and durability of polycrystalline silicon thin films in ambient air”, Sensors Actuators A, vol. 94, pp. 177-188, 2001
Namazu T. and Isono Y., “Fatigue Life Prediction Criterion for Micro-Nanoscale Single-Crystal Silicon Structures”, J. Microelectromech Sys. vol.18, pp. 129-137, 2009
Qian J. and Fatemi A., “Mixed mode fatigue crack growth: A literature survey”, Eng. Fract. Mech., vol. 55, pp. 969-990, 1996
Riethmuller W. and Benecke, W. “Thermally excited silicon microactuators”, IEEE Transactions on Electron Dev., Vol. 35, pp. 758-763, 1988
Shan X. C., Ikehara T., Murakoshi Y. and Maeda R., “Applications of micro hot embossing for optical switch formation”, Sens. Actuators A, vol. 119, pp. 433-440, 2005
Sharpe Jr. W. N. and Bagdahn J., “Fatigue testing of polysilicon-a review”, Mech. Mater., vol. 36, pp. 3-11, 2004
Sharpe Jr. W. N. and Bagdahn J., Jackson K. and Coles G., “Tensile testing of MEMS materials - recent progress”, J. Mater. Sci., vol. 38, pp. 4075-4079, 2003
Sharpe Jr. W. N., Yuan B. and Edwards R. L., “A new technique for measuring the mechanical properties of thin films”, J. Microelectromech Sys., vol. 6, pp. 193-199, 1997
Shigely J. E. and Mischke C. R., “Mechanical engineering design”, McGraw-Hill, 6th ed., 2001
Shigely J. E., Mischke C. R. and Budynas R. G, “Mechanical engineering design”, McGraw-Hill, 7th ed., 2004
Tang T. L., Hsu C. P., Chen W. C. and Fang W., “Design and implementation of a torque-enhancement 2-axis magnetostatic SOI optical scanner”, J. Micromech. Microeng., vol. 20, 025020, 2010
Timoshenko S. P. and Gere J. M., “Mechanical of materials”, 4th ed., PWS Publishing Co., 1997
Tsuchiya T., Tabata O., Sakata J. and Taga Y., “Specimen size effect on tensile strength of surface micromachined polycrystalline silicon thin films”, Proc. IEEE 10th Annu. Int. Workshop Micro Electro Mechanical Systems, pp. 529-534, 1997
Tsuchiya T., Tabata O., Sakata J. and Taga Y., “Specimen size effect on tensile strength of surface-micromachined polycrystalline silicon thin films”, J. Microelectromech Sys., vol. 7, pp. 106-113, 1998
Tsuchiya T., Shikida M. and Sato K., “Tensile testing system for sub-micrometer thick films”, Sens. Actuators A, vol. 97-98, pp. 492-496, 2002
Virwani K. R., Malshe A. P., Schmidt W. F. and Sood D. K., “Young’s modulus measurements of silicon nanostructures using a scanning probe system: a non-destructive evaluation approach”, Smart Mater. Struct., vol. 12, pp. 1028-1032, 2003
Wiliams K. R. and Muller R. S., “Etch rates for micromachining processing”, J. Microelectromech Sys., vol. 5, pp. 256-269, 1996
Yi T. and Kim C. J., “Measurement of mechanical properties for MEMS materials”, Meas. Sci. Technol., vol. 10, pp. 706-716, 1999