近年來半導體產業不斷藉由縮小電晶體尺寸來提升效能，為了配合先進奈米製程，勢必尋求新的替代材料與元件設計概念，二硫化鉬(MoS2)特殊的電子傳導、熱導、光學與機械特性，且易整合於現今元件製成，將可運用於新一代電子元件與積體電路上，為了確保以二硫化鉬薄膜為材料製造出的奈米元件，在製造及使用過程中皆能保有其結構完整性，已有多位學者研究其機械性質，包含彈性模數、破壞強度、韌性、拉伸測試等，但鮮少提及二硫化鉬薄膜的疲勞特性。在半導體製程及元件使用的過程中，由於電、熱或機械外力引起的循環應力，長期下來可能使材料內部產生微裂縫，造成元件失效，因此研究薄膜材料之疲勞行為，對保證微奈米元件之可靠度非常重要。
此外，為了瞭解二硫化鉬是否具有適當的機械性質，使之能整合於可延展性聚合物基板上，以製備出柔性電路板(flexible electronics)，本研究第一部分先以分子動力學軟體LAMMPS配合REBO (second-generation reactive bond-order)势能函數，進行等應變率拉伸，分別模擬單層二硫化鉬薄膜受2*1010 /s、2*109 /s、2*108 /s、2*107 /s之等應變率，單軸拉伸直至破壞之力學行為，並與奈米壓痕實驗結果與其它數值分析模擬文獻比較。
第二部分模擬應變控制疲勞測試(strain-control fatigue test)，使整個模擬盒子以等應變率往AC方向均勻變形，觀察在不同應變幅(strain amplitude)下，二硫化鉬薄膜之低週疲勞行為(Low-Cycle fatigue)。
第三部分以微觀角度探討疲勞損傷累積的過程，運用OVITO可視化軟體匯出動畫與各個原子的應力、非仿射變形(non-affine displacement)，以觀察原子在反覆載重下擴散(diffusion)之情形及裂縫型態與沿伸方向。

Recently, the semiconductor industry has reduced the size of the transistor in order to improve the performance of it. Advanced nanometer devices require new materials and new design concepts. Graphene-like two-dimensional(2D) transition metal dichalcogenides(TMDs) have been attracting a lot of interests because of it astonishing properties. Molybdenum disulfide(MoS2) is one of TMDs. It has direct band gap of 1.8eV in monolayer and it’s bandgap can change with the number of layers. These properties tackle the gapless problem of graphene, thus make it industrial important. In order to ensure the reliability of these nano-devices made by MoS2, many scholars have studied their mechanical properties including elastic modulus, stiffness and breaking strength. However only limited experimental and simulation studies on cyclic deformation and fracture behavior. In this thesis, low-cycle fatigue behavior of single layer MoS2(SLMoS2) was studied by using Large-scale Atomic/Molecular Masively Parallel Simulation(LAMMPS) package.
First, we bulid two modle ,one is the perfect SLMoS2, the other is the SLMoS2 containing a notch at the center. Then, uniaxial tension simulation under single loading along (airmchair)AC direction was carried out at 1K with four different strain rate (2*1010 /s、2*109 /s、2*108 /s、2*107 /s ) and the result was compared to the data of other literature[14][21][23][24]. Second-generation Reactive Bond-Order(REBO) potential sutiable for MoS2 has been chosen to describe the interatomic interaction.
Second, strain-control tention-tention fatigue simulation was carried out at 1K with various strain amplitude on SLMoS2 containing a notch at the center. Strain rate employed in cyclic loading was 2*109/s. The direction of cyclic loading is also AC direction. From the simulation result, effect of cyclic strain amplitude on fatigue life and cyclic stress-strain behavior has been determined.
Third, the development of fatigue damage with sucessive number of cycles has been examined using OVITO software. The diffusion of atoms under cyclic loading ,the defect type, crack propagation and the fracture machanisum have also been examined.

參考文獻
[1]摩爾定律，維基百科，取自
https://zh.wikipedia.org/wiki/%E6%91%A9%E5%B0%94%E5%AE%9A%E5%BE%8B
[2] 世界上最小的電晶體，取自
http://mp.weixin.qq.com/s?__biz=MzA3NTIyODUzNA==&mid=2649526000&idx=2&sn=c0cf37d1f8db6640521d1f82e841e32d&chksm=876b9ae9b01c13ffe0ecfa765546ab426bf54fbd2f821a3b74c3130658aff12938fbde6ffa94&mpshare=1&scene=1&srcid=1014QxOYUvYcgUtNz8v98tyM&from=singlemessage&isappinstalled=0#wechat_redirect
[3] 蘇雅雯(2014)，神奇的二維材料 – Graphene與MoS2，奈米通訊 21卷
No.2 國家奈米元件實驗室/奈米元件組，pp. 36-38.
[4] S.B. Desai, S.R. Madhvapathy, A.B. Sachid, J.P. Llinas, Q. Wang, G.H. Ahn, G.
Pitner, G. Pitner, M.J. Kim, J. Bokor, C. Hu, H.S.P. Wong, A. Javey(2017), “MoS2
transistors with 1-nanometer gate lengths”, Science, vol.354, pp.99-102.
[5] M.A. Alam(2012), “Flexible Electronics”, School of Electrical and Computer
Engineering, Purdue University, pp.860-865.
[6] D. Akinwande (2016), “MoS2 monolayers make GHz transisitor”, IOP, A
community website from IOP Publishing, from
http://nanotechweb.org/cws/article/tech/63633.
[7] A. Gupta, T. Sakthivel, S. Seal (2015), “Recent development in 2D materials beyond graphen”, Progress in Material Science, vol.73, pp.44-126.
[8] A.K. Geim, I.V. Grigorieva (2013), “Van der Waals heterostructures”, Nature,
vol.499, pp.419-425.
[9] Mutiscale Modeling, from http://lammm.epfl.ch/Research/Multiscale-Modeling.
[10] LAMMPS User Manual. Sandia National Labs and Temple University (2004).
Retrieved from http://lammps.sandia.gov/.
[11] A. Stukowski. OVITO User Manual. Retrieved from http://www.ovito.org/.
[12] D.Liu, X.Chen, D. Li, F. Wang, X. Luo, B. Yang (2010), “Simulation of MoS2
crystal structure and the experimental study of thermal decomposition”, Journal
of Molecular Structure, vol.980, pp.66-71.
[13] T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu,
J. Feng(2012), “Valley-selective circular dichroism of monolayer molybdenum
disulphide”, Nature Communication, vol.3, no.887.
[14] X. Guo, G. Yang, J. Zhang, X. Xu (2015), “Structural, mechanical and electronic
properties of in-plane 1T/2H phase interface of MoS2 heterostrctures”, AIP
Advances, vol. 5, pp. 097174.
[15] 二硫化鉬，維基百科，出自https://zh.wikipedia.org/wiki/二硫化鉬
[16] Z.Yin, H.Li, L Jiang, Y. Shi, Y. Sun (2012) , “Single layer MoS2 pototransisitors”,
ACS Nano, vol.6, pp.74-80.
[17] X. Li, H. Zhu (2015), “Two-dimentional MoS2 : Properties, preparation,and
applications”, Journal of Materiomics, vol.1, pp. 33-44.
[18] A.C. Gomez, R. Roldan, E. Cappelluti, M. Buscema, F. Guinea, H.S.J. Zant, G.A.
Steele (2013) , “Local Strain Engineering in Atomically Thin MoS2”, Nano Lett, vol.13, pp.5361-5366.
[19] S. Bertolazzi, J. Brivio, A.Kis (2011), “Stretching and Breaking of Ultrathin
MoS2”, ACSNANO, vol.5, no.12, pp.9703-9709.
[20] T. Lorenz, J.O. Joswing, G. Seifert (2014), “Streching and breaking of monolayer MoS2 – an atomistic simulation”, 2D Mater., vol.2, pp.011007.
[21] 李明林，万亚玲，胡建玥、王卫东 (2016)，「單層二硫化鉬立學性能和手性效應的分子動力學模擬」，物理學報，vol.65，No.17，pp.176201.
[22] J.W. Jiang (2014), “The buckling of single-layer MoS2 under uniaxial
compression”, Nanotechnology, vol.25, pp.355402.
[23] S. Xiong, G.Cao (2015), “Molecular dynamics simulations of mechanical
properties of monolayer MoS2”, Nanotechnology, vol.26, pp.185705.
[24] Z. Yu (2016), “Multi-layer MoS2 Fracture mechanism”, Department of
Mechanical and Biomedical Engineering, City University of Hong Kong, Ph.D.
[25] S. Wang, Z. Qin, G.S. Jung, F.J. Martin-Martinez, K. Zhang, M.J. Buehler, J.H.
Warner (2016), “Atomically Sharp Crack Tip in Monolayer MoS2 and Their
Enhanced Toughness by Vacancy Defects”, ACS Nano, vol.10, pp.9831-9839.
[26] Y. Guo, C.Liu, Q. Yin, C.Wei, S. Lin, T.B. Hoffman, Y. Zhao, J.h. Edgar, Q. Chen, S.P. Lau, J. Dai, H.Yao, H.S.P. Wong, Y. Chai(2016), “Distinctive in-Plane
Cleavage Behavior of Two-Dimensional Layered Materials”, ACS Nano, vol.10, pp.8980-8988.
[27] 陳冠廷(民101年7月)，「ITO薄膜鍍製於可撓性基板得彎曲疲勞壽命分析」，國立成功大學機械工程系，碩士論文。
[28] N.E. Dowling (2011), “Mechanical Behavior of Materials – Engineering Methods for Deformation , Fracture, and Fatigue”, 4th edition.
[29] G. Paradee (2014), “Fatigue Properties of Graphene Interconnects on Flexible
Substrates”, Materials Science and Engineering, University of Maryland, Ph.D.
[30] 郭巧能，曹义剛，孫強，劉忠俠，賈瑜，霍裕平 (2013)，「溫度對超薄銅薄膜疲勞性能影響的分子動力學模擬」，物理學報，vol.62，No.10。
[31] J.Luo, K. Dahmen, P. K. Liw, Y. Shi (2015), “ Low-cycle fatigue of metallic glass nanowire”, Acta Materialia, vol.87, pp.225-232.
[32] S. Park, K.S. Lee, G. Bozoklu,W. Cai, S.T. Nguyen,R.S. Ruoff (2017), “Graphene Oxide Paper Modified by Divalent Ions – Eenhancing Mechanical Properties via Chemical Cross-Linking”, ACS NANO, vol.2, no.3, pp.572-578.
[33] J. Veerababu, S.Goyal, R. Sandhya, K. Laha (2017), “Understanding the Low
Cycle Fatigue Behavior of Single Crystal Cu at the Nano-scale: A Molecular
Dynamics Study”, Transactions of the Indian Institute of Metals, vol.70,
pp.867-874.
[34] V.S. Srinivasan, G. Sainath, B.K. Choudhary, M.D. Mathew, T. Jayakumar
(2013), “Effect of Temperature and Strain Amplitude on Fatigue Behaviour of
BCC Iron Single Crystal using Molecular Dynamics Simulation”, Procedia
Engineering, vol.55, pp.742-746.
[35] 張躍, 谷景華, 尚家香, 馬岳（民96），計算材料基礎，北京航空航天大
學出版社，pp. 83-135。
[36] J. Meller (2001),”Molecular Dynamics”, encyclopedia of life sciences, nature
publish group, from www.els.net.
[37] M.P. Allen (2004), “Introduction to Molecular Dynamics Simulation”, NIC Series, vol.23, pp.1-28.
[38] 徐偉盛 (民97年6月)，「以分子動力學及原子力顯微鏡估測單必奈米碳管之楊氏係數」，國立成功大學航空太空工程系，碩士論文。
[39] 廖柏源 (民104年7月)，「以分子動力學模擬二硫化鉬奈米線機械性質與熱穩定性質」，國立中山大學機械與機電工程學系，碩士論文。
[40] LAMMPS，維基百科，出自https://zh.wikipedia.org/wiki/LAMMPS.
[41] Cauchy stress tensor，維基百科，出自
https://en.wikipedia.org/wiki/Cauchy_stress_tensor.
[42] 黃貞文(民104年7月)，「以分子靜力學模擬預測鎢奈米線之機械性質」，國立中山大學機械與機電工程學系，碩士論文。
[43] N. Miyazaki, Y. Shiozaki (1996), “Calculation of mechanical properties of solids using molecular dynamics method”, Jsme International Journal Series a-Mechanics and Material Engineering, vol.39, pp. 606-612.
[44]F. Shimizu, S. Ogata, J. Li (2007), “Theory of Shear Banding in Metallic Glasses and Molecular Dynamic Calculations”, Material Transactions, vol.48, pp.2923-2927.
[45]W. Zhou, X. Zou, S.Najmaei, Z. Liu, Y. Shi, J. Kong, J.Lou, P.M.Ajayan, B.I. Yakoboson, J.C. Idrobo (2013), “Intrinsic Structural Defect in Monolayer Molybdenum Disulfide”, Nano Letter, vol.13, pp.2615-2622.