本論文主要探討碳化矽基板與銅/碳化矽基板的破壞行為，一般在進行以碳化矽為基板的晶片設計時，會選用半導體材料4H-SiC，銅則是作為金屬導線，配置於4H-SiC基板上為了探討材料的破壞行為，本文採用分子動力學和考慮化學反應的ReaxFF勢能函數，搭配數值模擬軟體LAMMPS進行壓痕與研磨製程的模擬。由於4H-SiC需摻雜氮原子，才能成為N型半導體。本文會選用三種不同摻雜濃度轉換成摻雜原子占比為0%、2%與10%，且因市面上4H-SiC晶圓會分為C面與Si面，因此選用三種平面，分別為C、Si與SiC平面同時並探討溫度效應，分別採用300K與1000K來進行模擬。由4H-SiC基板壓痕與研磨模擬結果顯示，C平面能夠承受較大應力與摩擦力，且結構較能抵抗破壞，但破壞過程中，原子結構逐漸鬆散，容易產生化學變化，意謂著化學性會不如另外兩種平面。隨著摻雜濃度增加與高溫，結構能夠承受的應力會降低，但造成的勢能能量卻會增加。由Cu/4H-SiC壓痕與研磨模擬，結果顯示，以C平面作為接合平面，能使整體結構承受較大摩擦力，且從研磨後的外觀判斷，C平面的結構完整度會最好。但微觀結構C平面卻產生最多的HCP結構占比，會使銅結構機械性能、導電性與熱膨脹性能下降。由差排分析結果表明，壓痕過程則會同時產生Hirth差排。而研磨過程會產生Hirth與Stair-rod 差排，但隨著摻雜濃度增加，能夠減少差排的產生。而高溫則會使銅結構弱化，呈現非晶態結構，導致差排產生較少，意謂著結構崩壞較快。在摻雜氮原子選擇上，採用2%最適宜，各項指標都呈現穩定的表現，而10%在指標呈現兩極化，極為不穩定，因此2%會是最適合4H-SiC的摻雜濃度。

The purpose of this study is to investigate the failure behavior of silicon carbide (SiC) substrates and copper/silicon carbide (Cu/SiC) substrates. In chip designs using SiC as the substrate, the semiconductor material 4H-SiC is commonly chosen, while copper is used as a metal conductor deposited on the 4H-SiC substrate. To study the failure behavior of the materials, this study employs molecular dynamics simulations with the ReaxFF potential, which considers chemical reactions. These simulations are performed using the numerical simulation software LAMMPS to simulate the processes of indentation and grinding. Due to the need for nitrogen doping, 4H-SiC can become an N-type semiconductor. In this study, three different doping concentrations were selected, resulting in doping atomic ratios of 0%, 2%, and 10%. Additionally, since 4H-SiC wafers are divided into C-face and Si-face, three different crystal planes were examined: C-plane, Si-plane, and SiC-plane. The temperature effects were also investigated, with simulations conducted at 300K and 1000K. The results of the indentation and grinding simulations on the 4H-SiC substrate reveal that the C-plane can withstand higher stress and friction, and its structure is more resistant to damage. However, during the process of destruction, the atomic structure gradually becomes looser and more prone to chemical changes, indicating that its chemical properties may not be as favorable as the other two planes. As the doping concentration and temperature increase, the stress that the structure can withstand decreases, but the potential energy increases. In the case of Cu/4H-SiC indentation and grinding simulations, the results demonstrate that using the C-plane as the bonding surface allows the overall structure to withstand greater friction, and from the appearance after grinding, the C-plane exhibits the best structural integrity. However, at the microscopic level, the C-plane generates the highest proportion of HCP structures, which may lead to decreased mechanical performance, conductivity, and thermal expansion of the copper structure. Dislocation analysis indicates that both Hirth dislocations and Hirth-Stair-rod dislocations are simultaneously generated during the indentation process, while the grinding process generates Hirth and Stair-rod dislocations. However, as the doping concentration increases, the generation of dislocations can be reduced. At high temperatures, the copper structure weakens and exhibits an amorphous structure, resulting in fewer dislocations, indicating faster structural failure. Regarding the choice of nitrogen doping, 2% is considered the most suitable as it demonstrates stable performance in all indicators, while 10% exhibits polarized and unstable behavior. Therefore, 2% is the optimal doping concentration for 4H-SiC.

[1] Xichun Luo, Saurav Goel, and Robert L. Reuben, "A quantitative assessment of nanometric machinability of major polytypes of single crystal silicon carbide", The Journal of the European Ceramic Society, vol. 32 ,pp. 3423-3434, 2012.
[2] C. Kittel, Introduction to Solid State Physics, 7th edition, New York：John Wiley and Sons, Inc. (1996).
[3] 中國半導體照明網。第三代寬禁帶半導體材料SiC和GaN的研究現狀。檢自:http://www.china-led.net/news/202005/19/45095.html(Jun.6,2023)
[4] Yi Lv, Cheng Cheng Peng, Feng Liao, and Mo Yang, "Molecular dynamics study on the contribution of 4H–SiC surface morphology and crystal orientation to the wetting behavior of molten Al droplet", Materials Science in Semiconductor Processing, vol. 146 , 2022.
[5]Rohm研討會講義。何謂碳化矽(Silicon Carbide)。檢自:https://techweb.rohm.com.tw/product/power-device/sic/sic-basic/3669/(Jun.6,2023)
[6]崔秉鉞。第三代半導體明日之星—碳化矽功率元件近況與展望。檢自:https://www.edntaiwan.com/20220412ta31-status-and-trend-of-sic-power-semiconductor/(Jun.6,2023)
[7]J. H. Irving and J. G. Kirkwood, "The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics", The Journal of Chemical Physics, vol. 18, no. 6, pp. 817-829, 1950.
[8]B. J. Alder and T. E. Wainwright, "Studies in molecular dynamics. I. General method", The Journal of Chemical Physics, vol. 31, no. 2, pp. 459-466, 1959.
[9]J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, "Dynamics of radiation damage", Physical Review, vol. 120, pp. 1229-1253, 1960.
[10]A. Rahman, "Correlations in the motion of atoms in liquid argon", Physical Review, vol. 136, pp. 405-441, 1964.
[11]G. Ciccotti and W. G. Hoover, "Molecular-dynamics simulation of statistical-mechanical systems", North Holland, pp. 622, 1986.
[12]M. P. Allen and D. J. Tildesley, "Computer simulation of liquids", Oxford, Claredon, 1987.
[13]J. M. Haile, "Molecular dynamics simulation elementary methods", New York: Wiley, 1993.
[14]L. Verlet, "Computer "experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules", Physical Review, vol. 159, pp. 98-103, 1967.
[15]B. Quentrec and C. P. Brot, " New method for searching for neighbors in molecular dynamics computations," Journal of Computational Physics, vol. 13, pp.430-432, 1973
[16]D. J. Auerbach, W. Paul, A. F. Bakker, C. Lutz, W. E. Rudge, and F. F. Abraham, "A special purpose parallel computer for molecular dynamics: motivation, design, implementation, and application", The Journal of Physical Chemistry, vol. 91, pp. 4881-4890, 1987.
[17]G. S. Grest, B. Dünweg, and K. Kremer, "Vectorized link cell Fortran code for molecular dynamics simulations for a large number of particles", Computer Physics Communications, vol. 51, no. 3, pp. 269-285, 1989.
[18]J.-F. Barbot, M.-F. Beaufort, and V. Audurier, "Effects of helium implantation on the mechanical properties of 4H-SiC ", Materials Science Forum, vol. 645-648, pp. 721-724, 2010.
[19]Zige Tian, Xipeng Xu, Feng Jiang, Jing Lu, Qiufa Luo, and Jiaming Lin, "Study on nanomechanical properties of 4H-SiC and 6H-SiC by molecular dynamics simulations", Ceramics International, vol. 45, part A, 2019.
[20]Bo Zhu, Dan Zhao, and Hongwei Zhao, "A study of deformation behavior and phase transformation in 4H-SiC during nanoindentation process via molecular dynamics simulation", Ceramics International, vol. 45, pp.5150-5157 , 2019.
[21]Xiaoshuang Liu, Junran Zhang, Binjie Xu, Yunhao Lu, Yiqiang Zhang, Rong Wang, Deren Yang, and Xiaodong Pi , "Deformation of 4H-SiC: The role of dopants", Applied Physics Letters, vol. 120, 2022.
[22]Lianghao Xue, Gan Feng, and Sheng Liu, "Molecular dynamics study of temperature effect on deformation behavior of m-plane 4H–SiC film by nanoindentation",Vacuum, vol. 202, 2022.
[23]Lianghao Xue, Gan Feng, Gai Wu, Fang Dong, Kang Liang, Rui Li, Shizhao Wang, and Sheng Liu, "Study of deformation mechanism of structural anisotropy in 4H–SiC film by nanoindentation", Materials Science in Semiconductor Processing, vol. 146, 2022.
[24]Qiang Kang, Xudong Fang, Chen Wu, Prateek Verma, Hao Sun, Bian Tian, Libo Zhao, Songli Wang, Nan Zhu, Ryutaro Maeda, and Zhuangde Jiang,"Mechanical properties and indentation-induced phase transformation in 4H–SiC implanted by hydrogen ions", Ceramics International, vol. 48, pp.15334-15347 , 2022.
[25]Xiaoshuang Liu, Rong Wang, Junran Zhang, Yunhao Lu, Yiqiang Zhang, Deren Yang, and Xiaodong Pi, "Anisotropic deformation of 4H-SiC wafers: insights from nanoindentation tests", Journal of Physics D: Applied Physics, vol. 55 , 2022.
[26]Suhua Shi, Yiqing Yu, Ningchang Wang, Yong Zhang, Weibin Shi, Xinjiang Liao, and Nian Duan, "Investigation of the Anisotropy of 4H-SiC Materials in Nanoindentation and Scratch Experiments", Mechanics of Materials, 2022.
[27]Hideki Sako, Hirofumi Matsuhata, Masayuki Sasaki, Masatake Nagaya, Takanori Kido, Kenji Kawata, Tomohisa Kato, Junji Senzaki, Makoto Kitabatake, and Hajime Okumura,"Micro-structural analysis of local damage introduced in subsurface regions of 4H-SiC wafers during chemo-mechanical polishing", Journal of Applied Physics, vol. 119 , 2016.
[28]Jing Lu, Qiufa Luo, Xipeng Xu, Hui Huang, and Feng Jiang," Removal mechanism of 4H- and 6H-SiC substrates (0001 and 000¯1) in mechanical planarization machining", Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 233, 2017.
[29]Jialin Wen, Tianbao Ma, Xinchun Lu, Weiwei Zhang, and Adri C.T. van Duin," Atomic Insights into Material Removal Mechanisms in Si and Cu Chemical Mechanical Polishing Processes: ReaxFF Reactive Molecular Dynamics Simulations", ICPT , 2017.
[30]Yixin Xu, Miaocao Wang, Fulong Zhu, Xiaojian Liu, Qian Chen, Jianxiong Hu, Zilin Lu, Pengjun Zeng, and Yuhong Liu," A molecular dynamic study of nano-grinding of a monocrystalline copper-silicon substrate", Applied Surface Science, vol. 493, pp.933-947,2019.
[31]Fenglin Guo, Chen Shao, Xiufang Chen, Xiejian Xie, Xianglong Yang, Xiaobo Hu , and Xiangang Xu," Shape modulation due to sub-surface damage difference on N-type 4H–SiC wafer during lapping and polishing", Materials Science in Semiconductor Processing, vol. 152,2022.
[32]Ruyi Gou, Xun Luo, Jingjing Chen, Xinghao Wang, Chenchen Kang, and Zhongqing Lei," Study on the tribological properties of diamond and SiC interactions using atomic scale numerical simulations", Tribology International, vol. 178, part B,2023.
[33]R. W. Hockney and J. W. Eastwood, "Computer Simulations Using Particles", CRC Press, 1981.
[34]J. E. Lennard-Jones,Proc. Roy. Soc. ,106A, 441(1924)
[35]P. M. Morse, Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev. 1929, 34, 57-64
[36]Murray S. Daw and M. I. Baskes," Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals", PHYSICAL REVIEW B,1984.
[37]J. Tersoff," New empirical approach for the structure and energy of covalent systems", Physical Review B,1988.
[38]M. W. Finnis and J. E. Sinclair,"A simple empirical N-body potential for transition metals", Philosophical Magazine A, vol. 50,1984.
[39]A. C. T. van Duin, S. Dasgupta, F. Lorant, and W. A. Goddard, "ReaxFF: a reactiveforce field for hydrocarbons ", J. Phys. Chem. A, vol .105, pp. 9396–9409, 2001.
[40]T. P. Senftle, S. Hong, M. M. Islam, and S. B. Kylasa, "The ReaxFF reactive force-field: development, applications and future directions", NPJ Computational Materials , vol.2,15011.1-14,2016.
[41]Ju Li and Futoshi Shimizu, "Least-Square Atomic Strain",2005
[42]Linlin Zhou, Tao Yang, Zhi Fang, Jiadong Zhou, Yapeng Zheng, Chunyu Guo, Laipan Zhu, Enhui Wang, Xinmei Hou, Kuo-Chih Chou, and Zhong Lin Wang, "Boosting of water splitting using the chemical energy simultaneously harvested from light, kinetic energy and electrical energy using N doped 4H-SiC nanohole arrays", Nano Energy, vol. 104,part A,2022.
[43]Linlin Zhou, Tao Yang, Laipan Zhu, Weijun Li , Shuize Wang, Xinmei Hou ,Xinping Mao, and Zhong Lin Wang, "Piezoelectric nanogenerators with high performance against harsh conditions based on tunable N doped 4H-SiC nanowire arrays", Nano Energy, vol. 83,2021.
[44]Yuhua Huang, Yuqi Zhou, Jinming Li, and Fulong Zhu, "Materials removal mechanism and multi modes feature for silicon carbide during scratching", International Journal of Mechanical Sciences, vol. 235,2022.
[45]陳弘儒，"以分子動力學搭配ReaxFF勢能模擬銅化學機械研磨在不同研磨液下之奈米磨擦行為",國立成功大學,碩士論文,2021。
[46]邱詩庭，"以分子動力學搭配ReaxFF勢能模擬銅矽基板化學機械研磨在不同研磨液下之奈米磨擦行為",國立成功大學,碩士論文,2022。
[47]M. L. Falk and J. S. Langer, "Dynamics of viscoplastic deformation in amorphous solids", Physical Review E, 1998.
[48]E. Maras, O. Trushin, A. Stukowski, T. Ala-Nissila, and H. Jónsson, "Global transition path search for dislocation formation in Ge on Si(001)",Computer Physics Communications, vol. 205, pp.13-21,2016.
[49]OVITO User Manual(2023). Identify diamond structure. Retrieved from https://www.ovito.org/docs/current/reference/pipelines/modifiers/identify_diamond.html(Jun.6,2023)
[50]S. Yuan, X. Guo, M. Lu, Z. Jin, R. Kang, and D. Guo, "Diamond nanoscale surface processing and tribochemical wear mechanism," Diam. Relat. Mater., vol .94, pp. 8-13, 2019.
[51]X. Guo, S. Yuan, X. Wang, Z. Jin, and R. Kang , "Atomistic mechanisms of chemical mechanical polishing of diamond (1 0 0) in aqueous H2O2/pure H2O: Molecular dynamics simulations using reactive force field (ReaxFF)" , Computational Materials Science , vol .157 , pp. 99-106, 2019.
[52]J. Dana. Honeycutt and Hans C. Andersen, "Molecular dynamics study of melting and freezing of small Lennard-Jones clusters" , The Journal of Physical Chemistry ,1987.
[53]Daniel Faken and Hannes Jónsson, "Systematic analysis of local atomic structure combined with 3D computer graphics" , Computational Materials Science, vol .2, pp. 279-286, 1994.
[54]Alexander Stukowski and Karsten Albe , "Extracting dislocations and non-dislocation crystal defects from atomistic simulation data" , Modelling and Simulation in Materials Science and Engineering , 2010.
[55]Alexander Stukowski, Vasily V Bulatov, and Athanasios Arsenlis, "Extracting dislocations and non-dislocation crystal defects from atomistic simulation data" , Modelling and Simulation in Materials Science and Engineering , 2012.
[56]OVITO User Manual(2023). Dislocation analysis (DXA). Retrieved from https://www.ovito.org/docs/current/reference/pipelines/modifiers/dislocation_analysis.html (Jun.6,2023)
[57]Reza Abbaschian, Lara Abbaschian, and Robert E. Reed-Hill(2008). Physical Metallurgy Principles 4th Edition,USA: cengage learning
[58]D. Hull and D. J. Bacon. Introduction to Dislocations 3rd Edition ,Int. Series on Mat. Science and Technology, Vol. 37 :Pergamon Press
[59]R.E. SmallmanandA.H.W. Ngan ," Chapter 4 - Introduction to Dislocations" , Modern Physical Metallurgy (Eighth Edition), pp. 121-158, 2014.
[60]SuFeng Fan, XiaoCui Li, Rong Fan, and Yang Lu," Compressive elastic behavior of single-crystalline 4H-silicon carbide (SiC) nanopillars" , Science China Technological Sciences, pp. 37-43, 20212.
[61]R. Bennewitz, T. Gyalog, M. Guggisberg, M. Bammerlin, E. Meyer, and H.-J. Güntherodt , " Atomic-scale stick-slip processes on Cu(111)" , Phys. Rev. B ,vol 60 ,1999.
[62]A. Schirmeisen, L. Jansen, and H. Fuchs , "Tip-jump statistics of stick-slip friction" , Phys. Rev. B ,vol .71 ,245403.1-7,2005.