本論文研究藉由動態蒙地卡羅法(Kinetic Monte Carlo)，來模擬金原子在金基板上團簇擴散形成的的形貌。首先利用分子動力學(Molecule Dynamics)及Nudged Elastic band法求出金原子對金基板的能量屏障(energy barrier)，求取金原子與基板間的躍遷頻率以決定其擴散的方向，再利用三維的動態蒙地卡羅法來模擬團簇擴散後表面反應系統的微觀機制和表面形貌，以模擬較符合真實的情形。並且建立不同晶格面的基板來做模擬。
隨著不同溫度和不同團簇大小的條件，模擬所產生的型態做分析比較，最後，觀察團簇聚積及團簇擴散形成的因素及組成機制，以能量統計分析討論不同條件對金原子在金基板上動態行為的影響，並對照文獻數據，了解不同製程參數對薄膜形貌影響的機制，來驗證並修改模擬的模型，以得到更準確的模擬數據。
由本研究所模擬分析的結果，除了可得知基板溫度、團簇尺寸大小和不同的晶格面對表面型態的影響，並進而可作為奈米材料的研發與製造的重要參考依據。發現在低溫至500 K時，半穩態結構的四面型金字塔的型態及金原子擴散的機制。

Kinetic Monte Carlo(KMC) algorithm are used to simulate the evolution of Au cluster on the Au substrate . The morphology of the thin film and detailed diffusion mechanism can be demonstrated in this study. Molecular dynamics simulation (MD) is used to determine the energy barrier(activation energy) of an Au atom adsorbed on the clean surface of the substrate. Then, the thin cluster evolution process, surface reaction and surface diffusion of the Au atoms is modeled by KMC method. The morphologies of the clusters at different temperatures with different number of atoms are also investigated. The simulation results are compared with literature on experimental results to demonstrate the diffusion mechanism, which is difficultly observed in experiments.
A three-dimensional KMC simulation model is used in this study. The results are compared with those from experiments in order to identity the reliability of this KMC model and to modify this model. Nudged Elastic band simulation is used to determine the adsorption energy barrier of an Au atom on a clean Au substrate surface. From the KMC result a surface diffusion of Au migration process is proposed. The effect of the substrate temperature, and the number of atoms duration on the morphology of the Au cluster is obtained. The simulation results show a pyramid structure is built and collapsed from the corner and edge atoms fellow suit and then the atoms of top layers do so as well. Then results indicate that it is possible to to produce nano-gold (metal)-pyramid from Au cluster s by 1, melting clusters in short period and then quenching them, or 2. Depositing Au atoms at lower temperature as well as 500 K with
controlled rate.

致謝 II
中文摘要 III
Abstract IV
目錄 V
表目錄 VIII
圖目錄 VIIIΧ
第 一 章 緒論 11
1-1 前言 11
1-2 研究目的 12
第 二 章 理論方法 18
2-1 分子動力學法 18
2-1.1 分子動力學模擬流程 18
2-1.2 勢能模型 20
2-1.3 尋找反應路徑的模型(Nudged Elastic band) 22
2-2 動態蒙地卡羅法 25
2-2.1 蒙地卡羅法(Monte Carlo) 25
2-2.2 動態蒙地卡羅法(Kinetic Monte Carlo) 29
第 三 章 數值方法 35
3-1 數值統計方法 35
3-1.1 吸附能圖(Cohesive energy) 35
3-1.2 勢能圖(potnetial-energy map) 與平均吸附能(cohesive energy) 36
3-1.3 深寬比(aspect ratio) 37
3-1.4 自由能(free energy) 37
3-2 模擬流程圖 39
3-2.1 分子動力學流程圖 39
3-2.2 Nudged Elastic band流程圖 40
3-2.3 求取原子不同方向擴散率流程圖 41
3-2.4 等溫下KMC流程圖 42
第四章 結果與討論 43
4-1 不同溫度對單一團簇的影響 43
4-1.1物理模型之建構 43
4-1.2不同溫度下擴散的形貌 45
4-1.3 動態行為 47
4-1.4 吸附性質 48
4-2 不同大小的團簇對結構的影響 52
4-2-1 團簇大小對時間和擴散步階數的關係 52
4-2-2不同的初始團簇結構 55
4-2-3自由能統計 57
4-3 不同的基板排列對團簇結構之影響 63
4-3-1 物理模型之建構 63
4-3-2 團簇置於<111>基板排列擴散的形貌 64
第五章 結論 65
5-1 結論 65
5-2 未來展望及建議 67
第六章 參考文獻 68

[1] Kuo Chin-Lung, Paulette Clancy, “MEAN molecular dynamics study of a gold thin film on a silicon substrate,” Surf. Sci. 551(2004) 39–58
[2] N. Schell, T. Jensen, J.H. Petersen, K.P. Andreasen, J. Bøttiger, J. Chevallier, “The nanostructure evolution during and after magnetron deposition of Au films,” Thin Solid Films 441 (2003) 96–103
[3] C. Suryanarayana , C.C. Koch, “ Nanocrystalline materials – Current research and futuredirections, “ Hyper. Inter. 130 (2000) 5
[4] C. Suryanarayana, “Does a disorderedγ-TiAl phase exist in mechanically alloyed Ti-AI powders,” Intermetallics 3 (1995) 153-160
[5] Dong Ni, Panagiotis D. Christofides, “Dynamics and control of thin film surface microstructure in a complex deposition process,” Chem. Eng. Sci., 60 (2005) 1603–1617
[6] T.L. Einstein, “Handbook of Surf. Sci., vol. 1. Elsevier, Amsterdam,” Chapter 11 (1996) 577–650
[7] H.N.G. Wadley, X.Zhou, R.A. Johnson, M. Neurock , “Mechanisms, models and method of vapor deposition ,” Prog. In Mat. Sci. 46 (2001) 329–377
[8] M. Kotrla, “Numerical simulations in the theory of crystal growth,” Comput.
Phys. Commun., 97 (1996) 82–100
[9] B. Adamsa James, Zhiyong Wangb, Youhong Lia, “Modeling Cu thin film
growth,” Thin Solid Films 365 (2000) 201–210
[10] A. Fichthorn Kristen, Matthias Scheffler, “Island Nucleation in Thin-Film Epitaxy: A First-Principles Investigation,” Phys. Rev. Lett., 84 (2000) 5371–5374
[11] A. Fichthorn Kristen, L. Merrick Michael, “Nanostructures at surfaces from substrate-mediated interactions” Phys. Rev. B 68 (2003) 041404,1–4
[12] N. N. Negulyaev, V. S. Stepanyuk, L. Niebergall, W. Hergert,1 H. Fangohr, and P. Bruno, “Self-organization of Ce adatoms on Ag(111): A kinetic Monte Carlo study” Phys. Rev. B 74 (2006) 035421,1–5
[13] Erik Cox, Maozhi Li, Po-Wen Chung, C. Ghosh, T. S. Rahman, C. J. Jenks, J. W. Evans, and P. A. Thiel,” Temperature dependence of island growth shapes during submonolayer deposition of Ag on Ag(111) ”, Phys. Rev. B 71 (2005) 115414.1–9
[14] J Frantz, M Rusanen, K Nordlund and I T Koponen,” Evolution of Cu nanoclusters on Cu(100)”, J. Phys.: Condens. Matter 16 (2004) 2995–3003
[15] Pavel Kocán, Pavel Sobotík, Ivan O t''ádal and Miroslav Kotrla, “Self-organized growth of Ag islands on Si(111)-(7×7)-optimization of an STM experiment by means of KMC simulations,” Surf. Sci., Volumes 566-568, Part 1, 20 September (2004) 216–220
[16] J. M. Pomeroy, J. Jacobsen, C. C. Hill, B. H. Cooper, and J. P. Sethna
“Kinetic Monte Carlo-molecular dynamics investigation of hyperthermal copper deposition on Cu(111),” Phys. Rev. B, 66 (2002) 235412,1–8
[17] C. Ghosh, Da-Jiang Liu, K.J. Schnitzenbaumer, C.J. Jenks, P.A. Thiel, J.W. Evans, “Island formation during Al deposition on 5 fold Al-Cu-Fe
quasicrystalline surfaces Kinetic Monte Carlo simulation of a disordered-
bond-network lattice-gas model,” Surf. Sci. 600 (2006) 2220–2230
[18] G. Le Saux, P. Kru‥ger, B. Domenichini, L. Imhoff , S. Bourgeois, “Dynamics of molybdenum nano structure formation on the TiO2(1 1 0) surface: A kinetic Monte Carlo approach,” Applied Surf. Sci. 252 (2006) 5399–5402
[19] Dong Ni, Panagiotis D. Christofides, “Dynamics and control of thin film surface microstructure in a complex deposition process,” Chem. Eng. Sci. 60 (2005) 1603–1617
[20] G. C. Kallinteris., N. I. Papanicolaou., G. A. Evangelakis, “Tight-binding interatomic potentials based on total-energy calculation: Application to noble metals using molecular-dynamics simulation,” Phys. Rev. B. 55 (1997) 2150
[21] L. W Lynn., H. G Smith., and R. M. Nicklow, “Lattice dynamics of gold” , Phys.Rev.B.8 (1973) 3493.
[22] F. Cleri, and V. Rosato, “Tight-binding potentials for transition metals and alloys” ,Phys. Rev. B 48 (1993) 22–33
[23] E. Spohr,”Ion adsorption on metal surface. The role of water-metal interaction”, J. Mol. Liq. 64 (1995) 91–100
[24] Stefano Piana, Julian D. Gale, ”Understanding the Barriers to Crystal Growth: Dynamical Simulation of the Dissolution and Growth of Urea from Aqueous Solution”, J. Am. Chem. Soc. 127 (2005) 1975–1982
[25] Graeme Henkelman, Hannes Jo′nsson, “Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points” J. Chem. Phys., 113 (2000) 9978–9985
[26] K. P. McKenna, P. V. Sushko and A. L. Shluger ,“Transient atomic configurations of supported gold nanocrystallites at finite temperature”, J. Phys . Chem. C, 111 (2007) 2823–2826
[27] L. Mandreoli, J. Neugebauer,“Adatoms density kinetic Monte Carlo: A
hybrid approach to perform epitaxial growth simulation”, Phys. Rev. B 68,
(2003) 155429,1–9
[28] A. Fichthorn Kristen, W. H. Weinberg, ”Theoretical foundations of dynamical Monte Carlo simulations”, J. Chem. Phys.,95 (1991) 1090–1096
[29] Graeme Henkelman, Hannes Jo′nsson, “Long time scale kinetic
Monte Carlo simulations without lattice approximation and predefined event
table”, J. Chem. Phys.,115 (2001) 9657–9666
[30] I. Abou Hamad, P.A. Rikvold, G. Brown, ”Determination of the basic timescale in kinetic Monte Carlo simulations by comparison with cyclic-voltammetry experiments”, Surf. sci. 572 (2004) L355–L361
[31] J. Goniakowski, C. Mottet, ” Palladium nano-clusters on the MgO(1 0 0) surface：substrate induced characteristics of morphology and atomic structure
”, J. Cryst. Growth, 275 (2005) 29–38
[32] Conyers Herring., “Some theorems on the free energies of crystal surfaces,” Phys. Rev. 82 (1951) 87–93
[33] Dmitrii E. Makarov, Horia Metiu , ” A model for the kinetics of protein folding: Kinetic Monte Carlo simulations and analytical results”, J. Chem. Phys. 116 (2002) 5205–5216
[34] C. Barnes Mark, In-D. Jeon, Doh-Y. Kim, Nong M. Hwang , ” Generation of charged clusters during thermal evaporation of gold”, J. Cryst. Growth 242 (2002) 455–462
[35] R. Henry Claude , ”Morphology of supported nanoparticles”, Progress in Surf. Sci. 80 (2005) 92–116