薄膜生长的三维元胞自动机模拟及其分形研究
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摘要
薄膜材料的发展对微电子,微机械等高科技领域的发展有着重要影响,而薄膜的原子尺度的生长过程将影响薄膜材料的各种应用性能,因此关于薄膜生长过程的开展了大量从实验到理论的研究工作。随着计算机科学等新型科学技术的发展,计算机模拟可以从原子尺度模拟薄膜形成的动态过程,解释实验观察到各种现象,分析各种实验条件对成膜的影响,为解决在实验中难以完全跟踪原子沉积和薄膜生长物理过程的难题提供了途径,而成为搭建理论与实际应用的桥梁,对寻找合成有特殊性能的薄膜材料的实验技术及手段具有十分重要的指导意义。
元胞自动机方法是根据微观个体的简单局域自组织相互作用机制来描述宏观系统整体复杂行为及其时间演化的“自下而上”的计算机模拟方法。本文针对薄膜生长过程粒子迁移扩散的复杂性,在分析薄膜生长过程及生长模式的基础上,结合蒙特卡诺方法,建立薄膜材料的三维元胞自动机生长模型。该模型通过元胞及其领域状态在按薄膜生长过程特征抽象得到的元胞自动机模型的局域自组织作用规则下的并行演化过程,利用OpenGL技术,在VC7.0环境下编程实现了对薄膜生长过程的直观模拟。
通过对薄膜生长过程的计算机模拟,研究了薄膜生长过程中沉积速率和沉积温度等对薄膜表面形貌的影响以及薄膜生长过程三维分维数随覆盖率的变化情况。研究结果表明:在相同温度下较低的沉积速率范围内,薄膜粗糙度几乎不随沉积速率发生变化;随着沉积速率的逐步升高,薄膜粗糙度将逐渐增大;在相同沉积速率时,薄膜粗糙度随沉积温度的升高达到一个最小值,之后粗糙度又将随温度升高而增加,这说明并非沉积温度越高薄膜粗糙度越低;通过对薄膜生长过程三维分维数的计算,表面三维分形维数能够反映薄膜整体的自相似情况。模拟结果与实际情况相符,说明建立的模型是正确的,可以用于薄膜材料生长过程的模拟研究。
The development of thin film materials has important effects in high-tech field such as microelectronics and MEMS. A considerable number of experimental and theoretical studies are focused on film growth,because many properties of thin film materials depend on the film morphology and microstructure which is influenced by the atom-level growing process. Use of computer simulation, dynamic process of atom-level thin film growth can be obtained, experiment phenomenon can be made clear and influence of experiment condition can be analyzed. It provides a way to find out the whole physical process of particle deposition and thin film growth. Because of these, it builds a bridge between theory and application and has important instructional meaning for finding experiment technology and means for obtaining thin film with special performance.
Cellular automata model is a kind of computational model which can describe macroscopic complex behavior and its“bottom-up”evolution in a system which based on simple microscopic local interaction mechanism and self-organization evolutionary rules of components in the system. This paper aims at the complexity of migration and diffusion of particles. After analyzing the process and mode of thin film growth, a simulation model of thin film growth based on 3D Cellular Automata combine with Monte Carlo was built. The model based on cell and its neighbor and the local self-organization rules of cellular automata abstracted from the characteristic of thin film growth, use of OpenGL technology to achieved intuitive simulation of film growth process in the programming environment VC7.0.
In this paper, through computer simulation of film growth, the effect of the deposition rate and deposition temperature on the surface morphology of film was investigated with the model, and the relationship between 3-D fractal dimension and covering rate was studied too. The relationship between roughness and covering rate for film under different conditions and relationship between 3-D fractal dimension and covering rate are discussed in detail in this dissertation. The results demonstrated that at the same deposition temperature, when the deposition rate is low, the roughness of film does not change with the increasing of deposition rate. However, the roughness of film rises with the increasing the deposition rate further. Especially, if they have the same deposition rate, the roughness of film will reach a minimum value and then increase with the increasing of deposition temperature. Therefore, it can be concluded that the roughness of film does not rise with the increasing of deposition rate. The 3-D fractal dimension calculated can reflect the whole self-similarity of thin film. Result of the Simulation is in line with the real situation and shows that the model built is correct and can be used to simulate the process of thin film growth.
元胞自动机方法是根据微观个体的简单局域自组织相互作用机制来描述宏观系统整体复杂行为及其时间演化的“自下而上”的计算机模拟方法。本文针对薄膜生长过程粒子迁移扩散的复杂性,在分析薄膜生长过程及生长模式的基础上,结合蒙特卡诺方法,建立薄膜材料的三维元胞自动机生长模型。该模型通过元胞及其领域状态在按薄膜生长过程特征抽象得到的元胞自动机模型的局域自组织作用规则下的并行演化过程,利用OpenGL技术,在VC7.0环境下编程实现了对薄膜生长过程的直观模拟。
通过对薄膜生长过程的计算机模拟,研究了薄膜生长过程中沉积速率和沉积温度等对薄膜表面形貌的影响以及薄膜生长过程三维分维数随覆盖率的变化情况。研究结果表明:在相同温度下较低的沉积速率范围内,薄膜粗糙度几乎不随沉积速率发生变化;随着沉积速率的逐步升高,薄膜粗糙度将逐渐增大;在相同沉积速率时,薄膜粗糙度随沉积温度的升高达到一个最小值,之后粗糙度又将随温度升高而增加,这说明并非沉积温度越高薄膜粗糙度越低;通过对薄膜生长过程三维分维数的计算,表面三维分形维数能够反映薄膜整体的自相似情况。模拟结果与实际情况相符,说明建立的模型是正确的,可以用于薄膜材料生长过程的模拟研究。
The development of thin film materials has important effects in high-tech field such as microelectronics and MEMS. A considerable number of experimental and theoretical studies are focused on film growth,because many properties of thin film materials depend on the film morphology and microstructure which is influenced by the atom-level growing process. Use of computer simulation, dynamic process of atom-level thin film growth can be obtained, experiment phenomenon can be made clear and influence of experiment condition can be analyzed. It provides a way to find out the whole physical process of particle deposition and thin film growth. Because of these, it builds a bridge between theory and application and has important instructional meaning for finding experiment technology and means for obtaining thin film with special performance.
Cellular automata model is a kind of computational model which can describe macroscopic complex behavior and its“bottom-up”evolution in a system which based on simple microscopic local interaction mechanism and self-organization evolutionary rules of components in the system. This paper aims at the complexity of migration and diffusion of particles. After analyzing the process and mode of thin film growth, a simulation model of thin film growth based on 3D Cellular Automata combine with Monte Carlo was built. The model based on cell and its neighbor and the local self-organization rules of cellular automata abstracted from the characteristic of thin film growth, use of OpenGL technology to achieved intuitive simulation of film growth process in the programming environment VC7.0.
In this paper, through computer simulation of film growth, the effect of the deposition rate and deposition temperature on the surface morphology of film was investigated with the model, and the relationship between 3-D fractal dimension and covering rate was studied too. The relationship between roughness and covering rate for film under different conditions and relationship between 3-D fractal dimension and covering rate are discussed in detail in this dissertation. The results demonstrated that at the same deposition temperature, when the deposition rate is low, the roughness of film does not change with the increasing of deposition rate. However, the roughness of film rises with the increasing the deposition rate further. Especially, if they have the same deposition rate, the roughness of film will reach a minimum value and then increase with the increasing of deposition temperature. Therefore, it can be concluded that the roughness of film does not rise with the increasing of deposition rate. The 3-D fractal dimension calculated can reflect the whole self-similarity of thin film. Result of the Simulation is in line with the real situation and shows that the model built is correct and can be used to simulate the process of thin film growth.
引文
[1]孙伟,常明,杨保和.分子动力学模拟纳米晶体铜的结构与性能[J].物理学报, 1998, 47(4): 591-597.
[2] Starostenkov M D, Andruhova V, Lomskikh N V, et al. Computer simulation of a thermo-activated process of atomic structure reconstruction in thin films[J]. Comput Mater Sci, 1999(2), 14(1-4):197-202.
[3]刘祖黎,张雪锋,姚凯伦,黄运米.溅射沉积Cu膜生长的Monte Carlo模拟[J].真空科学与技术学报, 2005, 25(2):83-114.
[4] James B, Aams, Wang Z Y, Li Y H. Modeling Cu thin film growth[J]. Thin Solid Films, 2000, (365):201-210.
[5]庄国策,朱晓斌,王炜. Pt/Pt(111)薄膜生长的计算机模拟研究[J].南京大学学报, 2001, 37(4):502-507.
[6] Gilme G H, Huang H, Roland C. Thin film deposition fundamentals and modeling [J]. Comput Mater Sci, 1998, 84(12): 354-380.
[7] Takano, Koguer Y. Molecular dynamics, Monte Carlo and their hybrid methods: applications to thin film growth dynamics[J]. Thin Solid Films, 1998,(334): 209-213.
[8]吴锋民,施建青,吴自勤.高温下金属薄膜生长初期的模拟研究[J].物理学报,2001,50(8):1555-1559.
[9]张庆瑜,马腾才. Au/ Au(100)外延薄膜生长的计算机模拟及其微观机制研究[J].物理学报, 2000, 49(2):297-305.
[10]张庆瑜,马腾才.载能原子沉积Au/ Au(100)外延薄膜生长的计算机模拟[J].物理学报, 2000, 49(6):1124-1131.
[11]王晓平,谢峰,石勤伟.晶格失配对异质外延超薄膜生长中成核特性的影响[J].物理学报, 2004, 53(8): 2699-2704.
[12]顾观菊,叶阳,吴锋民.各向异性基底上超薄膜生长的计算机模拟[J].浙江工业大学学报, 2000, 28(1):31-36.
[13]陆杭军.非均匀基底上薄膜生长的算机模拟[D].浙江师范大学硕士学位论文. 2002.
[14] Frenkel D, Smit B著.汪文川译.分子模拟[M].北京:化学工业出版社,2002.
[15] Foiles S M, Baskes M I, Daw M S. Embeded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys[J]. Phys Rev B, 1986,33(12):7983-7991.
[16]吴静.表面活性剂作用下外延生长初期二维岛的形核核生长机理[D].中科院物理所博士学位论文.2000.
[17]扬宁,陈光华.薄膜生长的理论模型与Monte Carlo模拟[J].物理学报,2000,49(11):2225-2228.
[18] David P. Landau. A Guide to Monte Carlo Simulation in Statistical Physics[M]. Cambridge : Cambridge University Press,2000,1-47.
[19]张雪锋.薄膜三维生长的Kinetic Monte Carlo模拟[D].华中科技大学硕士学位论文.2004.
[20]陆杭军.非均匀基底上薄膜生长的算机模拟[D].浙江师范大学硕士学位论文. 2002.
[21]刘涌,宋晨路等.薄膜生长初期形貌的计算机模拟与改进[J].材料科学与工程, 2002,20(3):393-395.
[22]乌明奇.薄膜生长的计算机模拟研究以及电子发射系统的全局优化设计[D].复旦大学物理电子学硕士学位论文.2003.
[23] Witten T A, Sander L M. Diffusion Limited Aggregation, A Kinetic Critical Phenomenon[J]. Phys Rev Lett., 1981, 47(19), 1400-1403.
[24] Meakin P. Formation of fractal clusters and networks by irreversible diffusion-limitted aggregation[J].Phys Rev Lett, 1983, 51(13), 1119-1122.
[25] Salik J.Monte Carlo study of reversible growth of clusters on a Surface[J].Phys Rev B, 1985, 32(3):1824-1826.
[26] Brusch P, Cagnoni P, Nanmin A. Temperature-dependent Monte Carlo simulation of thin metal film growth and percolation[J]. Phys Rev B, 1997, 55(12):7955-7963.
[27] Voter A F. Classically exact over-layer dynamics: diffusion of rhodium clusters on Rh(100)[J].Phys. Rev, 1986, B34: 6819-6829.
[28] Hamion J C, Soransen M R, Voter A F. Compact surface-cluster diffusion by concerted rotation and translation[J].Phys Rev B, 2000, 61(8):5125-5128.
[29] Mlichely T H, Bott M M. Inversion of Growth Speed Anisotropy in Two Dimensions[J].Phys Rev Lett., 1993,(70), 3943-3946.
[30] Brune H, Roder H, Boragno C, et al. Microscopic view of nucleation on surface[J].Phys Rev, 1994,(73), 1955-1958.
[31] Huang H, Gilmer G H. an Atomistic Simulator for Thin Film Deposition in Three Dimensions[J].Phys, 84(1998), 3636-3649.
[32] Huang H, Gilmer G H. Atomistic Simulation of Texture Competition During thin Film Deposition [J].J Comput Aided Mater Des, 2000,(7):203-215.
[33] Wolfram S. Computation theory of cellular automata[J]. Comm Math Phys, 1984, 96(1): 15-57.
[34] Chopard B,Droz M.祝玉学,赵学龙译.物理系统的元胞自动机模拟[M].北京:清华大学出版社,2003.
[35] Wolfram S. Cellular automata as models of complexity[J]. Nature, 1984, 311: 419-424.
[36]李元香,康丽山,陈毓屏.格子气自动机[M].北京:清华大学出版社;南宁:广西科学技术出版社.1994.
[37] Serguei M. Cellular automata simulation of the phenomenon of multiple crystallization[J]. Comput Mater Sci.,1997,(7):384-388.
[38]李洪,钱昌吉等.薄膜生长的元胞自动机模型[J].计算机仿真, 2004, 21(9):51-53.
[39] Mou W W, Xu X L. Multi-fractal and percolation study on thin film growth with a cell-automata[J].Phys Lett A,2006,(354):492–496.
[40]李强,李殿中等.元胞自动机方法模拟枝晶生长[J].物理学报,2004,53(10):3477-3481.
[41]单博炜,魏雷等.采用元胞自动机法模拟凝固微观组织的研究进展[J].铸造,2006,55(5):439-443.
[42] Davies C H J. Growth of nuclear in a cellular automaton simulation of recrystallization[J]. Scrip Mater, 1997, 36(1): 35-40.
[43] Serguei M. Cellular automata simulation of the phenomenon of multiple crystallization[J]. Comput Mater Sci, 1997,(7):384-388.
[44] Kosturek R, Malarz K. New cellular automaton designed to simulate epitaxial films growth[J]. Phys A, 2005,(345):538-546.
[45]应尚军,魏一鸣,蔡嗣经.元胞自动机及其在经济学中的应用[J].中国管理科学,2000, 8:272-278.
[46]赵星,熊范纶等.虚拟植物生长的双尺度自动机模型[J].计算机学报,2001, 24(6):608-615.
[47] Ermentrout G B. CA approaches to biological modeling[J]. J Theor Biol, 1993, 160: 97-133.
[48]薛郁,董力耘,戴世强.一种改进的一维元胞自动机交通流模型及减速概率的影响[J].物理学报, 2001, 50(3):445-449.
[49]周成虎,孙战利,谢一春.地理元胞自动机研究[M].北京:科学出版社,1999.
[50] Mandelbrot B B. The Fractal Geometry of Nature, Freeman, San Francisco:1983.
[51]曲喜新,过璧君.薄膜物理[M].北京:电子工业出版社,1994.
[52]鄢德平.薄膜生长[M].北京:科学出版社, 2001.
[53] Wolfram S. A New Kind of Science. Champaign, IL: Wolfram Media, Inc, 2002何腊梅.
[54]基于元胞自动机的炼钢生产物流仿真与调度优化方法研究[D].重庆大学博士论文.2006.
[55] Wolfram S. Cellular Automata as Simple Self-Organizing Systems[EB/OL].http://www. stephenwolfram.com/publications/articles/ca/82-cellular/index.html,1982/2008-4-25.
[56]吴自勤,王兵.薄膜生长[M].北京:科学出版社,2001.
[57]扬宁.薄膜生长的理论模型和蒙特卡诺模拟[D].北京工业大学硕士论文.2000.
[58]文家焱,施平安.数据库系统原理与应用[M].北京:冶金工业出版社,2002.
[59] OpenGL体系结构审核委员会著.邓郑祥泽.OpenGL编程指南(第四版)[M].北京:人民邮电出版神,2005.
[60]孙卿.基于OpenGL的卫星运行仿真[D].华中科技大学硕士学位论文.2004.
[61]唐武,徐可为等.微波集成电路(MIC)中Au/NiCr/Ta多层金属膜粗糙化机理的AFM研究[J].真空科学与技术,2006,23(2):140-142.
[62] Qi H J,Cheng C F,Yuan J M. Morphology analysis and growth mechanism of Zirconium dioxide thin films. Acta Optica Sinica,2003,23(8):974~979
[63]吴黎黎.分形生长的图象生成及其处理[D].浙江工业大学硕士学位论文.2003.
[64]杨展如.分形物理[M].上海:上海科技教育出版社,1996.209-233.
[65]褚武扬.材料科学中的分形[M].北京:化学工业出版社,2004.
[66]王恩哥.薄膜生长中的表面动力学(I) [J].物理学进展, 2003,23(1):1-61.
[67] Barvosa-Carter W, Ross R S. Atomic scale structure of InAs(001)-(2 x 4) steady-state surfaces determined by scanning tunneling microscopy and density functional theory [J]. Surf Sci Lett. 2002, 499(1): 129-134.
[68] Chang T C, Hwang I S, Tsong T T. Direct Observation of Reaction- Limited Aggregation on Semiconductor Surfaces[J]. Phys Rev Lett,1999, 83(6): 1191-1194.
[69]周成虎.地理元胞自动机研究[M].北京:科学出版社,1999.
[70] Culik. Discrete Systems[J]. Phys Rev Lett,1985,(55): 657-660.
[71] Hurd L P, Yu S. Computation Theoretic Aspects of Cellular Automata[J]. Phys D, 45:357-378, 1090.
[72]郭坤.絮凝体分形仿真模拟[D].西安建筑科技大学硕士学位论文.2006.
[2] Starostenkov M D, Andruhova V, Lomskikh N V, et al. Computer simulation of a thermo-activated process of atomic structure reconstruction in thin films[J]. Comput Mater Sci, 1999(2), 14(1-4):197-202.
[3]刘祖黎,张雪锋,姚凯伦,黄运米.溅射沉积Cu膜生长的Monte Carlo模拟[J].真空科学与技术学报, 2005, 25(2):83-114.
[4] James B, Aams, Wang Z Y, Li Y H. Modeling Cu thin film growth[J]. Thin Solid Films, 2000, (365):201-210.
[5]庄国策,朱晓斌,王炜. Pt/Pt(111)薄膜生长的计算机模拟研究[J].南京大学学报, 2001, 37(4):502-507.
[6] Gilme G H, Huang H, Roland C. Thin film deposition fundamentals and modeling [J]. Comput Mater Sci, 1998, 84(12): 354-380.
[7] Takano, Koguer Y. Molecular dynamics, Monte Carlo and their hybrid methods: applications to thin film growth dynamics[J]. Thin Solid Films, 1998,(334): 209-213.
[8]吴锋民,施建青,吴自勤.高温下金属薄膜生长初期的模拟研究[J].物理学报,2001,50(8):1555-1559.
[9]张庆瑜,马腾才. Au/ Au(100)外延薄膜生长的计算机模拟及其微观机制研究[J].物理学报, 2000, 49(2):297-305.
[10]张庆瑜,马腾才.载能原子沉积Au/ Au(100)外延薄膜生长的计算机模拟[J].物理学报, 2000, 49(6):1124-1131.
[11]王晓平,谢峰,石勤伟.晶格失配对异质外延超薄膜生长中成核特性的影响[J].物理学报, 2004, 53(8): 2699-2704.
[12]顾观菊,叶阳,吴锋民.各向异性基底上超薄膜生长的计算机模拟[J].浙江工业大学学报, 2000, 28(1):31-36.
[13]陆杭军.非均匀基底上薄膜生长的算机模拟[D].浙江师范大学硕士学位论文. 2002.
[14] Frenkel D, Smit B著.汪文川译.分子模拟[M].北京:化学工业出版社,2002.
[15] Foiles S M, Baskes M I, Daw M S. Embeded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys[J]. Phys Rev B, 1986,33(12):7983-7991.
[16]吴静.表面活性剂作用下外延生长初期二维岛的形核核生长机理[D].中科院物理所博士学位论文.2000.
[17]扬宁,陈光华.薄膜生长的理论模型与Monte Carlo模拟[J].物理学报,2000,49(11):2225-2228.
[18] David P. Landau. A Guide to Monte Carlo Simulation in Statistical Physics[M]. Cambridge : Cambridge University Press,2000,1-47.
[19]张雪锋.薄膜三维生长的Kinetic Monte Carlo模拟[D].华中科技大学硕士学位论文.2004.
[20]陆杭军.非均匀基底上薄膜生长的算机模拟[D].浙江师范大学硕士学位论文. 2002.
[21]刘涌,宋晨路等.薄膜生长初期形貌的计算机模拟与改进[J].材料科学与工程, 2002,20(3):393-395.
[22]乌明奇.薄膜生长的计算机模拟研究以及电子发射系统的全局优化设计[D].复旦大学物理电子学硕士学位论文.2003.
[23] Witten T A, Sander L M. Diffusion Limited Aggregation, A Kinetic Critical Phenomenon[J]. Phys Rev Lett., 1981, 47(19), 1400-1403.
[24] Meakin P. Formation of fractal clusters and networks by irreversible diffusion-limitted aggregation[J].Phys Rev Lett, 1983, 51(13), 1119-1122.
[25] Salik J.Monte Carlo study of reversible growth of clusters on a Surface[J].Phys Rev B, 1985, 32(3):1824-1826.
[26] Brusch P, Cagnoni P, Nanmin A. Temperature-dependent Monte Carlo simulation of thin metal film growth and percolation[J]. Phys Rev B, 1997, 55(12):7955-7963.
[27] Voter A F. Classically exact over-layer dynamics: diffusion of rhodium clusters on Rh(100)[J].Phys. Rev, 1986, B34: 6819-6829.
[28] Hamion J C, Soransen M R, Voter A F. Compact surface-cluster diffusion by concerted rotation and translation[J].Phys Rev B, 2000, 61(8):5125-5128.
[29] Mlichely T H, Bott M M. Inversion of Growth Speed Anisotropy in Two Dimensions[J].Phys Rev Lett., 1993,(70), 3943-3946.
[30] Brune H, Roder H, Boragno C, et al. Microscopic view of nucleation on surface[J].Phys Rev, 1994,(73), 1955-1958.
[31] Huang H, Gilmer G H. an Atomistic Simulator for Thin Film Deposition in Three Dimensions[J].Phys, 84(1998), 3636-3649.
[32] Huang H, Gilmer G H. Atomistic Simulation of Texture Competition During thin Film Deposition [J].J Comput Aided Mater Des, 2000,(7):203-215.
[33] Wolfram S. Computation theory of cellular automata[J]. Comm Math Phys, 1984, 96(1): 15-57.
[34] Chopard B,Droz M.祝玉学,赵学龙译.物理系统的元胞自动机模拟[M].北京:清华大学出版社,2003.
[35] Wolfram S. Cellular automata as models of complexity[J]. Nature, 1984, 311: 419-424.
[36]李元香,康丽山,陈毓屏.格子气自动机[M].北京:清华大学出版社;南宁:广西科学技术出版社.1994.
[37] Serguei M. Cellular automata simulation of the phenomenon of multiple crystallization[J]. Comput Mater Sci.,1997,(7):384-388.
[38]李洪,钱昌吉等.薄膜生长的元胞自动机模型[J].计算机仿真, 2004, 21(9):51-53.
[39] Mou W W, Xu X L. Multi-fractal and percolation study on thin film growth with a cell-automata[J].Phys Lett A,2006,(354):492–496.
[40]李强,李殿中等.元胞自动机方法模拟枝晶生长[J].物理学报,2004,53(10):3477-3481.
[41]单博炜,魏雷等.采用元胞自动机法模拟凝固微观组织的研究进展[J].铸造,2006,55(5):439-443.
[42] Davies C H J. Growth of nuclear in a cellular automaton simulation of recrystallization[J]. Scrip Mater, 1997, 36(1): 35-40.
[43] Serguei M. Cellular automata simulation of the phenomenon of multiple crystallization[J]. Comput Mater Sci, 1997,(7):384-388.
[44] Kosturek R, Malarz K. New cellular automaton designed to simulate epitaxial films growth[J]. Phys A, 2005,(345):538-546.
[45]应尚军,魏一鸣,蔡嗣经.元胞自动机及其在经济学中的应用[J].中国管理科学,2000, 8:272-278.
[46]赵星,熊范纶等.虚拟植物生长的双尺度自动机模型[J].计算机学报,2001, 24(6):608-615.
[47] Ermentrout G B. CA approaches to biological modeling[J]. J Theor Biol, 1993, 160: 97-133.
[48]薛郁,董力耘,戴世强.一种改进的一维元胞自动机交通流模型及减速概率的影响[J].物理学报, 2001, 50(3):445-449.
[49]周成虎,孙战利,谢一春.地理元胞自动机研究[M].北京:科学出版社,1999.
[50] Mandelbrot B B. The Fractal Geometry of Nature, Freeman, San Francisco:1983.
[51]曲喜新,过璧君.薄膜物理[M].北京:电子工业出版社,1994.
[52]鄢德平.薄膜生长[M].北京:科学出版社, 2001.
[53] Wolfram S. A New Kind of Science. Champaign, IL: Wolfram Media, Inc, 2002何腊梅.
[54]基于元胞自动机的炼钢生产物流仿真与调度优化方法研究[D].重庆大学博士论文.2006.
[55] Wolfram S. Cellular Automata as Simple Self-Organizing Systems[EB/OL].http://www. stephenwolfram.com/publications/articles/ca/82-cellular/index.html,1982/2008-4-25.
[56]吴自勤,王兵.薄膜生长[M].北京:科学出版社,2001.
[57]扬宁.薄膜生长的理论模型和蒙特卡诺模拟[D].北京工业大学硕士论文.2000.
[58]文家焱,施平安.数据库系统原理与应用[M].北京:冶金工业出版社,2002.
[59] OpenGL体系结构审核委员会著.邓郑祥泽.OpenGL编程指南(第四版)[M].北京:人民邮电出版神,2005.
[60]孙卿.基于OpenGL的卫星运行仿真[D].华中科技大学硕士学位论文.2004.
[61]唐武,徐可为等.微波集成电路(MIC)中Au/NiCr/Ta多层金属膜粗糙化机理的AFM研究[J].真空科学与技术,2006,23(2):140-142.
[62] Qi H J,Cheng C F,Yuan J M. Morphology analysis and growth mechanism of Zirconium dioxide thin films. Acta Optica Sinica,2003,23(8):974~979
[63]吴黎黎.分形生长的图象生成及其处理[D].浙江工业大学硕士学位论文.2003.
[64]杨展如.分形物理[M].上海:上海科技教育出版社,1996.209-233.
[65]褚武扬.材料科学中的分形[M].北京:化学工业出版社,2004.
[66]王恩哥.薄膜生长中的表面动力学(I) [J].物理学进展, 2003,23(1):1-61.
[67] Barvosa-Carter W, Ross R S. Atomic scale structure of InAs(001)-(2 x 4) steady-state surfaces determined by scanning tunneling microscopy and density functional theory [J]. Surf Sci Lett. 2002, 499(1): 129-134.
[68] Chang T C, Hwang I S, Tsong T T. Direct Observation of Reaction- Limited Aggregation on Semiconductor Surfaces[J]. Phys Rev Lett,1999, 83(6): 1191-1194.
[69]周成虎.地理元胞自动机研究[M].北京:科学出版社,1999.
[70] Culik. Discrete Systems[J]. Phys Rev Lett,1985,(55): 657-660.
[71] Hurd L P, Yu S. Computation Theoretic Aspects of Cellular Automata[J]. Phys D, 45:357-378, 1090.
[72]郭坤.絮凝体分形仿真模拟[D].西安建筑科技大学硕士学位论文.2006.
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