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本文提出了一个新的基于扩散界面的相场模型来描述外延生长中岛的形核、生长及熟化过程. 该模型同时考虑了弹性场、表面能、沉积、扩散、解吸和能量势垒等热力学及动力学过程对表面纳米形貌的影响. 采用经典的BCF模型来描述生长中的扩散形核过程, 而采用一个新的包含弹性应变能的自由能函数, 通过变分得到一个描述多层岛生长的相场方程, 该方法可以有效地描述外延生长中复杂的外延形貌. 采用有限差分格式对非线性耦合方程组进行求解. 数值结果显示, 该模型可以真实地再现外延生长中多层岛结构(即山丘状形貌)的演化过程, 模拟结果与已有实验结果一致. 同时模拟了生长过程中随外延形貌演化而形成的复杂生长应力, 研究表明, 在生长过程中, 岛中存在着复杂的应力分布, 且在岛边界处应力达到局部最大, 这与实验结果定性一致. 此外, 本文的重要发现是, 外延生长中的应力演化明显地影响原子的扩散过程, 当应力存在时, 外延结构变化较无弹性场时变快. 该项研究对理解外延生长中各物理机理的协同作用有重要的指导意义.In this paper, a new phase-field model based on diffusion interface is put forward to describe the epitaxial growth including island nucleation, growth, and ripening. Thermodynamics and kinetics play an important role in epitaxial morphology evolution. This model includes combined effects of the following processes, such as elastic field, surface energy, deposition, diffusion, desorption, and energy barrier etc. We use the classical BCF model to describe the atomic diffusion and nucleation processes, and use a new free energy function, including elastic strain energy, to obtain a phase-field equation that can describe the growth of dynamic multi-island by variation method. This model can effectively simulates the complex morphology in epitaxial growth. The nonlinear coupled equations can be solved by finite difference scheme. Numerical result shows that this model can reproduce the real multilayer epitaxial growth structure, and the simulation results are consistent with the experimental results. At the same time we also simulate the complex growth stress with morphology evolution. Results show that, accompanied with the epitaxial growth, a complex stress distribution is produced, and the stress reaches a local maximum on the boundaries of the island, which is consistent with the experimental results. Most importantly, the stress significantly affects the atomic diffusion process. While the stress exists, the epitaxial structure will change faster. These results can make a significance effect on the research of physical mechanism in epitaxial growth.
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Keywords:
- phase-field model /
- epitaxial growth /
- island /
- stress
[1] Capper P, Mauk M 2007 Liquid Phase Epitaxy of Electronic Optical and Optoelectronic Materials(West Sussex:Wiley) p16
[2] Peng J, Xu Z M, Wu X F, Sun T Y 2013 Acta Phys. Sin. 62 036104 (in Chinese) [彭静, 徐智谋, 吴小峰, 孙堂友 2013 物理学报 62 036104]
[3] Wang E G 2003 Progress in Physics 23 1( in Chinese) [王恩哥 2003 物理学进展 23 1]
[4] Maggic X, Michael C, Judy L H 2007 Semicond. Sci. Technol. 22 55
[5] Zhang B C, Zhou X, Luo Z J, Ding Z 2012 Chin. Phys. B 21 048101
[6] Hohenberg P, Kohn W 1964 Phys. Rev. B 136 864
[7] Silvio P, Enrico B, Giorgia B, Michal V, Marcel M, Stefano C 2012 Theor. Chem. Acc. 131 1274
[8] Andrea C L, Miroslav K 1997 J. Phys. Condens. Matter 9 299
[9] Wang X P, Xie F, Shi Q W, Zhao T X 2004 Acta Phys. Sin. 53 2699 (in Chinese) [王晓平, 谢峰, 石勤伟, 赵特秀 2004 物理学报 53 2699]
[10] Chen C, Chen Z, Zhang J, Yang T 2012 Acta Phys. Sin. 61 108103 (in Chinese) [陈成, 陈铮, 张静, 杨涛 2012 物理学报 61 108103]
[11] Yu Y M, Liu B G 2004 Phys. Rev. E 69 021601
[12] Fan M, Andrew Z 2010 Phys. Rev. B 81 235431
[13] Burton W, Cabrera N, Frank F 1951 Philos. Trans. R. Soc. Lond. Ser. A 243 299
[14] A Rötz, A Voigt 2004 App. Anal. 83 1015
[15] Hu Z Z, Li S W, Lowengrub J S 2007 Phys. D 233 151
[16] Adam Li, Feng Liu, Lagally M G 2000 Phy. Rev. Lett. 85 091922
[17] Shchukin V A, Bimbery D 2003 Phy. Rev. Lett. 90 076102
[18] Ni Y, He L H, Song J 2004 Surface Science 553 189
[19] Grridhar N, Jacques G A 2006 Phy. Rev. B 73 045409
[20] Li M Z, Yao Y G, Wu B, Zhang Z Y, Wang E G 2009 Euro Physics Letters 86 16001
[21] Xu Y C, Liu B G 2009 Phys. B 404 4303
[22] Uehara T, Fukuib M, Ohno N 2008 Journal of Crystal Growth 310 1331
[23] Evans J W, Thiel P A, Bartelt M C 2006 Surface Science Reports 61 1-128
[24] Kim S H, Kim J Y, Yu J, Lee T Y 2004 Journal of Electronic Materials 33 948
[25] Ioannou-Sougleridis V, Constantoudisa V, Alexeb M, Scholz R, Vellianitisc G, Dimoulas A 2004 Thin Solid Films 468 303
[26] Dai J L 2009 Electronic Components and Materials 28(7) 0033 (in Chinese) [戴结林 2009 电子元件与材料 28(7) 0033]
[27] Davood R, Ahmad K, Hamid R F, Amir S H R 2007 Appl. Surf. Sci. 253 9085
[28] Ernst H J, Fabre F, Folkerts R 1994 Phys. Rev. Lett. 72 112
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[1] Capper P, Mauk M 2007 Liquid Phase Epitaxy of Electronic Optical and Optoelectronic Materials(West Sussex:Wiley) p16
[2] Peng J, Xu Z M, Wu X F, Sun T Y 2013 Acta Phys. Sin. 62 036104 (in Chinese) [彭静, 徐智谋, 吴小峰, 孙堂友 2013 物理学报 62 036104]
[3] Wang E G 2003 Progress in Physics 23 1( in Chinese) [王恩哥 2003 物理学进展 23 1]
[4] Maggic X, Michael C, Judy L H 2007 Semicond. Sci. Technol. 22 55
[5] Zhang B C, Zhou X, Luo Z J, Ding Z 2012 Chin. Phys. B 21 048101
[6] Hohenberg P, Kohn W 1964 Phys. Rev. B 136 864
[7] Silvio P, Enrico B, Giorgia B, Michal V, Marcel M, Stefano C 2012 Theor. Chem. Acc. 131 1274
[8] Andrea C L, Miroslav K 1997 J. Phys. Condens. Matter 9 299
[9] Wang X P, Xie F, Shi Q W, Zhao T X 2004 Acta Phys. Sin. 53 2699 (in Chinese) [王晓平, 谢峰, 石勤伟, 赵特秀 2004 物理学报 53 2699]
[10] Chen C, Chen Z, Zhang J, Yang T 2012 Acta Phys. Sin. 61 108103 (in Chinese) [陈成, 陈铮, 张静, 杨涛 2012 物理学报 61 108103]
[11] Yu Y M, Liu B G 2004 Phys. Rev. E 69 021601
[12] Fan M, Andrew Z 2010 Phys. Rev. B 81 235431
[13] Burton W, Cabrera N, Frank F 1951 Philos. Trans. R. Soc. Lond. Ser. A 243 299
[14] A Rötz, A Voigt 2004 App. Anal. 83 1015
[15] Hu Z Z, Li S W, Lowengrub J S 2007 Phys. D 233 151
[16] Adam Li, Feng Liu, Lagally M G 2000 Phy. Rev. Lett. 85 091922
[17] Shchukin V A, Bimbery D 2003 Phy. Rev. Lett. 90 076102
[18] Ni Y, He L H, Song J 2004 Surface Science 553 189
[19] Grridhar N, Jacques G A 2006 Phy. Rev. B 73 045409
[20] Li M Z, Yao Y G, Wu B, Zhang Z Y, Wang E G 2009 Euro Physics Letters 86 16001
[21] Xu Y C, Liu B G 2009 Phys. B 404 4303
[22] Uehara T, Fukuib M, Ohno N 2008 Journal of Crystal Growth 310 1331
[23] Evans J W, Thiel P A, Bartelt M C 2006 Surface Science Reports 61 1-128
[24] Kim S H, Kim J Y, Yu J, Lee T Y 2004 Journal of Electronic Materials 33 948
[25] Ioannou-Sougleridis V, Constantoudisa V, Alexeb M, Scholz R, Vellianitisc G, Dimoulas A 2004 Thin Solid Films 468 303
[26] Dai J L 2009 Electronic Components and Materials 28(7) 0033 (in Chinese) [戴结林 2009 电子元件与材料 28(7) 0033]
[27] Davood R, Ahmad K, Hamid R F, Amir S H R 2007 Appl. Surf. Sci. 253 9085
[28] Ernst H J, Fabre F, Folkerts R 1994 Phys. Rev. Lett. 72 112
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