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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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