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In this paper, the strain effect on the morphological instability of the circular island is studied in terms of the BCF (Burton, Cabera, Frank) model. We introduce strains into the BCF model under the Gibbs-Thomson condition and investigate the instability of the island due to the combined effect of the misfit strain, applied strain, deposition flux, line tension, and the far-field flux. Thus, we obtain the perturbation growth rate and the critical deposition flux. Results indicate that the misfit strain and the far-field flux tend to destabilize the growth of the island, and the line tension has a stabilizing effect. In addition, the larger island is more stable during the growth of the island. Up to the critical radius, as the misfit strain increases, the critical flux increases. When taking into account the applied strain, the negatively applied strain stabilizes the growth of the island and decreases the critical flux. These results are almost opposite to the case of the positive strain. This could potentially provide on important theoretical basis for controlling the growth and stability of the films.
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Keywords:
- morphological instability /
- misfit strain /
- applied strain /
- circular island
[1] Capper P, Mauk M 2007 Liquid Phase Epitaxy of Electronic Optical and Optoelectronic Materials (West Sussex: Wiley) p16
[2] 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]
[3] Brune H, Bromann K, Röder H, Kern K 1995 Phys. Rev. B 52 R14380
[4] Song Y X, Yu Z Y, Liu Y M 2008 Acta Phys. Sin. 57 2399 (in Chinese) [宋禹忻, 俞重远, 刘玉敏 2008 物理学报 57 2399]
[5] Ling P, Kok-Keong L, Joan M R, Elizabeth C D 2005 Nano. Lett. 5 1081
[6] Maggie X, Michael C, Judy L H 2007 Semicond. Sci. Technol 22 55
[7] Zhang B C, Zhou Xun, Luo Z J, Guo X, Ding Z 2012 Chin. Phys. B 21 048101
[8] Liu Z L, Zhang X F, Yao K L, Wei H L, Huang Y M 2004 Chin. Phys. Soc. 13 2115
[9] Wu F M, Lu H J, Wu Z Q 2006 Chin. Phys. Soc. 15 0807
[10] Qiu J H, Ding J N, Yuan N Y, Wang X Q 2012 Chin. Phys. B 21 097701
[11] Jou H J, Leo P H, Lowengrub J S 1997 J. Comput. Phys. 131 109
[12] 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]
[13] Mullins W, Sekerka R F 1963 J. Appl. Phys. 34 323
[14] Bales G S, Zangwill A 1997 Phys. Rev. B 55 R1973
[15] Bales G S, Chrzan D C 1994 Phys. Rev. B 50 6057
[16] Shao Q Y, Fang R C, Zhu K G, Liao Y, Xue Z Q 2001 Chin. Phys. Lett. 18 1135
[17] Shao Q Y, Zhang J 2011 Chin. Phys. B 20 086803
[18] Colin J 2004 Acta Mater. 52 4985
[19] Colin J 2005 Phys. Rev. B 71 165403
[20] Colin J 2007 Int. J. Solids Struct. 44 3218
[21] Burton W, Cabrera N, Frank F 1951 Philos. Trans. R. Soc. Lond. Ser. A 243 299
[22] Bales G S, Zangwill A 1990 Phys. Rev. B 41 5500
[23] Caflisch R E, Li B 2003 Multiscale Model. Simul. 1 150
[24] Li B, Rätz A, Voigt A 2004 Phys. D 198 231
[25] Hu Z Z, Li S W, Lowengrub J S 2007 Phys. D 233 151
[26] Xu Z L, Wu Y Z 1964 Theory of elasticity (Beijing: Higher Education Press) p122 (in Chinese) [徐芝纶, 吴永祯 1964 弹性理论 (北京: 高等教育出版社) 第122页]
[27] Leo P H, Sekerka R H 1989 Acta Metall 37 3119
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[1] Capper P, Mauk M 2007 Liquid Phase Epitaxy of Electronic Optical and Optoelectronic Materials (West Sussex: Wiley) p16
[2] 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]
[3] Brune H, Bromann K, Röder H, Kern K 1995 Phys. Rev. B 52 R14380
[4] Song Y X, Yu Z Y, Liu Y M 2008 Acta Phys. Sin. 57 2399 (in Chinese) [宋禹忻, 俞重远, 刘玉敏 2008 物理学报 57 2399]
[5] Ling P, Kok-Keong L, Joan M R, Elizabeth C D 2005 Nano. Lett. 5 1081
[6] Maggie X, Michael C, Judy L H 2007 Semicond. Sci. Technol 22 55
[7] Zhang B C, Zhou Xun, Luo Z J, Guo X, Ding Z 2012 Chin. Phys. B 21 048101
[8] Liu Z L, Zhang X F, Yao K L, Wei H L, Huang Y M 2004 Chin. Phys. Soc. 13 2115
[9] Wu F M, Lu H J, Wu Z Q 2006 Chin. Phys. Soc. 15 0807
[10] Qiu J H, Ding J N, Yuan N Y, Wang X Q 2012 Chin. Phys. B 21 097701
[11] Jou H J, Leo P H, Lowengrub J S 1997 J. Comput. Phys. 131 109
[12] 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]
[13] Mullins W, Sekerka R F 1963 J. Appl. Phys. 34 323
[14] Bales G S, Zangwill A 1997 Phys. Rev. B 55 R1973
[15] Bales G S, Chrzan D C 1994 Phys. Rev. B 50 6057
[16] Shao Q Y, Fang R C, Zhu K G, Liao Y, Xue Z Q 2001 Chin. Phys. Lett. 18 1135
[17] Shao Q Y, Zhang J 2011 Chin. Phys. B 20 086803
[18] Colin J 2004 Acta Mater. 52 4985
[19] Colin J 2005 Phys. Rev. B 71 165403
[20] Colin J 2007 Int. J. Solids Struct. 44 3218
[21] Burton W, Cabrera N, Frank F 1951 Philos. Trans. R. Soc. Lond. Ser. A 243 299
[22] Bales G S, Zangwill A 1990 Phys. Rev. B 41 5500
[23] Caflisch R E, Li B 2003 Multiscale Model. Simul. 1 150
[24] Li B, Rätz A, Voigt A 2004 Phys. D 198 231
[25] Hu Z Z, Li S W, Lowengrub J S 2007 Phys. D 233 151
[26] Xu Z L, Wu Y Z 1964 Theory of elasticity (Beijing: Higher Education Press) p122 (in Chinese) [徐芝纶, 吴永祯 1964 弹性理论 (北京: 高等教育出版社) 第122页]
[27] Leo P H, Sekerka R H 1989 Acta Metall 37 3119
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