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本文利用BCF模型研究了应变对圆形岛形貌稳定性的影响. 通过Gibbs-Thomson关系将应变引入该模型中，讨论了在失配应变、外场应变以及沉积流量、线张力和远场流量等因素共同作用下圆形岛的稳定性，并得到了相应的扰动增长率以及临界沉积流量. 研究结果表明：较大的失配应变和远场流量都能促进岛在生长过程中失稳，而线张力可以抑制岛的失稳. 随着岛的生长，岛的半径越大越趋于稳定，当岛生长到临界半径后，临界沉积流量随着失配应变的增大而增大. 在外场应变存在的情况下，外场负应变对岛的生长起稳定作用并使临界沉积流量减小；相反，正应变促进岛的失稳，且使临界流量增大. 这些结论对在薄膜生长过程中控制原子岛的形貌及其稳定性提供了重要的理论依据.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 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 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 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 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 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 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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