Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

doi:10.1088/1674-1056/20/3/036402

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 36402-036402.doi: 10.1088/1674-1056/20/3/036402

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇下一篇

Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

唐刚, 夏辉, 郝大鹏, 寻之朋, 温荣吉, 陈玉岭

Department of Physics, China University of Mining and Technology, Xuzhou 221116, China

收稿日期:2010-05-14 修回日期:2010-10-10 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010LKWL04), and the Youth Foundation of China University of Mining &

Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

Tang Gang(唐刚)^†,Xia Hui(夏辉)^‡, Hao Da-Peng(郝大鹏),Xun Zhi-Peng(寻之朋), Wen Rong-Ji(温荣吉), and Chen Yu-Ling(陈玉岭)

Department of Physics, China University of Mining and Technology, Xuzhou 221116, China

Received:2010-05-14 Revised:2010-10-10 Online:2011-03-15 Published:2011-03-15
Supported by:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010LKWL04), and the Youth Foundation of China University of Mining & Technology, China (Grant No. 2008A035).

摘要/Abstract

摘要： According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of (1+1)-dimensional growth equation for molecular-beam epitaxy. The growth model includes the linear molecular-beam epitaxy (LMBE) and the nonlinear Lai--Das Sarma--Villain (LDV) equations. The anomalous scaling exponents in both the LMBE and the LDV equations are obtained, respectively. Numerical results are consistent with the corresponding analytical predictions.

Abstract: According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of (1+1)-dimensional growth equation for molecular-beam epitaxy. The growth model includes the linear molecular-beam epitaxy (LMBE) and the nonlinear Lai–Das Sarma–Villain (LDV) equations. The anomalous scaling exponents in both the LMBE and the LDV equations are obtained, respectively. Numerical results are consistent with the corresponding analytical predictions.

Key words: molecular-beam epitaxy, surface growth equation, anomalous scaling behaviour

中图分类号: (Dynamic critical phenomena)

64.60.Ht

05.70.Ln (Nonequilibrium and irreversible thermodynamics)

唐刚, 夏辉, 郝大鹏, 寻之朋, 温荣吉, 陈玉岭. Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation[J]. 中国物理B, 2011, 20(3): 36402-036402.

Tang Gang(唐刚),Xia Hui(夏辉), Hao Da-Peng(郝大鹏),Xun Zhi-Peng(寻之朋), Wen Rong-Ji(温荣吉), and Chen Yu-Ling(陈玉岭) . Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation[J]. Chin. Phys. B, 2011, 20(3): 36402-036402.

参考文献 18

[1]	Barab'asi A L and Stanley H E 1995 wxFractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
[2]	Family F and Vicsek T 1991 wxDynamics of Fractal Surfaces (Singapore: World Scientific)
[3]	Meakin P 1998 wxFractal, Scaling and Growth far from Equilibrium (Cambridge: Cambridge University Press).
[4]	Tang G, Hao D P, Xia H, Han K and Xun Z P 2010 wxChin. Phys. B 19 100508
[5]	Family F and Vicsek T 1985 wxJ. Phys. A 18 L75
[6]	Edwards S F and Wilkinson D R 1982 wxProc. R. Soc. London A 381 17
[7]	Kardar M, Parisi G and Zhang Y C 1986 wxPhys. Rev. Lett.56 889
[8]	Krug J 1994 wxPhys. Rev. Lett.72 2907
[9]	Das Sarma S, Lanczycki C J, Kotlyar R and Ghaisas S V 1996 wxPhys. Rev. E53 359
[10]	L'opez J M, Rodr'higuez M A and Cuerno R 1997 wxPhys. Rev. E56 3993
[11]	L'opez J M 1999 wxPhys. Rev. Lett.83 4594
[12]	Ramasco J, L'opez J M and Rodr'higuez M A 2000 wxPhys. Rev. Lett.84 2199
[13]	L'opez J M, Castro M and Gallego R 2005 wxPhys. Rev. Lett.94 166103
[14]	Pang N N, Li W J, Chang Y C, Tzeng W J and Wang J 2007 wxPhys. Rev. E75 011603
[15]	Xia H, Tang G, Xun Z P and Li Y F 2009 wxPhysica A388 1399
[16]	Lai Z W and Das Sarma S 1991 wxPhys. Rev. Lett.66 2348
[17]	Villain J 1991 wxJ. Phys.I 1 19
[18]	Hentschel H G E and Family F 1991 wxPhys. Rev. Lett.66 1982 endfootnotesize

Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

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