Cu台阶面多层弛豫的第一性原理研究

舒瑜; 张建民; 王国红; 徐可为

doi:10.7498/aps.59.4911

摘要

采用基于密度泛函理论的第一性原理赝势平面波方法对Cu(311),(511),(331)和(221)四个高指数台阶表面的弛豫结构和弛豫后表面各层的电子特性进行了系统研究.发现四个台阶面的层间弛豫规律依次为-+-…,--+-…,--+-…和---+-…,与其平台-阶梯n(hkl)×(uvw)的表示法2(100)×(111),3(100)×(111),3(111)×(111)和4(111)×(111)中的原子排数n相关,即

关键词:

Abstract

Using the pseudopotential plane wave (PPPW) method, we performed first principles calculation for the multilayer relaxations and the electron properties of the high-Miller-index stepped Cu(311), (511), (331) and (221) surfaces, which are expressed by 2(100)×(111), 3(100)×(111), 3(111)×(111) and 4(111)×(111), respectively, in the terrace-step notation, i.e. n(hkl)×(uvw). The interlayer relaxations of them are -+-…, --+-…, --+-… and ---+-…, respectively, which follow the atom-row trend: for stepped Cu surface which has n atom rows in the (100) or (111) terrace, the outermost n－1 interlayer spaces contract, then the n interlayer space expands, and the following n+1 interlayer space contracts again. For the stepped surfaces with the same (hkl)×(uvw), the larger the number of atom rows n in the terrace, the greater the contraction magnitude for Δd1,n. We did not find any indication of anomalous relaxation behavior for Cu(511) and (331) as mentioned in some references. Below Fermi energy level, the density of states of the first layer atom at stepped edge has the largest peak value in higher energy regions and has no peak in lower energy regions, so the first layer atom is most unstable and can be dislodged and peeled off more easily than other surface atoms. For the stepped surfaces with the same (hkl)×(uvw), the curves of the density of states have similar shapes for the atoms at the step edge, at the corner, at the terrace and near the corner, and the atoms under the step edge and near the corner.

Keywords:

作者及机构信息

(1)空军工程大学理学院,西安 710051; (2)陕西师范大学物理学与信息技术学院,西安 710062; (3)西安交通大学金属材料强度国家重点实验室,西安 710049

基金项目: 国家重点基础研究发展计划(批准号:2004CB619302)资助的课题.

Authors and contacts

(1)College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China; (2)State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China; (3)The Science Institute, Air Force Engineering University, Xi'an 710051, China

参考文献

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[2]	Zangwill A 1988 Physics at Surfaces (Cambridge: Cambridge University Press) p1
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[4]	Cai J Q, Tao X M, Chen W B, Zhao X X, Tan M Q 2005 Acta Phys. Sin. 54 5350 (in Chinese) [蔡建秋、陶向明、陈文斌、赵新新、谭明秋 2005 54 5350]
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[6]	Zhao W, Wang J D, Liu F B, Chen D R 2009 Acta Phys. Sin. 58 3352 (in Chinese) [赵巍、汪家道、陈峰斌、陈大荣 2009 58 3352]
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[9]	Sinnott S B, Stave M S, Raeker T J, DePristo A E 1991 Phys. Rev. B 44 8927
[10]	Silva D J L F, Schroeder K, Blügel S 2005 Phys. Rev. B 72 33405
[11]	Spiak D 2001 Surf. Sci. 489 151
[12]	Watson P R, Mitchell K A R 1988 Surf. Sci. 203 323
[13]	Parkin S R, Watson P R, McFarlane R A, Mitchell K A R 1991 Solid State Commun. 78 841
[14]	Yamaguchi M, Kaburaki H, Freeman A J 2004 Phys. Rev. B 69 45408
[15]	Heid R, Bohnen K P, Kara A, Rahman T S 2002 Phys. Rev. B 65 115405
[16]	Walko D A, Robinson I K 2001 Phys.Rev. B 64 045412
[17]	Walko D A, Robinson I K 1999 Phys. Rev. B 59 15446
[18]	Geng W T, Freeman A J 2001 Phys. Rev. B 64 115401
[19]	Durukanoglu S, Kara A, Rahman T S 1997 Phys. Rev. B 55 13894
[20]	Sklyadneva I Y, Rusina G G, Chulkov E V 1998 Surf. Sci. 416 17
[21]	Loisel B, Gorse D, Pontikis V, Lapujoulade J 1989 Surf. Sci. 221 365
[22]	Tian Y, Lin K W, Jona F 2000 Phys. Rev. B 62 12844
[23]	Silva D J L F, Schroeder K, Blügel S 2004 Phys. Rev. B 70 245432
[24]	Jona F 1999 Surf. Sci. Lett. 6 621
[25]	Vanderbilt D 1990 Phys. Rev. B 41 7892
[26]	Kresse G, Hafner J 1993 Phys. Rev. B 47 558
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[30]	Finnis M W, Heine V 1974 J. Phys. F: Met. Phys. 4 L37
[31]	Smoluchowski R 1941 Phys. Rev. 60 661

施引文献

[1]	Desjonquères M C, Spanjaard D 1995 Concepts in Surface Science (New York: Springer Press) p1
[2]	Zangwill A 1988 Physics at Surfaces (Cambridge: Cambridge University Press) p1
[3]	Widdra W, Trischberger P, Frieβ W, Menzel D, Payne S H, Kreuzer H J 1998 Phys. Rev. B 57 4111
[4]	Cai J Q, Tao X M, Chen W B, Zhao X X, Tan M Q 2005 Acta Phys. Sin. 54 5350 (in Chinese) [蔡建秋、陶向明、陈文斌、赵新新、谭明秋 2005 54 5350]
[5]	Zhao X X, Tao X M, Chen W B, Chen X, Shang X F, Tan M Q 2006 Acta Phys. Sin. 55 6001 (in Chinese) [赵新新、陶向明、陈文斌、陈鑫、尚学府、谭明秋 2006 55 6001]
[6]	Zhao W, Wang J D, Liu F B, Chen D R 2009 Acta Phys. Sin. 58 3352 (in Chinese) [赵巍、汪家道、陈峰斌、陈大荣 2009 58 3352]
[7]	Zhao X X, Tao X M, Chen W B, Chen X, Shang X F, Tan M Q 2006 Acta Phys. Sin. 55 3629 (in Chinese) [赵新新、陶向明、陈文斌、陈鑫、尚学府、谭明秋 2006 55 3629]
[8]	Silva D J L F, Schroeder K, Blügel S 2004 Phys. Rev. B 69 245411
[9]	Sinnott S B, Stave M S, Raeker T J, DePristo A E 1991 Phys. Rev. B 44 8927
[10]	Silva D J L F, Schroeder K, Blügel S 2005 Phys. Rev. B 72 33405
[11]	Spiak D 2001 Surf. Sci. 489 151
[12]	Watson P R, Mitchell K A R 1988 Surf. Sci. 203 323
[13]	Parkin S R, Watson P R, McFarlane R A, Mitchell K A R 1991 Solid State Commun. 78 841
[14]	Yamaguchi M, Kaburaki H, Freeman A J 2004 Phys. Rev. B 69 45408
[15]	Heid R, Bohnen K P, Kara A, Rahman T S 2002 Phys. Rev. B 65 115405
[16]	Walko D A, Robinson I K 2001 Phys.Rev. B 64 045412
[17]	Walko D A, Robinson I K 1999 Phys. Rev. B 59 15446
[18]	Geng W T, Freeman A J 2001 Phys. Rev. B 64 115401
[19]	Durukanoglu S, Kara A, Rahman T S 1997 Phys. Rev. B 55 13894
[20]	Sklyadneva I Y, Rusina G G, Chulkov E V 1998 Surf. Sci. 416 17
[21]	Loisel B, Gorse D, Pontikis V, Lapujoulade J 1989 Surf. Sci. 221 365
[22]	Tian Y, Lin K W, Jona F 2000 Phys. Rev. B 62 12844
[23]	Silva D J L F, Schroeder K, Blügel S 2004 Phys. Rev. B 70 245432
[24]	Jona F 1999 Surf. Sci. Lett. 6 621
[25]	Vanderbilt D 1990 Phys. Rev. B 41 7892
[26]	Kresse G, Hafner J 1993 Phys. Rev. B 47 558
[27]	Kresse G, Hafner J 1994 Phys. Rev. B 49 14251
[28]	Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 6 15
[29]	Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 54 11169
[30]	Finnis M W, Heine V 1974 J. Phys. F: Met. Phys. 4 L37
[31]	Smoluchowski R 1941 Phys. Rev. 60 661

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