考虑界面散射的金属纳米线热导率修正

李静; 冯妍卉; 张欣欣; 黄丛亮; 杨穆

doi:10.7498/aps.62.186501

摘要

理论分析了声子和电子输运对Cu, Ag金属纳米线热导率的贡献. 采用镶嵌原子作用势模型描述纳米尺寸下金属原子间的相互作用, 应用平衡分子动力学方法和Green-Kubo函数模拟了金属纳米线的声子热导率; 采用玻尔兹曼输运理论和Wiedemann-Franz定律计算电子热导率; 并通过散射失配模型和Mayadas-Shatzkes模型引入晶界散射的影响. 在此基础上, 考察分析了纳米线尺度和温度的影响. 研究结果表明: Cu, Ag纳米线热导率的变化规律相似; 电子输运对金属纳米线的导热占主导地位, 而声子热导率的贡献也不容忽视; 晶界散射导致热导率减小, 尤其对电子热导率作用显著; 纳米线总热导率随着温度的升高而降低; 随着截面尺寸减小而减小, 但声子热导率所占份额有所增加.

关键词:

Abstract

The contributions of phonon and electron transport to the thermal conductivities of Cu and Ag nanowires are studied theoretically. The effects of surface and grain boundary scatterings are involved. The embeded atom method is employed to express the interatomic potential of nanowires. While the molecular dynamic simulation and Green-Kubo formulation are used to obtain the lattice thermal conductivity, a model derived from Boltzmann transport equation and the Wiedemann-Franz relation are used to calculate electronic thermal conductivity. In addition, diffuse mismatch model is used to calculate thermal resistance of grain boundary to modify the lattice thermal conductivity, meanwhile, Mayadas-Shatzkes model is used to consider the influence of grain boundary scattering on the electronic thermal conductivity. By coupling the lattice and electronic thermal conductivity, the effective thermal conductivity of nanowire is obtained. On this base, the influences of size and temperature are analyzed. It turns out that Cu and Ag nanowires have a similar tendency in the thermal conductivity. The contribution of electron transport to the thermal conductivity of nanowire is dominated, but the contribution of phonon transport cannot be ignored on the nanoscale. The thermal conductivity of nanowire decreases due to the grain boundary scattering. And it decreases with temperature increasing or size decreasing. The contribution of phonon transport becomes more important in the case of smaller size.

Keywords:

作者及机构信息

1.
北京科技大学机械工程学院, 北京 100083;

2.
北京科技大学材料科学与工程学院, 北京 100083

基金项目: 国家重点基础研究发展计划(批准号:2012CB720404);国家自然科学基金重点项目(批准号:50836001)和中央高校基本科研业务费专项资金(批准号:FRF-AS-12-002,FRF-TP-11-001B)资助的课题.

Authors and contacts

1.
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;

2.
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China

Funds: Project supported by National Basic Research Program of China(Grant No. 2012CB720404), Key Program of the National Natural Science Foundation of China (Grant No. 50836001) and Fundamental Research Funds for the Central Universities, China(Grant No. FRF-AS-12-002, FRF-TP-11-001B).

参考文献

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[2]	Lu X, Shen W Z, Chu J H 2002 J. Appl. Phys. 91 1542
[3]	Stojanovic N, Maithripala D H S, Berg J M, Holtz M 2010 Phys. Rev. B 82 075418
[4]	Wu D M 2007 Fundamentals of Solid State Physics (Beijing: Higher Education Press) p5 (in Chinese) [吴代鸣 2007 固体物理基础 (北京: 高等教育出版社) 第5页]
[5]	Broido D A, Reinecke T L 2004 Phys. Rev. B 70 081310
[6]	Glavin B A 2001 Phys. Rev. Lett. 86 4318
[7]	Li D Y, Wu Y Y, Fan R, Yang P D, Majumdar A 2003 Appl. Phys. Lett. 83 3186
[8]	Zheng X J, Zhu L L, Zhou Y H 2005 Appl. Phys. Lett. 87 242101
[9]	Wang T, Luo Z Y, Guo S S, Cen K F 2007 J. Zhejiang Univ. 41 514 (in Chinese) [王涛, 骆仲泱, 郭顺松, 岑可法 2007 浙江大学学报 41 514]
[10]	Nolas G S, Lyon H B, Cohn J L, Tritt T M, Slack G A 1997 16th International Conference on Thermoelectrics, University of Texas, August 26-29 1997 p321
[11]	Yang J, Morelli D T, Meisner G P, Chen W, Dyck J S, Uher C 2003 Phys. Rev. B 67 165207
[12]	Nolas G S, Yang J, Takizawa H 2004 Appl. Phys. Lett. 84 5210
[13]	Ju S, Liang X 2010 J. Appl. Phys. 108 104307
[14]	Maiti A, Mahan G D, Pantelides S T 1997 Solid State Commun. 102 517
[15]	Crocombette J, Gelebart L 2009 J. Appl. Phys. 106 083520
[16]	Schelling P K, Phillpot S R, Keblinski P 2004 J. Appl. Phys. 95 6082
[17]	Ziman J M 1960 Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford: Oxford University Press) pp460-469
[18]	Dames C, Chen G 2004 J. Appl. Phys. 95 682
[19]	Chen G 1998 Phys. Rev. B 57 14960
[20]	Lu X, Shen W Z, Chu J H 2002 J. Appl. Phys. 91 1542
[21]	Doyama M, Kogure Y 1999 Comp. Mater. Sci. 14 80
[22]	Patrick K S, Simon R P, Pawel K 2002 Phys. Rev. B 65 144306
[23]	Feng B, Li Z X, Zhang X 2009 J. Appl. Phys. 105 104315
[24]	Heino P, Ristolainen E 2003 Microelectr. J. 34 773
[25]	Tritt T M 2004 Thermal Conductivity: Theory, Properties, and Applications (New York: Kluwer)
[26]	Swartz E T, Pohl R O 1989 Rev. Mod. Phys. 61 605
[27]	Maitrejean S, Gers R, Mourier T, Toffoli A, Passemard G 2006 Microelectron. Eng. 83 2396
[28]	Fuchs K, Wills H H 1938 Proc. Cambridge Philos. Soc. 34 100
[29]	Sondheimer E H 1952 Adv. Phys. 1 1
[30]	Chambers R G 1950 Proc. R. Soc. 202 378
[31]	Yuan S P, Jiang P X 2006 Int. J. Thermophys. 27 581
[32]	Lu X 2009 J. Appl. Phys. 105 094301
[33]	Ponomareva I, Srivastava D, Menon M 2007 Nano Lett. 7 1155

施引文献

[1]	Stewart D A, Norris P M 2000 Microscale Therm. Eng. 4 89
[2]	Lu X, Shen W Z, Chu J H 2002 J. Appl. Phys. 91 1542
[3]	Stojanovic N, Maithripala D H S, Berg J M, Holtz M 2010 Phys. Rev. B 82 075418
[4]	Wu D M 2007 Fundamentals of Solid State Physics (Beijing: Higher Education Press) p5 (in Chinese) [吴代鸣 2007 固体物理基础 (北京: 高等教育出版社) 第5页]
[5]	Broido D A, Reinecke T L 2004 Phys. Rev. B 70 081310
[6]	Glavin B A 2001 Phys. Rev. Lett. 86 4318
[7]	Li D Y, Wu Y Y, Fan R, Yang P D, Majumdar A 2003 Appl. Phys. Lett. 83 3186
[8]	Zheng X J, Zhu L L, Zhou Y H 2005 Appl. Phys. Lett. 87 242101
[9]	Wang T, Luo Z Y, Guo S S, Cen K F 2007 J. Zhejiang Univ. 41 514 (in Chinese) [王涛, 骆仲泱, 郭顺松, 岑可法 2007 浙江大学学报 41 514]
[10]	Nolas G S, Lyon H B, Cohn J L, Tritt T M, Slack G A 1997 16th International Conference on Thermoelectrics, University of Texas, August 26-29 1997 p321
[11]	Yang J, Morelli D T, Meisner G P, Chen W, Dyck J S, Uher C 2003 Phys. Rev. B 67 165207
[12]	Nolas G S, Yang J, Takizawa H 2004 Appl. Phys. Lett. 84 5210
[13]	Ju S, Liang X 2010 J. Appl. Phys. 108 104307
[14]	Maiti A, Mahan G D, Pantelides S T 1997 Solid State Commun. 102 517
[15]	Crocombette J, Gelebart L 2009 J. Appl. Phys. 106 083520
[16]	Schelling P K, Phillpot S R, Keblinski P 2004 J. Appl. Phys. 95 6082
[17]	Ziman J M 1960 Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford: Oxford University Press) pp460-469
[18]	Dames C, Chen G 2004 J. Appl. Phys. 95 682
[19]	Chen G 1998 Phys. Rev. B 57 14960
[20]	Lu X, Shen W Z, Chu J H 2002 J. Appl. Phys. 91 1542
[21]	Doyama M, Kogure Y 1999 Comp. Mater. Sci. 14 80
[22]	Patrick K S, Simon R P, Pawel K 2002 Phys. Rev. B 65 144306
[23]	Feng B, Li Z X, Zhang X 2009 J. Appl. Phys. 105 104315
[24]	Heino P, Ristolainen E 2003 Microelectr. J. 34 773
[25]	Tritt T M 2004 Thermal Conductivity: Theory, Properties, and Applications (New York: Kluwer)
[26]	Swartz E T, Pohl R O 1989 Rev. Mod. Phys. 61 605
[27]	Maitrejean S, Gers R, Mourier T, Toffoli A, Passemard G 2006 Microelectron. Eng. 83 2396
[28]	Fuchs K, Wills H H 1938 Proc. Cambridge Philos. Soc. 34 100
[29]	Sondheimer E H 1952 Adv. Phys. 1 1
[30]	Chambers R G 1950 Proc. R. Soc. 202 378
[31]	Yuan S P, Jiang P X 2006 Int. J. Thermophys. 27 581
[32]	Lu X 2009 J. Appl. Phys. 105 094301
[33]	Ponomareva I, Srivastava D, Menon M 2007 Nano Lett. 7 1155

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