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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.
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Keywords:
- nanowire /
- thermal conductivity /
- surface scattering /
- grain boundary scattering
[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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[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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