Graded thermal conductivity in nano “hot spot” systems

Wu Zhi-Peng; Zhang Chuang; Hu Shi-Qian; Ma Deng-Ke; Yang Nuo

doi:10.7498/aps.72.20230687

Abstract

The graded thermal conductivity in nanoscale “hot spot” system is a new phenomenon in nanoscale heat conduction. It is found that the thermal conductivity is no longer uniform, and the thermal conductivity gradually increases from the inside to the outside in the radial direction, which no longer obeys Fourier’s law of thermal conductivity. An in-depth understanding of the mechanism of the graded thermal conductivity can provide a theoretical basis for solving engineering problems such as heat dissipation of nanochip. This paper first reviews the new phenomenon of heat conduction recently discovered in nanosystem, then, focuses on the graded thermal conductivity in the “hot spot” system, and expounds the variation law of the graded thermal conductivity in different dimensional systems. According to the changes of atomic vibration mode and phonon scattering, the physical mechanism of the graded thermal conductivity is explained. Finally, the new challenges and opportunities brought by the graded thermal conductivity characteristics of nano “hot spot” to the heat dissipation of nanodevices are summarized, and the future research in this direction is also prospected.

Keywords:

Authors and contacts

1.
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2.
Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
3.
School of Physics and Astronomy, Yunnan University, Kunming 650091, China
4.
School of Physical Science and Technology, Nanjing Normal University, Nanjing 210000, China

Corresponding author: Ma Deng-Ke, dkma@njnu.edu.cn ; Yang Nuo, nuo@hust.edu.cn

Funds: Project supported by the National Key Research and Development Project of China (Grant No. 2018YFE0127800).

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Cited By

图 1 纳米“热点”系统示意图　(a)准一维结构, 例如碳纳米锥(台); (b)二维结构, 例如石墨烯圆盘; (c)三维结构剖视图

Figure 1. Schematic diagram of nanometer “hot spot” system: (a) Quasi-one-dimensional structures, such as carbon nanocones and truncated carbon nanocones; (b) two-dimensional structures, such as graphene disks; (c) three-dimensional cross-sectional view of the structure.

DownLoad: Full-Size Img PowerPoint

图 2 “热点”石墨烯圆盘的温度梯度分布和热导率对归一化半径的依赖关系^[30]　(a), (b)固定系统外半径$L = 20$μm, 改变系统的温度; (c), (d)固定系统的参考温度${T_0} = 300$ K, 热点温度T_h和边缘的温度T_c分别为${T_0} \pm {{\Delta T} \mathord{\left/ {\vphantom {{\Delta T} 2}} \right. } 2}$, 改变系统的尺寸

Figure 2. Dependence of temperature gradient distribution and thermal conductivity on normalized radius of “hot spot” graphene disk^[30]: (a), (b) Fix the outer radius of the system $L = 20$ μm, change the temperature of the system; (c), (d) fix the reference temperature of the system ${T_0} = 300$ K, the hot spot temperature T_h and the temperature T_c of the edge are ${T_0} \pm {{\Delta T} \mathord{\left/ {\vphantom {{\Delta T} 2}} \right. } 2}$, respectively, change the size of the system.

DownLoad: Full-Size Img PowerPoint

[1]	Bar-Cohen A, Maurer J J, Altman D H 2019 J. Electron. Packag. 141 40803 Google Scholar
[2]	Hao X, Peng B, Xie G, Chen Y 2016 Appl. Therm. Eng. 100 170 Google Scholar
[3]	Yan Z, Liu G, Khan J M, Balandin A A 2012 Nat. Commun. 3 827 Google Scholar
[4]	Wu F, Tian H, Shen Y, Hou Z, Ren J, Gou G, Sun Y, Yang Y, Ren T 2022 Nature 603 259 Google Scholar
[5]	Wang Z, Zhao R, Chen Y 2010 Sci. China Technol. Sci. 53 429 Google Scholar
[6]	Chen Y, Li D, Yang J, Wu Y, Lukes J R, Majumdar A 2004 Phys. B Condens. Matter 349 270 Google Scholar
[7]	Yang N, Zhang G, Li B 2010 Nano Today 5 85 Google Scholar
[8]	Yang N, Zhang G, Li B 2008 Nano Lett. 8 276 Google Scholar
[9]	Zhang G, Zhang Y 2015 Mech. Mater. 91 382 Google Scholar
[10]	Cao B, Yao W, Ye Z 2016 Carbon 96 711 Google Scholar
[11]	Hao Q, Xiao Y, Chen Q 2019 Mater. Today Phys. 10 100126 Google Scholar
[12]	Zhang D, Wang K, Chen S, Zhang L, Ni Y, Zhang G 2023 Nanoscale 15 1180 Google Scholar
[13]	Zhang H, Sun B, Hu S, Wang H, Cheng Y, Xiong S, Volz S, Ni Y 2020 Phys. Rev. B 101 205418 Google Scholar
[14]	Yang N, Xu X, Zhang G, Li B 2012 AIP Adv. 2 41410 Google Scholar
[15]	Maruyama S 2002 Phys. B Condens. Matter 323 193 Google Scholar
[16]	Zhang G, Li B 2005 J. Chem. Phys. 123 14705 Google Scholar
[17]	Yang L, Tao Y, Zhu Y, Akter M, Wang K, Pan Z, Zhao Y, Zhang Q, Xu Y, Chen R, Xu T T, Chen Y, Mao Z, Li D 2021 Nat. Nanotechnol. 16 764 Google Scholar
[18]	Xu X, Pereira L F C, Wang Y, Wu J, Zhang K, Zhao X, Bae S, Tinh Bui C, Xie R, Thong J T L, Hong B H, Loh K P, Donadio D, Li B, Ozyilmaz B 2014 Nat. Commun. 5 3689 Google Scholar
[19]	Xu X, Chen J, Li B 2016 J. Phys. Condens. Matter 28 483001 Google Scholar
[20]	Nika D L, Ghosh S, Pokatilov E P, Balandin A A 2009 Appl. Phys. Lett. 94 203103 Google Scholar
[21]	Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896 Google Scholar
[22]	Prosen T, Campbell D K 2000 Phys. Rev. Lett. 84 2857 Google Scholar
[23]	Lepri S 2003 Phys. Rep. 377 1 Google Scholar
[24]	Dhar A 2008 Adv. Phys. 57 457 Google Scholar
[25]	Wang L, Hu B, Li B 2012 Phys. Rev. E 86 40101 Google Scholar
[26]	Pan D, Zong Z, Yang N 2022 Acta Phys. Sin. 71 86302 (in Chinses) [潘东楷, 宗志成, 杨诺 2022 物理学报 71 86302 Google Scholar Pan D, Zong Z, Yang N 2022 Acta Phys. Sin. 71 86302 (in Chinses)Google Scholar
[27]	Chen G 2000 J. Nanopart. Res. 2 199 Google Scholar
[28]	Yang N, Hu S, Ma D, Lu T, Li B 2015 Sci. Rep. 5 14878 Google Scholar
[29]	Ma D, Ding H, Wang X, Yang N, Zhang X 2017 Int. J. Heat Mass Tran. 108 940 Google Scholar
[30]	Zhang C, Ma D, Shang M, Wan X, Lü J, Guo Z, Li B, Yang N 2022 Mater. Today Phys. 22 100605 Google Scholar
[31]	Markworth A J, Ramesh K S, Parks W P 1995 J. Mater. Sci. 30 2183 Google Scholar
[32]	Liew K M, Kitipornchai S, Zhang X Z, Lim C W 2003 Int. J. Solids Struct. 40 2355 Google Scholar
[33]	Gang C 1996 J. Heat Transfer 118 539 Google Scholar
[34]	Huang D, Sun Q, Liu Z, Xu S, Yang R, Yue Y 2023 Adv. Sci. 10 2204777 Google Scholar
[35]	Tang X, Xu S, Wang X 2013 Plos One 8 e58030 Google Scholar
[36]	Luo S, Fan A, Zhang Y, Wang H, Ma W, Zhang X 2022 Int. J. Heat Mass Trans. 184 122271 Google Scholar
[37]	Braun O, Furrer R, Butti P, Thodkar K, Shorubalko I, Zardo I, Calame M, Perrin M L 2022 NPJ 2D Mater. Appl. 6 1 Google Scholar
[38]	Balandin A A, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau C N 2008 Nano Lett. 8 902 Google Scholar
[39]	Cahill D G 2004 Rev. Sci. Instrum. 75 5119 Google Scholar
[40]	Schmidt A J, Chen X, Chen G 2008 Rev. Sci. Instrum. 79 114902 Google Scholar
[41]	Minnich A J 2012 Phys. Rev. Lett. 109 205901 Google Scholar
[42]	Zeng L, Collins K C, Hu Y, Luckyanova M N, Maznev A A, Huberman S, Chiloyan V, Zhou J, Huang X, Nelson K A, Chen G 2015 Sci. Rep. 5 17131 Google Scholar
[43]	Hu Y, Zeng L, Minnich A J, Dresselhaus M S, Chen G 2015 Nat. Nanotechnol. 10 701 Google Scholar
[44]	An M, Song Q, Yu X, Meng H, Ma D, Li R, Jin Z, Huang B, Yang N 2017 Nano Lett. 17 5805 Google Scholar
[45]	Xiong Y, Yu X, Huang Y, Yang J, Li L, Yang N, Xu D 2019 Mater. Today Phys. 11 100139 Google Scholar
[46]	Deng C, Huang Y, An M, Yang N 2021 Mater. Today Phys. 16 100305 Google Scholar
[47]	Lindsay L, Broido D A, Mingo N 2009 Phys. Rev. B 80 125407 Google Scholar
[48]	Li X, Lee S 2019 Phys. Rev. B 99 85202 Google Scholar

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