纳米“热点”系统中的梯度热导率

吴志鹏; 张创; 胡世谦; 马登科; 杨诺

doi:10.7498/aps.72.20230687

摘要

纳米“热点”系统中的梯度变化热导率, 是纳米尺度热传导中的新现象. 背后的新机理, 为解决纳米器件散热等工程问题提供理论基础. 首先回顾了近期在纳米体系中发现的热传导新现象. 然后, 重点围绕“热点”梯度热导率, 阐述了不同维度体系的梯度热导率变化规律. 并根据原子振动模式与声子散射的变化, 阐释了梯度热导率的物理机制. 最后, 概述了纳米“热点”的梯度热导率特性给纳米器件散热带来的新挑战和新机遇, 并对未来在该方向研究进行展望.

关键词:

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:

作者及机构信息

1.
华中科技大学能源与动力工程学院, 武汉　430074

2.
杭州电子科技大学物理系, 杭州　310018

3.
云南大学物理与天文学院, 昆明　650091

4.
南京师范大学物理科学与技术学院, 南京　210000

通信作者: 马登科, dkma@njnu.edu.cn ; 杨诺, nuo@hust.edu.cn

基金项目: 国家重点研发计划政府间联合项目(批准号: 2018YFE0127800)资助的课题.

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).

[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

施引文献

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

Fig. 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.

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

[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

[1]	申开波, 刘英光, 李鑫, 李亨宣. 石墨烯纳米网中的声子干涉效应. 物理学报, 2023, 72(12): 123102. doi: 10.7498/aps.72.20230361
[2]	罗天麟, 丁亚飞, 韦宝杰, 杜建迎, 沈翔瀛, 朱桂妹, 李保文. 低维微纳尺度体系声子热传导和热调控: 来自芯片散热的非平衡统计物理问题. 物理学报, 2023, 72(23): 234401. doi: 10.7498/aps.72.20231546
[3]	潘东楷, 宗志成, 杨诺. 纳米尺度热物理中的声子弱耦合问题. 物理学报, 2022, 71(8): 086302. doi: 10.7498/aps.71.20220036
[4]	李含灵, 曹炳阳. 微纳尺度体点导热的拓扑优化. 物理学报, 2019, 68(20): 200201. doi: 10.7498/aps.68.20190923
[5]	陈礼诚, 张冬仙, 章海军, 王旭龙琦. 基于微纳结构与金属纳米层的颜色调控技术研究. 物理学报, 2015, 64(3): 038102. doi: 10.7498/aps.64.038102
[6]	华钰超, 曹炳阳. 多约束纳米结构的声子热导率模型研究. 物理学报, 2015, 64(14): 146501. doi: 10.7498/aps.64.146501
[7]	华钰超, 董源, 曹炳阳. 硅纳米薄膜中声子弹道扩散导热的蒙特卡罗模拟. 物理学报, 2013, 62(24): 244401. doi: 10.7498/aps.62.244401
[8]	唐晶晶, 冯妍卉, 李威, 崔柳, 张欣欣. 碳纳米管电缆式复合材料的热导率. 物理学报, 2013, 62(22): 226102. doi: 10.7498/aps.62.226102
[9]	李静, 冯妍卉, 张欣欣, 黄丛亮, 杨穆. 考虑界面散射的金属纳米线热导率修正. 物理学报, 2013, 62(18): 186501. doi: 10.7498/aps.62.186501
[10]	黄丛亮, 冯妍卉, 张欣欣, 李静, 王戈, 侴爱辉. 金属纳米颗粒的热导率. 物理学报, 2013, 62(2): 026501. doi: 10.7498/aps.62.026501
[11]	曹炳阳, 董若宇, 孔杰, 陈恒, 徐雁, 容启亮, 蔡岸. 纳米孔模板浸润法制备聚乙烯纳米线阵列的热导率的实验研究. 物理学报, 2012, 61(4): 046501. doi: 10.7498/aps.61.046501
[12]	金蔚, 惠宁菊, 屈世显. 螺旋纳米带中的声子输运. 物理学报, 2011, 60(1): 016301. doi: 10.7498/aps.60.016301
[13]	严雄伟, 於海武, 郑建刚, 李明中, 蒋新颖, 段文涛, 曹丁象, 王明哲, 单小童, 张永亮. 梯度掺杂Yb ∶YAG重频激光器热管理研究. 物理学报, 2011, 60(4): 047801. doi: 10.7498/aps.60.047801
[14]	侯泉文, 曹炳阳, 过增元. 碳纳米管的热导率:从弹道到扩散输运. 物理学报, 2009, 58(11): 7809-7814. doi: 10.7498/aps.58.7809
[15]	王照亮, 梁金国, 唐大伟, Y. T. Zhu. 单根单壁碳纳米管导热系数随长度变化尺度效应的实验和理论. 物理学报, 2008, 57(6): 3391-3396. doi: 10.7498/aps.57.3391
[16]	王照亮, 唐大伟, 贾涛, 毛安民. 3ω法加热/测温膜中温度波解析及其在微/纳米薄膜导热系数测量中的应用. 物理学报, 2007, 56(2): 747-754. doi: 10.7498/aps.56.747
[17]	张慧鹏, 金庆华, 王玉芳, 李宝会, 丁大同. 单壁碳纳米管手性角对声子振动频率的影响. 物理学报, 2005, 54(9): 4279-4284. doi: 10.7498/aps.54.4279
[18]	张滨, 王玉芳, 金庆华, 李宝会, 丁大同. 单壁碳纳米扶手椅、锯齿管声子色散关系的计算. 物理学报, 2005, 54(3): 1325-1329. doi: 10.7498/aps.54.1325
[19]	肖杨, 颜晓红, 曹觉先, 丁建文. 单壁纳米碳管的声子谱研究. 物理学报, 2003, 52(7): 1720-1725. doi: 10.7498/aps.52.1720
[20]	阎守胜, 高利明, 万君佐, 彭正伟, 应志强. FeMnAl合金低温声子热导率的反常行为. 物理学报, 1985, 34(6): 809-812. doi: 10.7498/aps.34.809

2023年184401补充材料.pdf

计量

文章访问数: 4456
PDF下载量: 169
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板