-
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:
- phonon engineering /
- micro-nanoscale thermal conduction /
- nanochip thermal management /
- nano “hot spots” /
- graded thermal conductivity
[1] Bar-Cohen A, Maurer J J, Altman D H 2019 J. Electron. Packag. 141 40803Google Scholar
[2] Hao X, Peng B, Xie G, Chen Y 2016 Appl. Therm. Eng. 100 170Google Scholar
[3] Yan Z, Liu G, Khan J M, Balandin A A 2012 Nat. Commun. 3 827Google Scholar
[4] Wu F, Tian H, Shen Y, Hou Z, Ren J, Gou G, Sun Y, Yang Y, Ren T 2022 Nature 603 259Google Scholar
[5] Wang Z, Zhao R, Chen Y 2010 Sci. China Technol. Sci. 53 429Google Scholar
[6] Chen Y, Li D, Yang J, Wu Y, Lukes J R, Majumdar A 2004 Phys. B Condens. Matter 349 270Google Scholar
[7] Yang N, Zhang G, Li B 2010 Nano Today 5 85Google Scholar
[8] Yang N, Zhang G, Li B 2008 Nano Lett. 8 276Google Scholar
[9] Zhang G, Zhang Y 2015 Mech. Mater. 91 382Google Scholar
[10] Cao B, Yao W, Ye Z 2016 Carbon 96 711Google Scholar
[11] Hao Q, Xiao Y, Chen Q 2019 Mater. Today Phys. 10 100126Google Scholar
[12] Zhang D, Wang K, Chen S, Zhang L, Ni Y, Zhang G 2023 Nanoscale 15 1180Google Scholar
[13] Zhang H, Sun B, Hu S, Wang H, Cheng Y, Xiong S, Volz S, Ni Y 2020 Phys. Rev. B 101 205418Google Scholar
[14] Yang N, Xu X, Zhang G, Li B 2012 AIP Adv. 2 41410Google Scholar
[15] Maruyama S 2002 Phys. B Condens. Matter 323 193Google Scholar
[16] Zhang G, Li B 2005 J. Chem. Phys. 123 14705Google 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 764Google 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 3689Google Scholar
[19] Xu X, Chen J, Li B 2016 J. Phys. Condens. Matter 28 483001Google Scholar
[20] Nika D L, Ghosh S, Pokatilov E P, Balandin A A 2009 Appl. Phys. Lett. 94 203103Google Scholar
[21] Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896Google Scholar
[22] Prosen T, Campbell D K 2000 Phys. Rev. Lett. 84 2857Google Scholar
[23] Lepri S 2003 Phys. Rep. 377 1Google Scholar
[24] Dhar A 2008 Adv. Phys. 57 457Google Scholar
[25] Wang L, Hu B, Li B 2012 Phys. Rev. E 86 40101Google 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 86302Google Scholar
Google ScholarPan D, Zong Z, Yang N 2022 Acta Phys. Sin.71 86302 (in Chinses)[27] Chen G 2000 J. Nanopart. Res. 2 199Google Scholar
[28] Yang N, Hu S, Ma D, Lu T, Li B 2015 Sci. Rep. 5 14878Google Scholar
[29] Ma D, Ding H, Wang X, Yang N, Zhang X 2017 Int. J. Heat Mass Tran. 108 940Google Scholar
[30] Zhang C, Ma D, Shang M, Wan X, Lü J, Guo Z, Li B, Yang N 2022 Mater. Today Phys. 22 100605Google Scholar
[31] Markworth A J, Ramesh K S, Parks W P 1995 J. Mater. Sci. 30 2183Google Scholar
[32] Liew K M, Kitipornchai S, Zhang X Z, Lim C W 2003 Int. J. Solids Struct. 40 2355Google Scholar
[33] Gang C 1996 J. Heat Transfer 118 539Google Scholar
[34] Huang D, Sun Q, Liu Z, Xu S, Yang R, Yue Y 2023 Adv. Sci. 10 2204777Google Scholar
[35] Tang X, Xu S, Wang X 2013 Plos One 8 e58030Google Scholar
[36] Luo S, Fan A, Zhang Y, Wang H, Ma W, Zhang X 2022 Int. J. Heat Mass Trans. 184 122271Google 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 1Google Scholar
[38] Balandin A A, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau C N 2008 Nano Lett. 8 902Google Scholar
[39] Cahill D G 2004 Rev. Sci. Instrum. 75 5119Google Scholar
[40] Schmidt A J, Chen X, Chen G 2008 Rev. Sci. Instrum. 79 114902Google Scholar
[41] Minnich A J 2012 Phys. Rev. Lett. 109 205901Google 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 17131Google Scholar
[43] Hu Y, Zeng L, Minnich A J, Dresselhaus M S, Chen G 2015 Nat. Nanotechnol. 10 701Google Scholar
[44] An M, Song Q, Yu X, Meng H, Ma D, Li R, Jin Z, Huang B, Yang N 2017 Nano Lett. 17 5805Google Scholar
[45] Xiong Y, Yu X, Huang Y, Yang J, Li L, Yang N, Xu D 2019 Mater. Today Phys. 11 100139Google Scholar
[46] Deng C, Huang Y, An M, Yang N 2021 Mater. Today Phys. 16 100305Google Scholar
[47] Lindsay L, Broido D A, Mingo N 2009 Phys. Rev. B 80 125407Google Scholar
[48] Li X, Lee S 2019 Phys. Rev. B 99 85202Google Scholar
-
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.
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Th和边缘的温度Tc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 Th and the temperature Tc of the edge are${T_0} \pm {{\Delta T} \mathord{\left/ {\vphantom {{\Delta T} 2}} \right. } 2}$ , respectively, change the size of the system. -
[1] Bar-Cohen A, Maurer J J, Altman D H 2019 J. Electron. Packag. 141 40803Google Scholar
[2] Hao X, Peng B, Xie G, Chen Y 2016 Appl. Therm. Eng. 100 170Google Scholar
[3] Yan Z, Liu G, Khan J M, Balandin A A 2012 Nat. Commun. 3 827Google Scholar
[4] Wu F, Tian H, Shen Y, Hou Z, Ren J, Gou G, Sun Y, Yang Y, Ren T 2022 Nature 603 259Google Scholar
[5] Wang Z, Zhao R, Chen Y 2010 Sci. China Technol. Sci. 53 429Google Scholar
[6] Chen Y, Li D, Yang J, Wu Y, Lukes J R, Majumdar A 2004 Phys. B Condens. Matter 349 270Google Scholar
[7] Yang N, Zhang G, Li B 2010 Nano Today 5 85Google Scholar
[8] Yang N, Zhang G, Li B 2008 Nano Lett. 8 276Google Scholar
[9] Zhang G, Zhang Y 2015 Mech. Mater. 91 382Google Scholar
[10] Cao B, Yao W, Ye Z 2016 Carbon 96 711Google Scholar
[11] Hao Q, Xiao Y, Chen Q 2019 Mater. Today Phys. 10 100126Google Scholar
[12] Zhang D, Wang K, Chen S, Zhang L, Ni Y, Zhang G 2023 Nanoscale 15 1180Google Scholar
[13] Zhang H, Sun B, Hu S, Wang H, Cheng Y, Xiong S, Volz S, Ni Y 2020 Phys. Rev. B 101 205418Google Scholar
[14] Yang N, Xu X, Zhang G, Li B 2012 AIP Adv. 2 41410Google Scholar
[15] Maruyama S 2002 Phys. B Condens. Matter 323 193Google Scholar
[16] Zhang G, Li B 2005 J. Chem. Phys. 123 14705Google 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 764Google 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 3689Google Scholar
[19] Xu X, Chen J, Li B 2016 J. Phys. Condens. Matter 28 483001Google Scholar
[20] Nika D L, Ghosh S, Pokatilov E P, Balandin A A 2009 Appl. Phys. Lett. 94 203103Google Scholar
[21] Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896Google Scholar
[22] Prosen T, Campbell D K 2000 Phys. Rev. Lett. 84 2857Google Scholar
[23] Lepri S 2003 Phys. Rep. 377 1Google Scholar
[24] Dhar A 2008 Adv. Phys. 57 457Google Scholar
[25] Wang L, Hu B, Li B 2012 Phys. Rev. E 86 40101Google 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 86302Google Scholar
Google ScholarPan D, Zong Z, Yang N 2022 Acta Phys. Sin.71 86302 (in Chinses)[27] Chen G 2000 J. Nanopart. Res. 2 199Google Scholar
[28] Yang N, Hu S, Ma D, Lu T, Li B 2015 Sci. Rep. 5 14878Google Scholar
[29] Ma D, Ding H, Wang X, Yang N, Zhang X 2017 Int. J. Heat Mass Tran. 108 940Google Scholar
[30] Zhang C, Ma D, Shang M, Wan X, Lü J, Guo Z, Li B, Yang N 2022 Mater. Today Phys. 22 100605Google Scholar
[31] Markworth A J, Ramesh K S, Parks W P 1995 J. Mater. Sci. 30 2183Google Scholar
[32] Liew K M, Kitipornchai S, Zhang X Z, Lim C W 2003 Int. J. Solids Struct. 40 2355Google Scholar
[33] Gang C 1996 J. Heat Transfer 118 539Google Scholar
[34] Huang D, Sun Q, Liu Z, Xu S, Yang R, Yue Y 2023 Adv. Sci. 10 2204777Google Scholar
[35] Tang X, Xu S, Wang X 2013 Plos One 8 e58030Google Scholar
[36] Luo S, Fan A, Zhang Y, Wang H, Ma W, Zhang X 2022 Int. J. Heat Mass Trans. 184 122271Google 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 1Google Scholar
[38] Balandin A A, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau C N 2008 Nano Lett. 8 902Google Scholar
[39] Cahill D G 2004 Rev. Sci. Instrum. 75 5119Google Scholar
[40] Schmidt A J, Chen X, Chen G 2008 Rev. Sci. Instrum. 79 114902Google Scholar
[41] Minnich A J 2012 Phys. Rev. Lett. 109 205901Google 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 17131Google Scholar
[43] Hu Y, Zeng L, Minnich A J, Dresselhaus M S, Chen G 2015 Nat. Nanotechnol. 10 701Google Scholar
[44] An M, Song Q, Yu X, Meng H, Ma D, Li R, Jin Z, Huang B, Yang N 2017 Nano Lett. 17 5805Google Scholar
[45] Xiong Y, Yu X, Huang Y, Yang J, Li L, Yang N, Xu D 2019 Mater. Today Phys. 11 100139Google Scholar
[46] Deng C, Huang Y, An M, Yang N 2021 Mater. Today Phys. 16 100305Google Scholar
[47] Lindsay L, Broido D A, Mingo N 2009 Phys. Rev. B 80 125407Google Scholar
[48] Li X, Lee S 2019 Phys. Rev. B 99 85202Google Scholar
计量
- 文章访问数: 4360
- PDF下载量: 168
- 被引次数: 0