Interface thermal conductance and phonon thermal transport characteristics of diamond/carbon nanotube interface

Liu Zi-Yi; Chu Fu-Qiang; Wei Jun-Jun; Feng Yan-Hui

doi:10.7498/aps.73.20240323

Abstract

Diamond, an ultra-wide band gap semiconductor material, is an ideal material for high-power, high-frequency, high-temperature, and low-power loss electronic devices. However, high-frequency and high-power working environment leads to ultra-high local hot spots. Thermal interface material (TIM) is urgently needed to improve interface heat dissipation. Carbon nanotube (CNT), a brand-new generation of TIM, has ultra-high thermal conductivity (6000 W/(m·K)) and is expected to solve the heat dissipation problem of diamond semiconductor.Based on this, we first propose to combine diamond and CNT to improve the performance and stability of semiconductor device, reduce packaging size, and achieve miniaturized design of devices. Here we use reverse non-equilibrium molecular dynamics (RNEMD) method to study the thermal transport characteristics and interface thermal conductance (ITC) at the diamond/CNT interface. The results reveal that increasing CNT layers enhances the overall vibration density of states (VDOS) of CNT and shifts the peak value towards the low frequency band, which is more conducive to interface heat transfer. Alternatively, the enhancement of the phonon overlap energy strengthens the coupling vibration of phonon and thus improving the efficiency of the interfacial heat transfer. Moreover, in a certain range, the increase of system temperature and CNT length-to-diameter ratio can raise the cutoff frequency of the VDOS of diamond and CNT near the interface and the peak value of the low frequency band. This further improves the coupling vibration of phonon on both sides. Finally, by orthogonal test simulation, the optimal value of ITC is determined to be 2.65 GW/(m²·K) when the temperature, chirality, layers and length are 900 K, (6, 6), 6 layers and 5 nm respectively. This result greatly exceeds the current ITC of general semiconductors/metal. Compared with general composite materials, diamond/CNT composite material has great potential to enhance heat dissipation. Furthermore, according to P-value test, the number of layers has an extremely significant influence on interfacial thermal transport, while the influence of length, temperature and diameter decrease in turn.This work provides insights into optimizing heat transport at diamond/carbon nanotube interface and will be beneficial for device thermal management and chip material design.

Keywords:

Authors and contacts

1.
School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
Institute for Advanced Materials and Technology, University of Science and Technology Beijing, Beijing 100083, China

Corresponding author: Chu Fu-Qiang, chufq@ustb.edu.cn ; Feng Yan-Hui, yhfeng@me.ustb.edu.cn

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References

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Cited By

图 1 金刚石/碳纳米管模型及计算原理　(a) 金刚石/碳纳米管模型; (b) 计算原理

Figure 1. Diamond/CNT model and calculation principle: (a) Diamond/CNT model; (b) calculation principle.

DownLoad: Full-Size Img PowerPoint

图 2 不同温度下体系的温度分布及界面热导　(a) 温度分布; (b) 界面热导随温度的变化

Figure 2. System temperature distribution and ITC at different temperatures: (a) Temperature distribution; (b) variation of ITC with temperature.

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图 3 不同温度下近界面处金刚石和碳纳米管的声子态密度　(a) 300 K; (b) 500 K; (c) 700 K; (d) 900 K. (e) 不同温度下体系界面处的声子态密度; (f) 不同温度下近界面处金刚石和碳纳米管的重叠能

Figure 3. VDOS of diamond and CNT close to interface at different temperatures: (a) 300 K; (b) 500 K; (c) 700 K; (d) 900 K. (e) VDOS at system interface at different temperatures; (f) overlap energy of diamond and CNT close to interface at different temperatures.

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图 4 不同层数碳纳米管对应金刚石/碳纳米管体系的温度分布和界面热导　(a) 体系沿z轴的温度分布; (b) 界面热导随碳纳米管层数的变化

Figure 4. Temperature distribution and ITC of diamond/CNT system with different CNT layers: (a) Temperature distribution of the system along z axis; (b) variation of ITC with CNT layers.

DownLoad: Full-Size Img PowerPoint

图 5 不同碳纳米管层数对应近界面处的金刚石和碳纳米管的声子态密度　(a) 2层; (b) 3层; (c) 4层; (d) 6层; (e) 8层. (f) 不同碳纳米管层数对应金刚石/碳纳米管界面处的声子态密度; (g) 不同碳纳米管层数对应体系中近界面处金刚石和碳纳米管的重叠能

Figure 5. VDOS of diamond and CNT close to interface with different layers of CNT: (a) 2 layers; (b) 3 layers; (c) 4 layers; (d) 6 layers; (e) 8 layers. (f) VDOS at diamond/CNT interface with different CNT layers; (g) overlap energy of diamond and CNT close to interface with different CNT layers.

DownLoad: Full-Size Img PowerPoint

图 6 金刚石/碳纳米管复合材料界面热导随碳纳米管长径比的变化

Figure 6. Variation of ITC with length-to-diameter ratio (L/d) of CNT.

DownLoad: Full-Size Img PowerPoint

图 7 不同碳纳米管长径比对应近界面处的金刚石和碳纳米管的声子态密度　(a) L/d = 2.3; (b) L/d = 2.6; (c) L/d = 3.0; (d) L/d = 4.5; (e) L/d = 6.0; (f) L/d = 12.4. (g) 不同碳纳米管长径比对应金刚石/碳纳米管界面处的声子态密度; (h) 不同碳纳米管长径比对应体系中近界面处金刚石和碳纳米管的重叠能

Figure 7. VDOS of diamond and CNT close to interface with different CNT length-to-diameter ratio: (a) L/d = 2.3; (b) L/d = 2.6; (c) L/d = 3.0; (d) L/d = 4.5; (e) L/d = 6.0; (f) L/d = 12.4. (g) VDOS at diamond/CNT interface with different CNT length-to-diameter ratio; (h) overlap energy of diamond and CNT close to interface with different CNT length-to-diameter ratio.

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图 8 正交试验结果分析　(a) 各因素水平均值表; (b) 最优组温度分布

Figure 8. Orthogonal test result analysis: (a) Average value diagram of each factor and each level; (b) optimal group temperature distribution.

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表 1 正交试验界面热导结果

Table 1. ITC results of orthogonal test.

Number	ITC/(MW·m^–2·K^–1)	Number	ITC/(MW·m^–2·K^–1)
1	146.21	9	614.33
2	237.72	10	816.90
3	394.06	11	135.93
4	528.635	12	430.075
5	249.165	13	1264.37
6	103.735	14	788.3
7	1208.075	15	267.035
8	553.91	16	137.12

DownLoad: CSV

表 2 正交试验极值分析

Table 2. Range analysis of orthogonal test.

Level	Temperature /K	Diameter /nm	Layers	Length /nm
K₁	326.66	568.52	130.75	643.16
K₂	528.72	486.66	296.00	547.98
K₃	499.31	501.28	587.65	399.31
K₄	614.21	412.44	954.50	378.43
R	287.55	156.08	823.75	264.73
Optimum level	4	1	4	1

DownLoad: CSV

[1]	王权杰, 邓宇戈, 王仁宗, 刘向军 2023 物理学报 72 226301 Google Scholar Wang Q J, Deng Y G, Wang R Z, Liu X J 2023 Acta Phys. Sin. 72 226301 Google Scholar
[2]	Hiraiwa A, Kawarada H 2015 J. Appl. Phys. 117 124503 Google Scholar
[3]	Berman R, Hudson P, Martinez M 1975 J. Phys. C: Solid State Phys. 8 L430 Google Scholar
[4]	Pernot J, Volpe P N, Omnès F, Muret P, Mortet V, Haenen K, Teraji T 2010 Phys. Rev. B 81 205203 Google Scholar
[5]	Chow T P, Omura I, Higashiwaki M, Kawarada H, Pala V 2017 IEEE Trans. Electron Devices 64 856 Google Scholar
[6]	Perez G, Maréchal A, Chicot G, Lefranc P, Jeannin P O, Eon D, Rouger N 2020 Diamond Relat. Mater. 110 108154 Google Scholar
[7]	Russell S A O, Sharabi S, Tallaire A, Moran D A J 2012 IEEE Electron Device Lett. 33 6291745 Google Scholar
[8]	Sato H, Kasu M 2013 Diamond Relat. Mater. 31 47 Google Scholar
[9]	Yang Y, Koeck F A, Dutta M, Wang X, Chowdhury S, Nemanich R J 2017 J. Appl. Phys. 122 155304 Google Scholar
[10]	Hodgson M, Lohstroh A, Sellin P, Thomas D 2017 Meas. Sci. Technol. 28 105501 Google Scholar
[11]	Bodie C S, Lioliou G, Lefeuvre G, Barnett A M 2022 Appl. Radiat. Isot. 180 110027 Google Scholar
[12]	Chaudhuri S K, Kleppinger J W, Karadavut O, Mandal K C 2021 IEEE Electron Device Lett. 42 200 Google Scholar
[13]	Yang Z, Zhou L H, Luo W, Wan J Y, Dai J Q, Han X G, Fu K, Henderson D, Yang B, Hu L B 2016 Nanoscale 8 19326 Google Scholar
[14]	Due J, Robinson A J 2013 Appl. Therm. Eng. 50 455 Google Scholar
[15]	Hone J, Whitney M, Piskoti C, Zettl A 1999 Phys. Rev. B 59 R2514 Google Scholar
[16]	Marconnet A M, Panzer M A, Goodson K E 2013 Rev. Mod. Phys. 85 1295 Google Scholar
[17]	Sho H, Takuma H, Takuma S, James E, Junichiro S 2013 Int. J. Heat Mass Transfer 67 1024 Google Scholar
[18]	常国, 段佳良, 王鲁华, 王西涛, 张海龙 2017 材料导报 31 72 Chang G, Duan J L, Wang L H, Wang X T, Zhang H L 2017 Mater. Rep. 31 72
[19]	Lee S, Lee A, Baek S, Sung Y, Jeong H 2022 Diamond Relat. Mater. 130 109428 Google Scholar
[20]	Yu H T, Feng Y Y, Chen C, Zhang Z X, Cai Y, Qin M M, Feng W 2021 Carbon 179 348 Google Scholar
[21]	Ma J K, Shang T Y, Ren L L, Yao Y M, Zhang T, Xie J Q, Zhang B T, Zeng X L, Sun R, Xu J B, Wong C P 2020 Chem. Eng. J. 380 122550 Google Scholar
[22]	Desai A, Mahajan S, Subbarayan G, Jones W, Geer J, Sammakia B 2005 J. Electron. Packag. 128 92 Google Scholar
[23]	Feng Y, Zhu J, Tang D W 2015 Phys. Lett. A 379 382 Google Scholar
[24]	Zhang D, Tang Y Z, Wang S, Lin H, He Y 2022 Compos. Interfaces 29 899 Google Scholar
[25]	潘东楷, 宗志成, 杨诺 2022 物理学报 71 086302 Google Scholar Pan D K, Zong Z C, Yang N 2022 Acta Phys. Sin. 71 086302 Google Scholar
[26]	Thompson A P, Aktulga H M, Berger R, et al. 2022 Comput. Phys. Commun. 271 108171 Google Scholar
[27]	Sha Z D, Branicio P S, Pei Q X, Sorkin V, Zhang Y W 2013 Comput. Mater. Sci 67 146 Google Scholar
[28]	Heinz H, Vaia R A, Farmer B L, Naik R R 2008 J. Phys. Chem. 112 17281 Google Scholar
[29]	Liu Y Z, Yue J C, Liu Y N, Nian L L, Hu S Q 2023 Chin. Phys. Lett. 40 086301 Google Scholar
[30]	Jund P, Jullien R 1999 Phys. Rev. B 59 13707 Google Scholar
[31]	秦成龙, 罗祥燕, 谢泉, 吴乔丹 2022 物理学报 71 030202 Google Scholar Qin C L, Luo X Y, Xie Q, Wu Q D 2022 Acta Phys. Sin. 71 030202 Google Scholar
[32]	Yao Z H, Wang J S, Li B W, Liu G R 2005 Phys. Rev. B 71 085417 Google Scholar
[33]	Li J Q, Shen H J 2018 Mol. Phys. 116 1297 Google Scholar
[34]	朱亚波, 鲍振, 蔡存金, 杨玉杰 2009 物理学报 58 7833 Google Scholar Zhu Y B, Bao Z, Cai C J, Yang Y J 2009 Acta Phys. Sin. 58 7833 Google Scholar
[35]	Seberry J 2017 Orthogonal Designs (Wollongong: Springer Cham) pp1–430
[36]	宗志成, 潘东楷, 邓世琛, 万骁, 杨哩娜, 马登科, 杨诺 2023 物理学报 72 034401 Google Scholar Zong Z C, Pan D K, Deng S C, Wan X, Yang L N, Ma D K, Yang N 2023 Acta Phys. Sin. 72 034401 Google Scholar

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