Recent progresses of thermal conduction in two-dimensional materials

Wu Xiang-Shui; Tang Wen-Ting; Xu Xiang-Fan

doi:10.7498/aps.69.20200709

Abstract

The two-dimensional (2D) materials represented by graphene and boron nitride provide an excellent platform for the study of thermal conduction and the interfacial thermal resistance in low-dimensional system. Recent studies recover exotic physics behind the novel thermal transport properties of 2D materials, such as length effect, dimensional effect, isotopic effect, anisotropic effect, etc. In this review, we introduce the recent progress of thermal properties in 2D materials in the last decade. The principle and development of thermal conduction measurement technologies used in 2D materials are introduced, followed by the experimental progress of thermal conduction and interfacial thermal resistance. Special attention is paid to the abnormal thermal transport and relevant physical problems. Finally, we present thermal management and heat dissipation in 2D electronic devices, summarize and point out the problems and bottlenecks, and forecast the future research directions and foregrounds.

Keywords:

Authors and contacts

Center for Phononics and Thermal Energy Science, School of Physical Science and Engineering, Tongji University, Shanghai 200092, China

Corresponding author: Xu Xiang-Fan, xuxiangfan@tongji.edu.cn

Funds: Project supported by the Key Research and development Plan of Guangdong Province (Grant No. 2020B010190004), the Key Special Project of the National Key Research and Development Plan of “Strategic Advanced Electronic Materials” (Grant No. 2017YFB0406000), and the National Natural Science Foundation of China (Grant Nos. 11674245, 11890703, 11935010)

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Cited By

图 1 (a)热桥器件示意图; (b)器件热流图; (c)接触热阻对测量的影响; (d)和(e)悬空热桥法改良——比较器法示意图及改良前(黑色实线)和改良后(红色及蓝色)系统温漂随时间变化关系^[39]

Figure 1. (a), (b) Sketch and heat flow of thermal bridge device; (c) influence of thermal contact resistance; (d), (e) diagram of modified comparator method and temperature drift of experimental system^[39].

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图 2 电子束自加热法^[54]　(a)示意图; (b)热流图; (c)同济大学测量装置图; (d)利用电子束自加热法测量多层硫化钼的热导率

Figure 2. The electron-beam self-heating method ^[54]: (a) Sketch; (b) heat flow of device; (c) experimental setup in Tongji University; (d) measuring thermal conductivity of few-layer MoS₂.

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图 3 (a) 拉曼法测量原理图; (b) (c) 单层悬空石墨烯拉曼G峰频率与温度以及激光能量的关系^[31,61]; (d) 双拉曼法示意图^[67]; (e) ET-Raman法示意图^[70]

Figure 3. (a) Sketch of the Raman method; (b), (c) experimental data for the Raman G peak shift with respect to temperature and laser power^[31,61]; (d), (e) sketch of the Two-Raman method^[67] and ET-Raman method^[70].

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图 4 (a)时域热反射法测量系统; (b)经正弦调制的飞秒脉冲激光、材料表面温度响应、锁相放大器所输出的同相信号和反相信号与延迟时间之间的关系; (c)采用时域热反射法测量GaN热导率及Al/GaN界面热导^[33]

Figure 4. (a) Experimental setup of the TDTR method; (b) femtosecond pulse laser with sinusoidal modulation, temperature response of sample surface, the in-phase signal and out-of-phase signal of Lock-in Amplifier versus delay-time; (c) using TDTR method to measure thermal conductivity of GaN and interface thermal conductance of Al/GaN^[33].

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图 5 (a) 悬空单层石墨烯中各声子模式贡献热导率比例^[102]; (b)实验观测单层悬空石墨烯中声子的(准)弹道输运^[17,35,111]

Figure 5. (a) Phonon modes contribution to thermal conductivity in suspended single-layer graphene^[102]; (b) experimental observation of (quasi-) ballistic phonon transport in suspended single-layer graphene^[17,35,111].

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图 6 实验测量石墨面间热导率与厚度的关系^{[112,114,115]}

Figure 6. out-of-plane thermal conductivity of graphite versus thickness in experiment^{[112,114,115]}.

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图 7 晶体结构　(a)硫化钼^[123]; (b)黑磷^[48]; (c)块体碲^[150]

Figure 7. crystal structure of (a) MoS₂^[123], (b) BP^[48], (c) bulk Te ^[150].

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图 8 (a) 室温下单层悬空石墨烯中声子平均自由程^[104]; (b), (c)理论及实验上单层悬空石墨烯室温热导率随长度变化^{[17,102,175,176]}; (d)实验上不同宽度的单层石墨烯悬空热导率随温度变化^{[17,98,177-180]}

Figure 8. Single-layer suspended graphene (a) the mean free path at room temperature^[104]; (b), (c) length-dependent thermal conductivity in theory and experiment respectively^{[17,102,175,176]}; (d) width-dependent thermal conductivity in experiment^{[17,98,177-180]}.

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图 9 使用拉曼法测量单层/多层硫化钼时热导率与悬空部分半径之间的关系^{[18,60,127,128]}

Figure 9. Thermal conductivity of single/multi-layer MoS₂ versus suspended radius using the Raman method. ^{[18,60,127,128]}

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图 10 (a) 石墨烯(悬空/衬底)面内热导率的厚度效应^{[64,103,110,196,197]}; (b) 四层氮化硼悬空热导率与温度之间的关系^[44]; (c) 氮化硼(悬空)面内热导率的厚度效应^{[41,44,56,120,198]}; (d) 硫化钼(悬空)面内热导率的厚度效应^[18]

Figure 10. (a) Thickness-dependent in-plane thermal conductivity of graphene (suspended and supported) ^{[64,103,110,196,197]}; (b) thermal conductivity of four-layers h-BN (suspended) versus temperature^[44]; (c) thickness-dependent in-plane thermal conductivity of h-BN (suspended) ^{[41,44,56,120,198]}; (d) thickness-dependent in-plane thermal conductivity of MoS₂ (suspended)^[18].

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图 11 室温下黑磷面内热导率的厚度效应及各向异性^{[48,49,73,77,146,147,168,200]}

Figure 11. Thickness-dependent and anisotropic in-plane thermal conductivity of the BP^{[48,49,73,77,146,147,168,200]}.

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图 12 (a) 多层黑砷悬空面内热导率的各向异性^[145]; (b)黑磷沿ZZ方向、AC方向悬空面内热导率以及杨氏模量数值(300 K)^[49]

Figure 12. (a) Anisotropic in-plane thermal conductivity of suspended few-layer BAs^[145]; (b) the Young modulus and in-plane thermal conductivity of suspended BP along AC and ZZ direction respectively at 300 K^[49].

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图 13 悬空石墨烯面内热导率　(a) 同位素效应^[202]; (b) 晶粒尺寸的影响^[205]; (c) 晶界夹角的影响^[207]; (d) 空位率的影响^[208]

Figure 13. In-plane thermal conductivity of suspended graphene: (a) Isotope effect^[202]; (b) influence of grain size^[205]; (c) influence of misorientation angle between grains^[207]; (d) influence of vacancy ratio^[208].

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图 14 悬空硫化钼面内热导率^[45]: 缺陷浓度的影响

Figure 14. In-plane thermal conductivity of suspended MoS₂ ^[45]: influence of defect concentration.

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图 15 微纳尺度热二极管设计原理　(a) 热导率随温度变化趋势不同; (b) 声子透射率不对称^[219]; 非对称结构悬空石墨烯^[224] (c)SEM图; (d) 热二极管实验结果

Figure 15. Design principle of thermal diode in micro/nano-scale: (a) Different tendency between thermal conductivity and temperature; (b) asymmetric phonon transmission ratio^[219]; asymmetric structure of suspended graphene^[224] (c) SEM image; (b) the experiment result of thermal diode.

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图 16 (a) 氮化硼厚度对金属/氮化硼/氧化硅界面热阻的影响^[234]; (b)利用3ω法测量不同方法制备的氮化硼对硒化钨器件的界面热阻的影响^[250]; (c)在界面处引入化学键对金属/单层石墨烯/氧化硅界面热导的影响^[256]; (d) 在界面处加电压对氧化硅/多层石墨烯/氧化硅界面热阻的影响^[257]

Figure 16. (a) Thickness-depend interfacial thermal resistance of metal/h-BN/SiO₂^[234]; (b) interfacial thermal resistance of WSe₂ device with h-BN prepared by different method^[250]; (c) improving interfacial thermal resistance of Al/single-layer graphene/SiO₂ by introducing chemical bond^[256]; (d) the influence of voltage at interface to interfacial thermal resistance of SiO₂/graphene/ SiO₂^[257].

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图 17 通过氧离子束轰击改善金属与非金属的界面热阻^[259]

Figure 17. Improving interfacial thermal resistance of metal/nonmetal by O₂-plasma^[259].

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图 18 (a)经高温退火的石墨烯薄膜的热导率与厚度之间的关系^[90]; (b) 石墨烯与环氧树脂混合作为TIMs材料^[270]

Figure 18. (a) Thickness-depend thermal conductivity of graphene film with high-temperature annealing^[90]; (b) mixture of graphene and epoxy as TIMs ^[270].

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图 19 氮化硼对硒化钨以及硫化钼器件中温度分布的影响^[250]:　(a)−(d) SThM温度扫描图; (e)器件边界处温度变化图; (f)器件中温度分布柱状统计图

Figure 19. Effect of h-BN on temperature distribution in WSe₂ and MoSe₂ devices ^[250]: (a)−(d) Temperature scanned by SThM; (e) temperature variation at device boundary; (f) histogram of temperature distribution in devices.

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表 1 不同文献中测量悬空石墨烯热导率实验细节

Table 1. Experimental detail of thermal conductivity in suspended single/few-layer graphene from different literature.

制备方式	石墨烯层数	热导率 κ /W·(m·K)^–1	备注
拉曼法
机械剥离^[31]	1层	~4840—5300 (室温)	数值高估, 见本节文字部分
机械剥离^[97]	1层	~3080—5150 (室温)	数值高估, 见本节文字部分
化学气相沉积^[66]	1层	~2500 +1100/–1050 (T = 350 K)	/
化学气相沉积^[66]	1层	~1400 +500/–480 (T = 500 K)	/
化学气相沉积^[98]	1层	~2600 — 3100 (T = 350 K)	/
机械剥离^[63]	1层	~630 (T = 660 K)	/
机械剥离^[99]	1层	~1800 (T = 325 K)	/
机械剥离^[99]	1层	~710 (T = 500 K)	/
化学气相沉积^[69]	1层	~850—1100 (T = 303—644 K)	/
机械剥离^[69]	1层	~1500 (T = 330—445 K)	/
机械剥离^[69]	2层	~970 (T = 303—630 K)	/
悬空热桥法
化学气相沉积^[100]	1层	~190(T = 280 K, L = 0.5 μm)	/
化学气相沉积^[43]	2层	~560—620(室温, L = 5 μm)	/
化学气相沉积^[17]	1层	~1689—1831(T = 300 K, L = 9 μm)	/
SThM
化学气相沉积^[85]	1层	~2100—2430(T = 335 K)	/

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表 2 不同实验中悬空单层/多层h-BN热导率实验测量细节表

Table 2. Experimental detail of thermal conductivity of suspended single/few-layer h-BN in different literature.

制备方式	氮化硼薄膜层数	测量方法	热导率(室温/300 K)
制备方式	氮化硼薄膜层数	测量方法	κ /(W(m·K)^–1)
机械剥离^[120]	5层	微桥电阻温度计法	~250
机械剥离^[120]	11层	微桥电阻温度计法	~360
化学气相沉积^[62]	9层	拉曼法	~227—280
化学气相沉积^[57]	2.1 nm	拉曼法	~223
化学气相沉积^[121]	10 nm/20 nm	稳态/瞬态	~100
机械剥离^[41]	2层	热桥法	~484 +141/–24
机械剥离^[44]	4层	热桥法	~286
机械剥离^[56]	1层	拉曼法	751 ± 340
机械剥离^[56]	2层	拉曼法	646 ± 242
机械剥离^[56]	3层	拉曼法	602 ± 247

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表 3 不同文献中硫化钼单层/多层热导率实验测量细节表

Table 3. Experimental detail of thermal conductivity of single/few-layer MoS₂ in different literature.

制备方式	硫化钼薄膜层数	测量方法	热导率 (300 K/室温)
制备方式	硫化钼薄膜层数	测量方法	κ /(W·(m·K)^–1)
悬空
化学气相沉积^[59]	11层	拉曼法	~52
机械剥离^[60]	1层	拉曼法	34.5 ± 4
机械剥离^[126]	4层	热桥法	~44—45
机械剥离^[126]	7层	热桥法	~48—52
机械剥离^[127]	1层	拉曼法	84 ± 17
机械剥离^[127]	2层	拉曼法	77 ± 25
机械剥离^[54]	4层	电子束自加热	34 ± 6
机械剥离^[54]	5层	电子束自加热	30 ± 3
化学气相沉积^[128]	1层	拉曼法	13.3 ± 1.4
化学气相沉积^[128]	2层	拉曼法	15.6 ± 1.5
化学气相沉积^[47]	1层	热桥法	~21—24
化学气相沉积^[18]	1层	拉曼法	60.3 ± 5.2
化学气相沉积^[18]	2层	拉曼法	38.4 ± 3.1
化学气相沉积^[18]	3层	拉曼法	44.8 ± 5.9
化学气相沉积^[18]	4层	拉曼法	36.9 ± 4.9
衬底
机械剥离^[129]	1层	拉曼法	~62.2
机械剥离^[65]	4层	拉曼法	60.3 ± 5

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表 4 除硫化钼外, 其他单层/多层过渡金属硫化物的悬空热导率实验测量细节表

Table 4. Experimental detail of thermal conductivity of single/few-layer transition metal sulfide (expect MoS₂) in different literature.

制备方式	薄膜层数	测量方法	热导率 (300 K/室温)
制备方式	薄膜层数	测量方法	κ/(W·(m·K)^–1)
硒化钼
机械剥离^[127]	1层	拉曼法	59 ± 18
机械剥离^[127]	2层	拉曼法	42 ± 13
机械剥离^[70]	45 nm	拉曼法	11.1 ± 0.4
机械剥离^[70]	140 nm	拉曼法	20.3 ± 0.9
机械剥离^[132]	5 nm	拉曼法	6.2 ± 0.9
机械剥离^[132]	36 nm	拉曼法	10.8 ± 1.7
硒化钽
机械剥离^[133]	45 nm	拉曼法	~9
机械剥离^[133]	55 nm	拉曼法	~11
硫化钨
化学气相沉积^[134]	1层	拉曼法	~32
化学气相沉积^[134]	2层	拉曼法	~53
化学气相沉积^[18]	1层	拉曼法	74.8 ± 17.2
硒化钨
化学气相沉积^[18]	1层	拉曼法	66 ± 20.9
碲化钨
机械剥离^[135]	220 nm	TDTR	~2
机械剥离^[136]	11.2 nm	拉曼	~0.639—0.743
硫化铼
机械剥离^[137]	150 nm	TDTR	~50—70

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表 5 常见二维材料的界面热导实验测量值

Table 5. Experimental results of interfacial thermal conductance of two-dimensional materials.

界面结构	室温界面热导	界面结构	室温界面热导
界面结构	G_int/MW·(m²·K)^–1	界面结构	G_int/MW·(m²·K)^–1
石墨烯 (G)		G/h-BN^[235]	~17
石墨烯 (G)		MoS₂/h-BN^[236]	~52.2
SiO₂/G/SiO₂^[237]	~83—179	硫化钼 (MoS₂)、硒化钼 (MoSe₂)
G/SiO₂^[238]	~50	硫化钼 (MoS₂)、硒化钼 (MoSe₂)
G/Al₂O₃^[239]	~17	MoS₂/SiO₂ or AlN^[240]	~15
Au/Ti/G/SiO₂^[241]	~25	MoS₂/Au^[127]	~0.44—0.74
Au/Ti/G/SiO₂^[196]	~20	MoS₂/SiO₂^[129]	~1.94
Al/G/Si^[242]	~62—65	MoS₂/SiO₂^[243]	~14
Al/G/SiO₂^[242]	~21—24	MoS₂/SiO₂^[244]	~21
Au/Ti/G/sapphire^[245]	~33.5	MoSe₂/SiO₂^[127]	~0.09—0.13
Au/Ti/G/diamond^[245]	~6.2	MoSe₂/SiO₂^[243]	~2
G/Au^[76]	~23	黑磷 (BP)
G/Al^[76]	~27	黑磷 (BP)
G/Ti^[76]	~31	BP/SiO_X^[246]	~21.7—114
G/Au^[66]	~18.8—44	BP/SiO_X^[247]	~202—60
氮化硼 (h-BN)		硒化钨 (WSe₂)
h-BN/SiO₂/Si^[248]	~8.3	WSe₂/Si/SiO₂^[249]	~10—32
Metal/h-BN/SiO₂^[234]	~29—63	WSe₂/SiO₂^[250]	~22

DownLoad: CSV

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