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Interfacial thermal conductance of gallium nitride/graphene/diamond heterostructure based on molecular dynamics simulation

Liu Dong-Jing Hu Zhi-Liang Zhou Fu Wang Peng-Bo Wang Zhen-Dong Li Tao

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Interfacial thermal conductance of gallium nitride/graphene/diamond heterostructure based on molecular dynamics simulation

Liu Dong-Jing, Hu Zhi-Liang, Zhou Fu, Wang Peng-Bo, Wang Zhen-Dong, Li Tao
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  • Gallium nitride chips are widely used in high-frequency and high-power devices. However, thermal management is a serious challenge for gallium nitride devices. To improve thermal dissipation of gallium nitride devices, the nonequilibrium molecular dynamics method is employed to investigate the effects of operating temperature, interface size, defect density and defect types on the interfacial thermal conductance of gallium nitride/graphene/diamond heterostructure. Furthermore, the phonon state densities and phonon participation ratios under various conditions are calculated to analyze the interface thermal conduction mechanism.The results indicate that interfacial thermal conductance increases with temperatures rising, highlighting the inherent self-regulating heat dissipation capabilities of heterogeneous. The interfacial thermal conductance of monolayer graphene structures is increased by 2.1 times as the temperature increases from 100 to 500 K. This is attributed to the overlap factor increasing with temperature rising, which enhances the phonon coupling between interfaces, leading the interfacial thermal conductance to increase.Additionally, in the study it is found that increasing the number of layers of both gallium nitride and graphene leads the interfacial thermal conductance to decrease. When the number of gallium nitride layers increases from 10 to 26, the interfacial thermal conductance decreases by 75%. The overlap factor diminishing with the layer number increasing is ascribed to the decreased match of phonon vibrations between interfaces, resulting in lower thermal transfer efficiency. Similarly, when the number of graphene layers increases from 1 to 5, the interfacial thermal conductance decreases by 74%. The increase in graphene layers leads the low-frequency phonons to decrease, consequently lowering the interfacial thermal conductance. Moreover, multilayer graphene enhances phonon localization, exacerbates the reduction in interfacial thermal conductance.It is found that introducing four types of vacancy defects can affect the interfacial thermal conductance. Diamond carbon atom defects lead its interfacial thermal conductance to increase, whereas defects in gallium, nitrogen, and graphene carbon atoms cause their interfacial thermal conductance to decrease. As the defect concentration increases from 0 to 10%, diamond carbon atom defects increase the interfacial thermal conductance by 40% due to defect scattering, which increases the number of low-frequency phonon modes and expands the channels for interfacial heat transfer, thus improving the interfacial thermal conductance. Defects in graphene intensify the degree of graphene phonon localization, consequently leading the interfacial thermal conductance to decrease. Gallium and nitrogen defects both intensify the phonon localization of gallium nitride, impeding phonon transport channels. Moreover, gallium defects induce more severe phonon localization than nitrogen defects, consequently leading to lower interfacial thermal conductance.This research provides the references for manufacturing highly reliable gallium nitride devices and the widespread use of gallium nitride heterostructures.
      Corresponding author: Liu Dong-Jing, ldj168168@126.com
    • Funds: Project supported by the Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology, China (Grant No. 19-050-44-002Z), the 2024 Project on Enhancement of Basic Research Ability for Young and Middle-aged Teachers in Guangxi Universities, China (Grant No. 2024KY0203), the Innovation Project of Graduate Education of Guilin University of Electronic Science and Technology, China (Grant No. 2024YCXS016), and the 2023 Guangxi Autonomous Region New Engineering Research and Practice Project, China (Grant No. XGK202309).
    [1]

    刘庆彬, 蔚翠, 郭建超, 马孟宇, 何泽召, 周闯杰, 高学栋, 余浩, 冯志红 2023 物理学报 72 098104Google Scholar

    Liu Q B, Yu C, Guo J C, Ma M Y, He Z Z, Zhou C J, Gao X D, Yu H, Feng Z H 2023 Acta Phys. Sin. 72 098104Google Scholar

    [2]

    贾鑫, 魏俊俊, 黄亚博, 邵思武, 孔月婵, 刘金龙, 陈良贤, 李成明, 叶海涛 2020 表面技术 49 111

    Jia X, Wei J J, Huang Y B, Shao S W, Kong Y C, Liu J L, Chen L X, Li C M, Ye H T 2020 Surf. Technol. 49 111

    [3]

    Wu Y J, Fang L, Xu Y 2019 npj Comput. Mater. 5 1Google Scholar

    [4]

    冯家驹, 范亚明, 房丹, 邓旭光, 于国浩, 魏志鹏, 张宝顺 2022 人工晶体学报 51 730Google Scholar

    Feng J J, Fan Y M, Fang D, Deng X G, Yu G H, Wei Z P, Zhang B S 2022 J. Synth. Cryst. 51 730Google Scholar

    [5]

    Francis D, Faili F, Babić D, Ejeckam F, Nurmikko A, Maris H 2010 Diamond Relat. Mater. 19 229Google Scholar

    [6]

    Cho J, Francis D, Altman D H, Asheghi M, Goodson K E 2017 J. Appl. Phys. 121 055105Google Scholar

    [7]

    Zhou Y, Anaya J, Pomeroy J, Sun H, Gu X, Xie A, Beam E, Becker M, Grotjohn T A, Lee C, Kuball M 2017 ACS Appl. Mater. Interfaces 9 34416Google Scholar

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    Huang X, Guo Z 2021 Int. J. Heat Mass Transfer 178 121613Google Scholar

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    Mu F, Xu B, Wang X, et al. 2022 J. Alloys Compd. 905 164076Google Scholar

    [10]

    Tao L, Theruvakkattil Sreenivasan S, Shahsavari R 2017 ACS Appl. Mater. Interfaces 9 989Google Scholar

    [11]

    Jia X, Huang L, Sun M, Zhao X, Wei J, Li C 2022 Coatings 12 672Google Scholar

    [12]

    Qi Z, Shen W, Li R, Sun X, Li L, Wang Q, Wu G, Liang K 2023 Appl. Surf. Sci. 615 156419Google Scholar

    [13]

    Middleton C, Chandrasekar H, Singh M, et al. 2019 Appl. Phys. Express 12 024003Google Scholar

    [14]

    Wu L, Sun X, Gong F, Luo J, Yin C, Sun Z, Xiao R 2022 Nanomaterials 12 894Google Scholar

    [15]

    Liu F, Zou R, Hu N, Ning H, Yan C, Liu Y, Wu L, Mo F, Fu S 2019 Nanoscale 11 4067Google Scholar

    [16]

    Hu S, Ju S, Shao C, Guo J, Xu B, Ohnishi M, Shiomi J 2021 Mater. Today Phys. 16 100324Google Scholar

    [17]

    Hu M, Poulikakos D 2013 Int. J. Heat Mass Transfer 62 205Google Scholar

    [18]

    Mischke J, Pennings J, Weisenseel E, Kerger P, Rohwerder M, Mertin W, Bacher G 2020 2D Mater. 7 035019Google Scholar

    [19]

    Suntornwipat N, Aitkulova A, Djurberg V, Majdi S 2023 Thin Solid Films 770 139766Google Scholar

    [20]

    Shen B, Ji Z, Lin Q, Gong P, Xuan N, Chen S, Liu H, Huang Z, Xiao T, Sun Z 2022 Chem. Mater. 34 3941Google Scholar

    [21]

    Jiang M, Chen C, Wang P, Guo D, Han S, Li X, Lu S, Hu X 2022 Proc. Natl. Acad. Sci. U. S. A. 119 e2201451119Google Scholar

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    Li D, Zou W, Jiang W, Peng X, Song S, Qin Q H, Xue J M 2020 Ceram. Int. 46 10885Google Scholar

    [23]

    Badokas K, Kadys A, Mickevičius J, Ignatjev I, Skapas M, Stanionytė S, Radiunas E, Juška G, Malinauskas T 2021 J. Phys. D: Appl. Phys. 54 205103Google Scholar

    [24]

    Barbier C, Largeau L, Gogneau N, et al. 2023 Cryst. Growth Des. 23 6517Google Scholar

    [25]

    Sun H, Simon R, Pomeroy J, Francis D, Faili F, Twitchen D, Kuball M 2015 Appl. Phys. Lett. 106 111906Google Scholar

    [26]

    Wang J, Shen Y, Yang P 2023 Compos. Commun. 40 101616Google Scholar

    [27]

    Tang Y, Liu J K, Yu Z H, Sun L G, Zhu L L 2023 Chin. Phys. B 32 066502Google Scholar

    [28]

    Liu D 2020 Phys. Lett. A 384 126077Google Scholar

    [29]

    Ou B, Yan J, Wang Q, Lu L 2022 Molecules 27 905Google Scholar

    [30]

    Sang L X, Li Z K 2024 Acta Phys. Sin. 73 103105 [桑丽霞, 李志康 2024 物理学报 73 103105]Google Scholar

    Sang L X, Li Z K 2024 Acta Phys. Sin. 73 103105Google Scholar

    [31]

    刘东静, 周福, 陈帅阳, 胡志亮 2023 物理学报 72 157901Google Scholar

    Liu D J, Zhou F, Chen S Y, Hu Z L, 2023 Acta Phys. Sin. 72 157901Google Scholar

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    Qu G D, Deng Z Y, Guo W, et al. 2023 IEEE Trans. Compon. Packag. Manuf. Technol. 13 816Google Scholar

    [33]

    Wu B Y, Zhou M, Xu D J, Liu J J, Tang R J, Zhang P 2022 Surf. Interfaces 32 102119Google Scholar

    [34]

    Tang Y Q, Zhang Z, Li L, Guo J, Yang P 2022 Int. J. Therm. Sci. 171 107231Google Scholar

    [35]

    Wu X, Han Q 2021 ACS Appl. Mater. Interfaces 13 32564Google Scholar

    [36]

    Huang H, Zhong Y, Cai B, Wang J, Liu Z, Peng Q 2023 Surf. Interfaces 37 102736Google Scholar

    [37]

    Ma D, Zhang L 2020 J. Phys. Condens. Matter 32 425001Google Scholar

    [38]

    Danilchenko B A, Paszkiewicz T, Wolski S, JeŻowski A, Plackowski T 2006 Appl. Phys. Lett. 89 061901Google Scholar

    [39]

    刘东静, 王韶铭, 杨平 2021 物理学报 70 187302Google Scholar

    Liu D J, Wang S M, Yang P 2021 Acta Phys. Sin. 70 187302Google Scholar

    [40]

    Yang N, Luo T, Esfarjani K, et al. 2015 J. Comput. Theor. Nanosci. 12 168Google Scholar

    [41]

    Liu Y, Qiu L, Liu J, Feng Y 2023 Int. J. Heat Mass Transfer 209 124123Google Scholar

    [42]

    Wei N, Zhou C, Li Z, Ou B, Zhao K, Yu P, Li S, Zhao J 2022 Mater. Today Commun. 30 103147Google Scholar

    [43]

    Li M, Zhou H, Zhang Y, Liao Y, Zhou H 2018 Carbon 130 295Google Scholar

    [44]

    Esfahani M N, Jabbari M, Xu Y, Soutis C 2021 Mater. Today Commun. 26 101856Google Scholar

    [45]

    Liu X, Zhang G, Zhang Y W 2016 Nano Lett. 16 4954Google Scholar

    [46]

    Wu K, Zhang L, Li F, et al. 2024 Carbon 223 119021Google Scholar

    [47]

    Loh G C, Teo E, Tay B K 2011 Diamond Relat. Mater. 20 1137Google Scholar

    [48]

    Yang B, Yang H, Li T, Yang J, Yang P 2021 Appl. Surf. Sci. 536 147828Google Scholar

    [49]

    Koh Y R, Bin Hoque M S, Ahmad H, et al. 2021 Phys. Rev. Mater. 5 104604Google Scholar

    [50]

    Li Y, Zhao Q, Liu Y, Huang M, Ouyang X P 2024 Phys. Scr. 99 025944Google Scholar

    [51]

    Liu Y, Qiu L, Wang Z, Li H, Feng Y 2024 Composites, Part A 178 108008Google Scholar

    [52]

    Wu S, Wang J, Xie H, Guo Z 2020 Energies 13 5851Google Scholar

    [53]

    Yang Y, Ma J, Yang J, Zhang Y 2022 ACS Appl. Mater. Interfaces 14 45742Google Scholar

    [54]

    Yang C, Wang J, Ma D, Li Z, He Z, Liu L, Fu Z, Yang J Y 2023 Int. J. Heat Mass Transfer 214 124433Google Scholar

  • 图 1  氮化镓(18层)/石墨烯/金刚石(18层)异质结构模型

    Figure 1.  Interface model of gallium nitride (18 layers)/graphene/diamond (18 layers) heterostructure.

    图 2  (a) 热源、热汇能量累计; (b) 沿热流方向的温度分布

    Figure 2.  (a) Accumulation of energy from heat source and heat sink; (b) temperature distribution along the direction of heat flow.

    图 3  温度对单层和三层石墨烯结构界面热导的影响

    Figure 3.  Relationship between the interfacial thermal conductance and temperature for 1-layer graphene and 3-layer graphene structures.

    图 4  温度对单层石墨烯结构PDOS的影响 (a) 氮化镓; (b) 石墨烯; (c) 重叠因子

    Figure 4.  PDOS diagrams of heterostructure with single-layer graphene under temperature change: (a) GaN; (b) graphene; (c) overlap factor.

    图 5  氮化镓/金刚石和石墨烯层数变化对界面热导的影响

    Figure 5.  Relationship between interfacial thermal conductance and the variation in the number of layers of GaN/diamond and graphene.

    图 6  氮化镓/金刚石层数变化对(a) 氮化镓、(b) 石墨烯和(c) 金刚石PDOS的影响; (d) PDOS重叠因子

    Figure 6.  (a) GaN, (b) graphene, and (c) diamond PDOS diagrams for varying layers in the GaN /diamond; (d) overlap factor.

    图 7  石墨烯层数变化对(a)氮化镓、(b) 石墨烯和(c) 金刚石PDOS的影响; (d) 石墨烯PPR

    Figure 7.  (a) GaN, (b) graphene, and (c) diamond PDOS diagrams with varying numbers of graphene layers; (d) PPR diagram.

    图 8  缺陷率对界面热导的影响

    Figure 8.  Relationship between interface thermal conductance and defect concentration.

    图 9  石墨烯缺陷对PDOS的影响 (a) 石墨烯PDOS; (b) 石墨烯PPR

    Figure 9.  Influence of graphene defects on PDOS: (a) PDOS diagram of graphene; (b) PPR of graphene.

    图 10  金刚石缺陷对PDOS的影响 (a) 金刚石PDOS; (b) 重叠因子

    Figure 10.  Influence of diamond defects on PDOS: (a) PDOS diagram of diamond; (b) overlap factor.

    图 11  镓原子缺陷对PDOS的影响 (a) 氮化镓PDOS; (b) 氮化镓PPR

    Figure 11.  Influence of Ga defects on PDOS: (a) PDOS diagram of GaN; (b) PPR diagram of GaN.

    图 12  氮原子缺陷对PDOS的影响 (a) 氮化镓PDOS; (b) 氮化镓PPR; (c) 镓和氮的PPR对比

    Figure 12.  Influence of N defects on PDOS: (a) PDOS diagram of GaN; (b) PPR diagram of GaN; (c) comparative PPR diagram of Ga and N.

    表 1  晶格参数

    Table 1.  Lattice parameters.

    方向氮化镓石墨烯金刚石
    x3.216292.460003.56679
    y5.570784.260843.56679
    z5.239663.56679
    DownLoad: CSV

    表 2  L-J势函数参数

    Table 2.  Lennard-Jones parameters.

    原子1 原子2 $ \varepsilon $/eV $ \sigma $/Å
    C C 0.00361 3.671
    C Ga 0.00905 3.668
    C N 0.00369 3.346
    DownLoad: CSV
  • [1]

    刘庆彬, 蔚翠, 郭建超, 马孟宇, 何泽召, 周闯杰, 高学栋, 余浩, 冯志红 2023 物理学报 72 098104Google Scholar

    Liu Q B, Yu C, Guo J C, Ma M Y, He Z Z, Zhou C J, Gao X D, Yu H, Feng Z H 2023 Acta Phys. Sin. 72 098104Google Scholar

    [2]

    贾鑫, 魏俊俊, 黄亚博, 邵思武, 孔月婵, 刘金龙, 陈良贤, 李成明, 叶海涛 2020 表面技术 49 111

    Jia X, Wei J J, Huang Y B, Shao S W, Kong Y C, Liu J L, Chen L X, Li C M, Ye H T 2020 Surf. Technol. 49 111

    [3]

    Wu Y J, Fang L, Xu Y 2019 npj Comput. Mater. 5 1Google Scholar

    [4]

    冯家驹, 范亚明, 房丹, 邓旭光, 于国浩, 魏志鹏, 张宝顺 2022 人工晶体学报 51 730Google Scholar

    Feng J J, Fan Y M, Fang D, Deng X G, Yu G H, Wei Z P, Zhang B S 2022 J. Synth. Cryst. 51 730Google Scholar

    [5]

    Francis D, Faili F, Babić D, Ejeckam F, Nurmikko A, Maris H 2010 Diamond Relat. Mater. 19 229Google Scholar

    [6]

    Cho J, Francis D, Altman D H, Asheghi M, Goodson K E 2017 J. Appl. Phys. 121 055105Google Scholar

    [7]

    Zhou Y, Anaya J, Pomeroy J, Sun H, Gu X, Xie A, Beam E, Becker M, Grotjohn T A, Lee C, Kuball M 2017 ACS Appl. Mater. Interfaces 9 34416Google Scholar

    [8]

    Huang X, Guo Z 2021 Int. J. Heat Mass Transfer 178 121613Google Scholar

    [9]

    Mu F, Xu B, Wang X, et al. 2022 J. Alloys Compd. 905 164076Google Scholar

    [10]

    Tao L, Theruvakkattil Sreenivasan S, Shahsavari R 2017 ACS Appl. Mater. Interfaces 9 989Google Scholar

    [11]

    Jia X, Huang L, Sun M, Zhao X, Wei J, Li C 2022 Coatings 12 672Google Scholar

    [12]

    Qi Z, Shen W, Li R, Sun X, Li L, Wang Q, Wu G, Liang K 2023 Appl. Surf. Sci. 615 156419Google Scholar

    [13]

    Middleton C, Chandrasekar H, Singh M, et al. 2019 Appl. Phys. Express 12 024003Google Scholar

    [14]

    Wu L, Sun X, Gong F, Luo J, Yin C, Sun Z, Xiao R 2022 Nanomaterials 12 894Google Scholar

    [15]

    Liu F, Zou R, Hu N, Ning H, Yan C, Liu Y, Wu L, Mo F, Fu S 2019 Nanoscale 11 4067Google Scholar

    [16]

    Hu S, Ju S, Shao C, Guo J, Xu B, Ohnishi M, Shiomi J 2021 Mater. Today Phys. 16 100324Google Scholar

    [17]

    Hu M, Poulikakos D 2013 Int. J. Heat Mass Transfer 62 205Google Scholar

    [18]

    Mischke J, Pennings J, Weisenseel E, Kerger P, Rohwerder M, Mertin W, Bacher G 2020 2D Mater. 7 035019Google Scholar

    [19]

    Suntornwipat N, Aitkulova A, Djurberg V, Majdi S 2023 Thin Solid Films 770 139766Google Scholar

    [20]

    Shen B, Ji Z, Lin Q, Gong P, Xuan N, Chen S, Liu H, Huang Z, Xiao T, Sun Z 2022 Chem. Mater. 34 3941Google Scholar

    [21]

    Jiang M, Chen C, Wang P, Guo D, Han S, Li X, Lu S, Hu X 2022 Proc. Natl. Acad. Sci. U. S. A. 119 e2201451119Google Scholar

    [22]

    Li D, Zou W, Jiang W, Peng X, Song S, Qin Q H, Xue J M 2020 Ceram. Int. 46 10885Google Scholar

    [23]

    Badokas K, Kadys A, Mickevičius J, Ignatjev I, Skapas M, Stanionytė S, Radiunas E, Juška G, Malinauskas T 2021 J. Phys. D: Appl. Phys. 54 205103Google Scholar

    [24]

    Barbier C, Largeau L, Gogneau N, et al. 2023 Cryst. Growth Des. 23 6517Google Scholar

    [25]

    Sun H, Simon R, Pomeroy J, Francis D, Faili F, Twitchen D, Kuball M 2015 Appl. Phys. Lett. 106 111906Google Scholar

    [26]

    Wang J, Shen Y, Yang P 2023 Compos. Commun. 40 101616Google Scholar

    [27]

    Tang Y, Liu J K, Yu Z H, Sun L G, Zhu L L 2023 Chin. Phys. B 32 066502Google Scholar

    [28]

    Liu D 2020 Phys. Lett. A 384 126077Google Scholar

    [29]

    Ou B, Yan J, Wang Q, Lu L 2022 Molecules 27 905Google Scholar

    [30]

    Sang L X, Li Z K 2024 Acta Phys. Sin. 73 103105 [桑丽霞, 李志康 2024 物理学报 73 103105]Google Scholar

    Sang L X, Li Z K 2024 Acta Phys. Sin. 73 103105Google Scholar

    [31]

    刘东静, 周福, 陈帅阳, 胡志亮 2023 物理学报 72 157901Google Scholar

    Liu D J, Zhou F, Chen S Y, Hu Z L, 2023 Acta Phys. Sin. 72 157901Google Scholar

    [32]

    Qu G D, Deng Z Y, Guo W, et al. 2023 IEEE Trans. Compon. Packag. Manuf. Technol. 13 816Google Scholar

    [33]

    Wu B Y, Zhou M, Xu D J, Liu J J, Tang R J, Zhang P 2022 Surf. Interfaces 32 102119Google Scholar

    [34]

    Tang Y Q, Zhang Z, Li L, Guo J, Yang P 2022 Int. J. Therm. Sci. 171 107231Google Scholar

    [35]

    Wu X, Han Q 2021 ACS Appl. Mater. Interfaces 13 32564Google Scholar

    [36]

    Huang H, Zhong Y, Cai B, Wang J, Liu Z, Peng Q 2023 Surf. Interfaces 37 102736Google Scholar

    [37]

    Ma D, Zhang L 2020 J. Phys. Condens. Matter 32 425001Google Scholar

    [38]

    Danilchenko B A, Paszkiewicz T, Wolski S, JeŻowski A, Plackowski T 2006 Appl. Phys. Lett. 89 061901Google Scholar

    [39]

    刘东静, 王韶铭, 杨平 2021 物理学报 70 187302Google Scholar

    Liu D J, Wang S M, Yang P 2021 Acta Phys. Sin. 70 187302Google Scholar

    [40]

    Yang N, Luo T, Esfarjani K, et al. 2015 J. Comput. Theor. Nanosci. 12 168Google Scholar

    [41]

    Liu Y, Qiu L, Liu J, Feng Y 2023 Int. J. Heat Mass Transfer 209 124123Google Scholar

    [42]

    Wei N, Zhou C, Li Z, Ou B, Zhao K, Yu P, Li S, Zhao J 2022 Mater. Today Commun. 30 103147Google Scholar

    [43]

    Li M, Zhou H, Zhang Y, Liao Y, Zhou H 2018 Carbon 130 295Google Scholar

    [44]

    Esfahani M N, Jabbari M, Xu Y, Soutis C 2021 Mater. Today Commun. 26 101856Google Scholar

    [45]

    Liu X, Zhang G, Zhang Y W 2016 Nano Lett. 16 4954Google Scholar

    [46]

    Wu K, Zhang L, Li F, et al. 2024 Carbon 223 119021Google Scholar

    [47]

    Loh G C, Teo E, Tay B K 2011 Diamond Relat. Mater. 20 1137Google Scholar

    [48]

    Yang B, Yang H, Li T, Yang J, Yang P 2021 Appl. Surf. Sci. 536 147828Google Scholar

    [49]

    Koh Y R, Bin Hoque M S, Ahmad H, et al. 2021 Phys. Rev. Mater. 5 104604Google Scholar

    [50]

    Li Y, Zhao Q, Liu Y, Huang M, Ouyang X P 2024 Phys. Scr. 99 025944Google Scholar

    [51]

    Liu Y, Qiu L, Wang Z, Li H, Feng Y 2024 Composites, Part A 178 108008Google Scholar

    [52]

    Wu S, Wang J, Xie H, Guo Z 2020 Energies 13 5851Google Scholar

    [53]

    Yang Y, Ma J, Yang J, Zhang Y 2022 ACS Appl. Mater. Interfaces 14 45742Google Scholar

    [54]

    Yang C, Wang J, Ma D, Li Z, He Z, Liu L, Fu Z, Yang J Y 2023 Int. J. Heat Mass Transfer 214 124433Google Scholar

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Metrics
  • Abstract views:  1456
  • PDF Downloads:  47
  • Cited By: 0
Publishing process
  • Received Date:  13 April 2024
  • Accepted Date:  18 May 2024
  • Available Online:  18 June 2024
  • Published Online:  05 August 2024

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