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Thermoelectric materials, which can convert wasted heat into electricity, have attracted considerable attention because they provide a solution to energy problems. The Si/Ge superlattices have shown tremendous promise as effective thermoelectric materials. The period lengths of the Si/Ge superlattices can effectively tailor the phonon's transport behaviors and control their thermal conductivities. In this paper, three kinds of Si/Ge superlattices with different period length distributions (uniform, gradient, random) are constructed. The non-equilibrium molecular dynamics (NEMD) method is used to calculate the thermal conductivities of Si/Ge superlattices under the different period length distributions. The effect of the sample’s total length and temperature on the superlattice's thermal conductivity are studied. The simulation result shows that the thermal conductivity of gradient and random periodical Si/Ge superlattices are significantly reduced at room temperature compared with that of the uniform period Si/Ge superlattices. Phonons are transported by wave or particle properties in the different periodical superlattices. The thermal conductivity of uniform period superlattices has an obvious size effect with the increasing of the sample total length. In contrast, the thermal conductivity of gradient, random periodical Si/Ge superlattices are weakly dependent on the sample’s total length. At the same time, temperature is an important factor affecting the heat transport properties. We find that the temperature affects the thermal conductivities of the three kinds of superlattices in different ways. With the increase of the temperature, (i) the thermal conductivity of uniform periodical superlattices shows an obvious temperature effect; (ii) the thermal conductivity of the gradient and random periodical Si/Ge superlattices are nearly unchanged due to the competition between phonon localization weakness and phonon-phonon scattering enhancement. In addition, the phonon densities of states of superlattices with three different periodical length distributions are calculated. We find that in the picture of uniform periodical Si/Ge superlattices, the number of pronounced peaks quickly decreases as the period length increases, particularly at higher frequencies. This indicates that as the period length increases, fewer coherent phonons will be formed over the superlattices. Moreover, the scattering mechanisms of phonons for gradient and random periodical Si/Ge superlattices are basically the same at 100 K and 500 K. These findings provide a developmental way to further reduce the thermal conductivity of superlattices.
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Keywords:
- superlattice /
- phonon /
- period length distribution /
- thermal conductivity
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图 1 不同周期长度分布的超晶格 (a)均匀周期; (b)梯度周期; (c)随机周期
Figure 1. The different period length distribution of superlattices: (a) Uniform period; (c) gradient period; (c) random period.
图 2 NEMD模拟计算热性质的示意图
Figure 2. Schematic diagram of the NEMD model for calculating the thermal properties.
图 3 热导率与周期长度的关系
Figure 3. Thermal conductivity of superlattice as a function of period length.
图 4 不同平均周期长度的均匀超晶格的声子态密度.
Figure 4. The phonon density of states of uniform superlattices with different average period lengths.
图 5 热导率与样品总长度的关系
Figure 5. Thermal conductivity of superlattice as a function of sample total length.
图 6 超晶格热导率随温度的变化
Figure 6. Thermal conductivity of superlattice as a function of temperature.
图 7 超晶格的声子参与率
Figure 7. The participation ratio of superlattices.
图 8 超晶格不同温度条件下的声子态密度: (a) 梯度周期超晶格; (b) 随机周期超晶格
Figure 8. The phonon density of states with different temperatures of superlattice: (a) Gradient period superlattice; (b) random.
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[1] Martín-González M, Caballero-Calero O, Díaz-Chao P 2013 Renew. Sust. Energ. Rev. 24 288
Google Scholar
[2] Feng T L, Ruan X L, Ye Z, Cao B 2015 Phys. Rev. B 91 224301
Google Scholar
[3] Chen Z Y, Wang R F, Wang G Y, Zhou X Y, Wang Z S, Yin C, Hu Q, Zhou B Q, Tang J, Anag R 2018 Chin. Phys. B 27 047202
Google Scholar
[4] Wang K X, Wang J, Li Y, Zou T, Wang X H, Li J B, Cao Z, Shi W J, Xinba Y E 2018 Chin. Phys. B 27 048401
Google Scholar
[5] 郭敬云, 陈少平, 樊文浩, 王雅宁, 吴玉程 2020 物理学报 69 146801
Google Scholar
Guo J Y, Chen S P, Fan W H, Wang Y N, Wu Y C 2020 Acta. Phys. Sin. 69 146801
Google Scholar
[6] 张玉, 吴立华, 曾李骄开, 刘叶烽, 张继业, 邢娟娟, 骆军 2016 物理学报 65 107201
Google Scholar
Zhang Y, Wu L H, Zengli J K, Liu Y F, Zhang J Y, Xing J J, Luo J 2016 Acta. Phys. Sin 65 107201
Google Scholar
[7] Lin K H, Strachan A 2013 Phys. Rev. B 87 115302
Google Scholar
[8] Chen Y F, Li D Y, Lukes J R, Ni Z H, Chen M H 2005 Phys. Rev. B 72 174302
Google Scholar
[9] Giri A, Hopkins P E, Wessel J G, Duda J C 2015 J. Appl. Phys. 118 165303
Google Scholar
[10] Zhou K K, Xu N, Xie G F 2018 Chin. Phys. B 27 026501
Google Scholar
[11] Xiong R, Yang C, Wang Q, Zhang Y, Li X 2019 Int. J. Thermophys. 40 86
Google Scholar
[12] Zhang C W, Zhou H, Zeng Y, Zheng L, Zhan Y L, Bi K D 2019 Int. J. Heat Mass Transf. 132 681
Google Scholar
[13] Samaraweera N, Larkin J M, Chan K L, Mithraratne K 2018 J. Appl. Phys. 123 244303
Google Scholar
[14] Juntunen T, Vanska O, Tittonen I 2019 Phys. Rev. Lett. 122 105901
Google Scholar
[15] Wang Y, Huang H X, Ruan X L 2014 Phys. Rev. B 90 165406
Google Scholar
[16] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[17] Dickey J M, Paskin A 1969 Phys. Rev. 188 1407
Google Scholar
[18] Xie G F, Ding D, Zhang G 2018 Adv. Phys.-X 3 1480417
Google Scholar
[19] Ravichandran J, Yadav A K, Cheaito R, Rossen P B, Soukiassian A, Suresha S J, Duda J C, Foley B M, Lee C-H, Zhu Y, Lichtenberger A W, Moore J E, Muller D A, Schlom D G, Hopkins P E, Majumdar A, Ramesh R, Zurbuchen M A 2014 Nat. Mater. 13 168
Google Scholar
[20] Simkin M V, Mahan G D 2000 Phys. Rev. Lett. 84 927
Google Scholar
[21] Maldovan M 2015 Nat. Mater. 14 667
Google Scholar
[22] Chernatynskiy A, Grimes R W, Zurbuchen M A, Clarke D R, Phillpot S R 2009 Appl. Phys. Lett. 95 161906
Google Scholar
[23] Chen X K, Xie Z X, Zhou W X, Tang L M, Chen K Q 2016 Appl. Phys. Lett. 109 023101
Google Scholar
[24] Luckyanova M N, Mendoza J, Lu H, Song B, Huang S, Zhou J, Li M, Dong Y, Zhou H, Garlow J, Wu L, Kirby B J, Grutter A J, Puretzky A A, Zhu Y, Dresselhaus M S, Gossard A, Chen G 2018 Sci. Adv. 338 936
Google Scholar
[25] Schelling P K, Phillpot S R, Keblinski P 2002 Phys. Rev. B 65 144306
Google Scholar
[26] 刘英光, 边永庆, 韩中合 2020 物理学报 69 033101
Google Scholar
Liu Y G, Bian Y Q, Han Z H 2020 Acta. Phys. Sin. 69 033101
Google Scholar
[27] Chen J, Zhang G, Li B W 2010 Nano Lett. 10 3978
Google Scholar
[28] Liang T, Zhou M, Zhang P, Yuan P, Yang D G 2020 Int. J. Heat Mass Transf. 151 119395
Google Scholar
[29] Zhang Z W, Chen Y P, Xie Y, Zhang S B 2016 Appl. Therm. Eng. 102 1075
Google Scholar
[30] Wang Y, Vallabhaneni A, Hu J, Qiu B, Chen Y P, Ruan X L 2014 Nano Lett. 14 592
Google Scholar
[31] Bodapati A, Schelling P K, Phillpot S R, Keblinski P 2006 Phys. Rev. B 74 245207
Google Scholar
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