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Owing to the huge degree of freedom of structure, the optimal design of thermoelectric conversion performance of defective graphene nanoribbons is one of the difficulties in the field of materials research. In this paper, the thermoelectric properties of graphene nanoribbons with 5-7 ring defects are optimized by using non-equilibrium Green's function combined with Bayesian algorithm.The results show that the Bayesian algorithm is effective and advantageous in the search of graphene nanoribbons with 5-7 ring defects with high thermoelectric conversion efficiency. It is found that the single configuration with the best thermoelectric conversion performance can be quickly and accurately searched from 32896 candidate structures by using Bayesian algorithm. Even in the least efficient round of optimization, only 1495 candidate structures (about 4.54% of all candidate structures) need to be calculated to find the best configuration. It is also found that the thermoelectric value ZT (about 1.13) of the optimal configuration of 5-7 ring defective graphene nanoribbons (21.162 and 1.23 nm in length and width, respectively) at room temperature is nearly one order of magnitude higher than that of the perfect graphene nanoribbons (about 0.14). This is mainly due to the fact that the 5-7 ring defects effectively inhibit the electron thermal conductivity of the system, which makes the maximum balance between the weakening effect of the power factor and the inhibiting effect of the thermal conductivity (positive effect). The results of this study provide a new feasible scheme for designing and fabricating the graphene nanoribbon thermoelectric devices with excellent thermoelectric conversion efficiencies.
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Keywords:
- thermoelectric conversion /
- 5-7 ring defective graphene nanoribbons /
- Bayes algorithm /
- nonequilibrium Green's function
[1] Zhu T, Liu Y, Fu C, Heremans J P, Snyder J G, Zhao X 2017 Adv. Mater. 29 1605884
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 四进制标志作为结构描述符 (a) “0”代表完美单元; (b) “1”代表5-7环缺陷位置在中间(黄色标注)的缺陷单元; (c) “2”代表5-7环缺陷位置在左边(紫色标注)的缺陷单元; (d) “3”代表5-7环缺陷位置在右边(蓝色标注)的缺陷单元
Figure 1. Quad symbol as structural descriptor: (a) ‘0’represents perfect unit; (b) ‘1’ represents the defect unit with 5-7 ring defects in the middle (marked in yellow); (c) ‘2’ represents the defect unit with the defect position on the left of the 5-7 ring (marked in purple); (d)‘3’ represents the defect unit of rings 5-7 where the defect position is on the right (marked in blue).
图 2 一个5-7环缺陷石墨烯纳米带的原子结构示意图, 分别采用四进制标志作为描述符, 示例结构的描述符集可表示为{01030120}
Figure 2. Schematic diagram of the atomic structure of a 5-7 ring defective graphene nanoribbon, respectively using quaternized symbols as descriptors. The descriptor set of the sample structure can be expressed as {01030120}.
图 3 非平衡格林函数与贝叶斯算法相结合的流程图
Figure 3. Flowchart of the combination of non-equilibrium Green’s function and Bayes algorithm.
图 4 选择不同初始候选结构进行的10轮贝叶斯算法的结果, 其中插图展示的是从所有候选结构计算中获得的ZT值的概率分布
Figure 4. Results of 10 rounds of Bayesian algorithm for selecting different initial candidate structures, in which the illustration shows the probability distribution of ZT values obtained from the calculation of all candidate structures.
图 5 贝叶斯算法和随机优化1495次的ZT值比较(a)以及ZT值的占比分布(b)
Figure 5. Comparison of ZT values between Bayesian algorithm and Random optimization for 1495 times (a) and proportion distribution of ZT values (b).
图 6 完美石墨烯纳米带和最佳5-7环缺陷石墨烯纳米带的电子性质 (a) 电子透射系数; (b) 电子电导; (c) 电子热导; (d) 塞贝克系数
Figure 6. Electronic properties of perfect graphene nanoribbons and best 5-7 ring defective graphene nanoribbons: (a) Electron transmission coefficient; (b) electronic conductivity; (c) electron thermal conductivity; (d) Seebeck coefficient.
图 7 比较原始石墨烯纳米带和最佳5-7环缺陷石墨烯纳米带的声子输运特性 (a) 声子热导; (b) 声子透射系数; (c), (d) 三个典型声子频率下的声子局域态密度图
Figure 7. Phonon transport characteristics of the original graphene nanoribbon and the best 5-7 ring defect graphene nanoribbon are compared: (a) Phonon thermal conductivity; (b) phonon transmission coefficient; (c), (d) local state density diagram at three typical phonon frequencies.
图 8 所有候选结构的平均功率因子、声子热导和ZT值与缺陷个数的关系图
Figure 8. The average power factor, phonon thermal conductance and ZT values of all candidate structures are correlated with the number of defects.
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[1] Zhu T, Liu Y, Fu C, Heremans J P, Snyder J G, Zhao X 2017 Adv. Mater. 29 1605884
Google Scholar
[2] Tritt T M 2011 Annu. Rev. Mater. Res. 41 433
Google Scholar
[3] Zhang X, Zhao L D 2015 J. Materiomics 1 92
Google Scholar
[4] Parrott J E 1982 J. Appl. Phys. 53 9105
Google Scholar
[5] Zheng X F, Liu C X, Yan Y Y, Wang Q 2014 Renewable Sustainable Energy Rev. 32 486
Google Scholar
[6] Wang X, Xu J, Liu G, Fu Y, Liu Z, Tan X, Shao H, Jiang H, Tan T, Jiang J 2016 Appl. Phys. Lett. 108 083902
Google Scholar
[7] Yang J, Xi L, Qiu W, Wu L, Shi X, Chen L, Yang J, Zhang W, Uher C, Singh D J 2016 NPJ. Comput. Mater. 2 1
Google Scholar
[8] Kim W, Zide J, Gossard A, Klenov D, Stemmer S, Shakouri A, Majumdar A 2006 Phys. Rev. Lett. 96 045901
Google Scholar
[9] Wan X, Ma D, Pan D, Yang L, Yang N 2021 Mater. Today Phys. 20 100445
Google Scholar
[10] Miyata K, Atallah T L, Zhu X-Y 2017 Sci. Adv. 3 e1701469
Google Scholar
[11] Sales B, Mandrus D, Chakoumakos B C, Keppens V, Thompson J R 1997 Phys. Rev. B 56 15081
Google Scholar
[12] Jaworski C M, Nielsen M D, Wang H, Girard S N, Cai W, Porter W D, Kanatzidis M G, Heremans J P 2013 Phys. Rev. B 87 045203
Google Scholar
[13] Pei Y, Heinz N A, LaLonde A, Snyder G J 2011 Energy Environ. Sci. 4 3640
Google Scholar
[14] Xie G, Ding D, Zhang G 2018 Adv. Phys. X 3 1480417
Google Scholar
[15] Ouyang T, Hu M 2014 Nanotechnology 25 245401
Google Scholar
[16] Wang T, Zhang C, Snoussi H, Zhang G 2020 Adv. Funct. Mater. 30 1906041
Google Scholar
[17] Wang J, Jiang J W, Park H S 2020 Carbon 157 262
Google Scholar
[18] Wan X, Feng W, Wang Y, Wang H, Zhang X, Deng C, Yang N 2019 Nano Lett. 19 3387
Google Scholar
[19] Yang L, Wan X, Ma D, Jiang Y, Yang N 2021 Phys. Rev. B 103 155305
Google Scholar
[20] Ju S, Shiga T, Feng L, Hou Z, Tsuda K, Shiomi J 2017 Phys. Rev. X 7 021024
Google Scholar
[21] Hu R, Iwamoto S, Feng L, Ju S, Hu S, Ohnishi M, Nagai N, Hirakawa K, Shiomi J 2020 Phys. Rev. X 10 021050
Google Scholar
[22] Yamawaki M, Ohnishi M, Ju S, Shiomi J 2018 Sci. Adv. 4 eaar4192
Google Scholar
[23] Dieb M T, Hou Z, Tsuda K 2018 J. Chem. Phys. 148 241716
Google Scholar
[24] Lu S, Zhou Q, Ouyang Y, Guo Y, Li Q, Wang J 2018 Nat. Commun. 9 3405
Google Scholar
[25] Yuan R, Liu Z, Balachandran P V, Xue D, Zhou Y, Ding X, Sun J, Xue D, Lookman T 2018 Adv. Mater. 30 1702884
Google Scholar
[26] Ju S, Shimizu S, Shiomi J 2020 J. Appl. Phys. 128 161102
Google Scholar
[27] Cui C, Ouyang T, Tang C, He C, Li J, Zhang C, Zhong J 2021 Carbon 176 52
Google Scholar
[28] Hu J, Ruan X, Chen Y P 2009 Nano Lett. 9 2730
Google Scholar
[29] Balandin A A 2011 Nat. Mater. 10 569
Google Scholar
[30] 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
[31] Seol J H, Jo I, Moore A L, Lindsay L, Aitken Z H, Pettes M T, Li X, Yao Z, Huang R, Broido D, Mingo N, Ruoff R S, Shi L 2010 Science 328 213
Google Scholar
[32] Balandin A A, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau C N 2008 Nano Lett. 8 902
Google Scholar
[33] Sevinçli H, Cuniberti G 2010 Phys. Rev. B 81 113401
Google Scholar
[34] Yang K, Chen Y, Xie Y, Ouyang T, Zhong J 2010 EPL-Europhys. Lett. 91 46006
Google Scholar
[35] Sevincli H, Sevik C, Çağın T, Cuniberti G 2013 Sci. Rep. 3 1228
Google Scholar
[36] Chen Y, Jayasekera T, Calzolari A, Kim K W, Nardelli M B 2010 J. Phys. Condens. Mater 22 372202
Google Scholar
[37] Mazzamuto F, Nguyen V H, Apertet Y, Caër C, Chassat C, Saint-Martin J, Dollfus P 2011 Phys. Rev. B 83 235426
Google Scholar
[38] Ouyang Y, Guo J 2009 Appl. Phys. Lett. 94 263107
Google Scholar
[39] Karamitaheri H, Neophytou N, Pourfath M, Faez R, Kosina H 2012 J. Appl. Phys. 111 054501
Google Scholar
[40] Huang J Y, Ding F, Yakobson B I, Lu P, Qi L, Li J 2009 Proc. Natl. Acad. Sci. 106 10103
Google Scholar
[41] Engelund M, Fürst J A, Jauho A P, Brandbyge M 2010 Phys. Rev. Lett. 104 036807
Google Scholar
[42] Cresti A, Carrete J, Okuno H, Wang T, Madsen G K, Mingo N, Pochet P 2020 Carbon 161 259
Google Scholar
[43] Wang J S, Wang J, Lü J T 2008 Eur. Phys. J. B 62 381
Google Scholar
[44] Yamamoto T, Watanabe K 2006 Phys. Rev. Lett. 96 255503
Google Scholar
[45] Li T C, Lu S P 2008 Phys. Rev. B 77 085408
Google Scholar
[46] Yang K, Chen Y, D'Agosta R, Xie Y, Zhong J, Rubio A 2012 Phys. Rev. B 86 045425
Google Scholar
[47] Ueno T, Rhone T D, Hou Z, Mizoguchi T, Tsuda K 2016 Mater. Discovery 4 18
Google Scholar
[48] Terayama K, Tsuda K, Tamura R 2019 Jpn. J. Appl. Phys. 58 098001
Google Scholar
[49] Franckié M, Faist J 2020 Phys. Rev. Appl. 13 034025
Google Scholar
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