基于贝叶斯算法的5-7环缺陷石墨烯纳米带热电性能优化设计

伍静; 崔春凤; 欧阳滔; 唐超

doi:10.7498/aps.72.20222135

摘要

由于结构巨大的自由度, 缺陷石墨烯纳米带热电转换性能的优化设计是材料研究领域的难点之一. 本文利用非平衡格林函数结合贝叶斯算法, 对5-7环缺陷石墨烯纳米带热电性能进行了优化设计. 研究结果表明, 在搜寻具有高热电转换效率5-7环缺陷石墨烯纳米带的过程中, 贝叶斯算法具备有效性和优越性. 计算发现, 利用贝叶斯算法能快速且准确地从32896个候选结构中搜索到具有最佳热电转换性能的唯一构型. 即使在效率最低的一轮优化中, 也仅需要计算1495个候选结构(约占所有候选结构的4.54%)即可寻找到最佳构型. 研究还发现, 在室温下的最佳构型5-7环缺陷石墨烯纳米带(长和宽分别为21.162 nm和1.23 nm)的热电优值ZT (约1.13)较完美石墨烯纳米带(约0.14)提升了近一个量级. 这主要归因于5-7环缺陷有效抑制了系统的电子热导率, 使得功率因子的减弱作用和热导率的抑制作用(正效应)之间达到了最大平衡. 研究结果为设计和制备具有优异热电转换效率的石墨烯纳米带热电器件提供了一种新的可行性方案.

关键词:

Abstract

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.

Keywords:

thermoelectric conversion /
5-7 ring defective graphene nanoribbons /
Bayes algorithm /
nonequilibrium Green's function

作者及机构信息

1.
湘潭大学物理与光电工程学院, 湘潭　411105

2.
湘潭大学, 微纳能源材料与器件湖南省重点实验室, 湘潭　411105

通信作者: 唐超, tang_chao@xtu.edu.cn

基金项目: 基金: 国家自然科学基金(批准号: 11974299)、湖南省青年科技人才项目 (批准号: 2022RC1197)和湖南省教育厅重点项目 (批准号: 20A503, 20K127)资助的课题.

Authors and contacts

1.
School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China

2.
Hunan Key Laboratory for Micro-Nano Energy Materials and Device, Xiangtan University, Xiangtan 411105, China

Corresponding author: Tang Chao, tang_chao@xtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11974299), the Youth Science and Technology Talent Project of Hunan Province, China (Grant No. 2022RC1197), and the Research Foundation of Education Bureau of Hunan Province, China (Grant Nos. 20A503, 20K127).

文章全文 : translate this paragraph

参考文献

[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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施引文献

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

Fig. 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).

下载: 全尺寸图片幻灯片

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}

Fig. 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}.

下载: 全尺寸图片幻灯片

图 3 非平衡格林函数与贝叶斯算法相结合的流程图

Fig. 3. Flowchart of the combination of non-equilibrium Green’s function and Bayes algorithm.

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

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)

Fig. 5. Comparison of ZT values between Bayesian algorithm and Random optimization for 1495 times (a) and proportion distribution of ZT values (b).

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

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

Fig. 8. The average power factor, phonon thermal conductance and ZT values of all candidate structures are correlated with the number of defects.

下载: 全尺寸图片幻灯片

map

[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 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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基于贝叶斯算法的5-7环缺陷石墨烯纳米带热电性能优化设计