并苯分子结的热电性质

谢忠祥; 喻霞; 贾聘真; 陈学坤; 邓元祥; 张勇; 周五星

doi:10.7498/aps.72.20230354

摘要

通过运用非平衡格林函数方法, 研究了基于并苯连接石墨烯纳米带的分子结的热电性质. 主要考虑了并苯分子长度、并苯分子与石墨烯纳米带电极的接触位置对并苯分子结热电参量的影响. 结果发现并苯分子结最大热电优值(ZT_max)对应的热导中声子贡献往往占据主导地位. 当并苯分子的长度增加, 声子热导单调减少, 最终变得与并苯分子长度几乎无关. 当并苯分子与石墨烯纳米带左(右)电极的中(上)部接触时, 对应的ZT_max是最高的, 然而当并苯分子与石墨烯纳米带左(右)电极的中(中)部接触时, 对应的ZT_max是最低的. 当温度增加时, ZT_max有单调增加的趋势, 无关于接触位置. 随着并苯分子长度的增加, ZT_max对应化学势的位置越靠近本征费米能级. 以上发现能对未来设计基于并苯分子结的热电器件提供有价值的参考.

关键词:

Abstract

By using non-equilibrium Green’s function method, we investigate the thermoelectric properties of molecular junctions based on acene-linked graphene nanoribbons. The effects of the length of the acene molecule, the contact position between the acene molecule and graphene nanoribbon electrode on the thermoelectric parameters are mainly considered in this work. It is found that the phonon contribution is dominant in the thermal conductance corresponding to the maximum of the thermoelectric figure of merit (ZT_max). As the length of the acene molecule increases, the phonon thermal conductance decreases monotonically, and eventually becomes almost independent of the acene molecule’ length. When the acene molecules contact the middle (upper) part of the left (right) electrode of graphene nanoribbon, the corresponding ZT_max is the highest. However, when the acene molecules contact the middle (middle) part of the left (right) electrode of graphene nanoribbons, the corresponding ZT_max is the lowest. As the temperature increases, ZT_max has a monotonically increasing tendency, regardless of the contact position. With the increase of the length of the acene molecule, the chemical potential corresponding to ZT_max becomes closer to the intrinsic Fermi level. The above findings may provide the valuable reference for the future design of thermoelectric devices based on the acene molecular junctions.

Keywords:

作者及机构信息

1.
湖南工学院理学院, 衡阳　421002

2.
南华大学数理学院, 衡阳　421001

3.
湖南科技大学材料科学与工程学院, 湘潭　411201

通信作者: 谢忠祥, xiezxhu@163.com ; 周五星, wuxingzhou@hnu.edu.cn

基金项目: 国家自然科学基金(批准号: 12074115, 11874145, 11904161)和湖南省自然科学基金(批准号: 2021JJ30202, 2021JJ30203, 2022JJ30222)资助的课题.

Authors and contacts

1.
School of Science, Hunan Institute of Technology, Hengyang 421002, China

2.
School of Mathematics and Physics, University of South China, Hengyang 421001, China

3.
School of Materials Science and Engineering, Hunan University of Science and Technology, Xiangtan 411201, China

Corresponding author: Xie Zhong-Xiang, xiezxhu@163.com ; Zhou Wu-Xing, wuxingzhou@hnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12074115, 11874145, 11904161) and the Natural Science Foundation of Hunan Province, China (Grant Nos. 2021JJ30202, 2021JJ30203, 2022JJ30222).

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施引文献

图 1 并苯连接石墨烯纳米带形成分子结的几何结构示意图. 并苯分子与石墨烯纳米带电极间的接触位置用整数1, 2, 3表示. 为了方便描述, 统一用AN(mn)来表示几何结构, 其中, “N”代表并苯分子长度(也就是苯环的数目), “m, n”分别表示左电极、右电极与中间并苯分子的接触位置. 例如: 本图可以用A5(22)表示

Fig. 1. Schematic geometric structure of the molecule junction formed by the acene linked with graphene nanoribbons. The contact positions between the acene molecule and graphene nanoribbon electrodes are denoted by the integers 1, 2, and 3. For the sake of description, we uniformly apply “AN(mn)” to represent the geometric structures, where “N” denotes the length of the acene molecule (namely the number of benzene rings), “m, n” denote the contact position between the left, right electrodes and the acene molecule, respectively. For example, this geometric structure is denoted by A5(22).

下载: 全尺寸图片幻灯片

图 2 声子热导$ {\sigma }_{{\rm{p}}} $与温度T的关系. 右下角的插图呈现了低温时声子热导$ {\sigma }_{{\rm{p}}} $与温度T关系的细节行为

Fig. 2. Phononic thermal conductance $ {\sigma }_{{\rm{p}}} $ versus the temperature T. The bottom-right inset shows the detailed behavior of the phononic thermal conductance $ {\sigma }_{{\rm{p}}} $ versus the temperature T at low temperatures.

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图 3 声子输运系数与入射声子能量的关系

Fig. 3. Phononic transmission coefficient versus the energy of incident phonons.

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图 4 A3(31), A3(22), A3(21)和A3(11)的(a)电导、(b) Seebeck系数、(c)热导和(d)ZT. 实线、划线、双点划线和点划线分别对应着A3(31), A3(22), A3(21)和A3(11). 图(c)中, 四条平整的曲线对应着声子热导

Fig. 4. (a) Electrical conductance, (b) Seebeck coefficient, (c) thermal conductance, and (d) ZT of A3(31), A3(22), A3(21)和A3(11). The solid, dashed, double-dot-dashed, and dot-dashed curves correspond to A3(31), A3(22), A3(21), and A3(11), respectively. In panel (c), four flat curves correspond to the phononic thermal conductance.

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图 5 电子输运系数和对应的投影局域态密度. (a1)和(a2), (b1)和(b2), (c1)和(c2), (d1)和(d2)分别对应着A3(31), A3(22), A3(21), A3(11)

Fig. 5. Electronic transmission coefficient and projected local density of states. (a1) and (a2), (b1) and (b2), (c1) and (c2), (d1) and (d2) correspond to A3(31), A3(22), A3(21), A3(11), respectively.

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图 6 $ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $与温度T的关系

Fig. 6. $ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $ versus the temperature T.

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图 7 (a) 电导$ G $和(b) 电子热导$ {\sigma }_{{\rm{e}}} $与化学势$ \mu $的关系. 实线、划线、双点划线、点划线分别对应着并三苯(N = 3)、并五苯(N = 5)、并七苯(N = 7)、并九苯(N = 9). 图(b)中插图表示的是温度为300 K时的声子热导

Fig. 7. (a) Electrical conductance and (b) electronic thermal conductance versus the versus the chemical potential $ \mu $. The solid, dashed, double-dot-dashed, and dot-dashed curves correspond to anthracene (N = 3), pentacene (N = 5), heptacene (N = 7), and nonacene (N = 9). The inset in (b) denotes the phononic thermal conductance at T = 300 K.

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图 8 (a) Seebeck系数和(b) 热电优值ZT与化学势$ \mu $的关系. 实线、划线、双点划线、点划线分别对应着并三苯(N = 3)、并五苯(N = 5)、并七苯(N = 7)、并九苯(N = 9)

Fig. 8. (a) Seebeck coefficient and (b) $ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $versus the versus the chemical potential $ \mu $. The solid, dashed, double-dot-dashed, and dot-dashed curves correspond to anthracene (N = 3), pentacene (N = 5), heptacene (N = 7), and nonacene (N = 9), respectively.

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表 1 最大热电优值ZT($ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $)对应的热电参数

Table 1. Thermoelectric parameters corresponding to the maximum of the thermoelectric figure of merit (ZT_max).

N	接触位置	$ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $	G/mS	S/(mV·K^–1)	σ_p/(nW·K^–1)	σ_e/(nW·K^–1)	σ_p+σ_e/(nW·K^–1)
N = 3	(31)	0.34	0.012	–0.194	0.342	0.044	0.385
	(22)	0.09	0.037	0.065	0.264	0.246	0.510
	(21)	0.51	0.032	0.150	0.242	0.184	0.425
	(11)	0.16	0.046	0.085	0.336	0.293	0.630
N = 5	(31)	0.28	0.015	–0.155	0.314	0.076	0.390
	(22)	0.10	0.030	0.071	0.232	0.217	0.449
	(21)	0.32	0.010	0.174	0.231	0.052	0.283
	(11)	0.14	0.027	–0.092	0.311	0.171	0.483
N = 7	(31)	0.42	0.017	–0.178	0.305	0.080	0.385
	(22)	0.23	0.025	0.103	0.210	0.144	0.350
	(21)	0.44	0.012	0.183	0.221	0.053	0.274
	(11)	0.40	0.017	0.176	0.304	0.086	0.390
N = 9	(31)	0.41	0.023	0.149	0.301	0.069	0.370
	(22)	0.35	0.017	–0.141	0.205	0.086	0.291
	(21)	0.44	0.018	–0.155	0.217	0.076	0.293
	(11)	0.36	0.016	0.163	0.298	0.055	0.353

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map

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[22]	Hochbaum A I, Chen R, Delgado R D, Liang W, Garnett E C, Najarian M, Majumdar A, Yang P 2008 Nature 451 163 Google Scholar
[23]	Chen I J, Burke A, Svilans A, Linke H, Thelander C 2018 Phys. Rev. Lett. 120 177703 Google Scholar
[24]	Ohnishi M, Shiga T, and Shiomi J 2017 Phys. Rev. B 95 155405 Google Scholar
[25]	Zhou G, Li L, Li G H 2010 Appl. Phys. Lett. 97 023112 Google Scholar
[26]	Dash A, Scheunemann D, Kemerink M 2022 Phys. Rev. Appl. 18 064022 Google Scholar
[27]	Huang N T, Nugraha A R T, Saito R 2019 Energies 12 4561 Google Scholar
[28]	Yang N X, Yan Q, Sun Q F 2020 Phys. Rev. B 102 245412 Google Scholar
[29]	Tang H, Wang X, Xiong Y, Zhao Y, Zhang Y, Zhang Y, Yang J, Xu D 2015 Nanoscale 7 6683 Google Scholar
[30]	Fan D D, Liu H J, Cheng L, Jiang P H, Shi J, Tang X F 2014 Appl. Phys. Lett. 105 133113 Google Scholar
[31]	Zberecki K, Wierzbicki M, Barnaś J, Swirkowicz R 2013 Phys. Rev. B 88 115404 Google Scholar
[32]	Liu W, Yan X, Chen G, Ren Z 2012 Nano Energy 1 42 Google Scholar
[33]	Tang J, Chen Y, McCuskey S R, Chen L, Bazan G C, Liang Z 2019 Adv. Electron. Mater. 5 1800943 Google Scholar
[34]	Foster S, Thesberg M, Neophytou N 2017 Phys. Rev. B 96 195425 Google Scholar
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