Thermoelectric properties of acene molecular junctions

Xie Zhong-Xiang; Yu Xia; Jia Pin-Zhen; Chen Xue-Kun; Deng Yuan-Xiang; Zhang Yong; Zhou Wu-Xing

doi:10.7498/aps.72.20230354

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:

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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References

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Cited By

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

Figure 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).

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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

Figure 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

Figure 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

Figure 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)

Figure 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

Figure 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

Figure 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)

Figure 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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[1]	Wu C W, Ren X, Xie G, Zhou W X, Zhang G, Chen K Q 2022 Phys. Rev. Appl. 18 014053 Google Scholar
[2]	Jia P Z, Xie J P, Chen X K, Zhang Y, Yu X, Zeng Y J, Xie Z X, Deng Y X, Zhou W X 2023 J. Phys. Condens. Matter 35 073001 Google Scholar
[3]	Li N, Ren J, Wang L, Zhang G, Hanggi P, Li B 2012 Rev. Mod. Phys. 84 1045 Google Scholar
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[5]	陈晓彬, 段文晖 2015 64 186302 Google Scholar Chen X B, Duan W H 2015 Acta Phys. Sin. 64 186302 Google Scholar
[6]	Jia P Z, Xie Z X, Deng Y X, Zhang Y, Tang L M, Zhou W X, Chen K Q 2022 Appl. Phys. Lett. 121 043901 Google Scholar
[7]	余泽浩, 张力发, 吴靖, 赵云山 2023 72 057301 Google Scholar Yu Z H, Zhang L F, Wu J, Zhao Y S 2023 Acta Phys. Sin. 72 057301 Google Scholar
[8]	Shi X L, Zou J, Chen Z G 2020 Chem. Rev. 120 7399 Google Scholar
[9]	Wang T, Zhang C, Snoussi H, Zhang G 2020 Adv. Funct. Mater. 30 1906041 Google Scholar
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[11]	Zhou Z Z, Liu H J, Fan D D, Cao G H, Sheng C Y 2019 Phys. Rev. B 99 085410 Google Scholar
[12]	Deng L, Chen G M 2021 Nano Energy 80 105448 Google Scholar
[13]	Xie Z X, Tang L M, Pan C N, Li K M, Chen K Q, Duan W 2012 Appl. Phys. Lett. 100 073105 Google Scholar
[14]	Ouyang Y, Guo J 2009 Appl. Phys. Lett. 94 263107 Google Scholar
[15]	王艳, 陈南迪, 杨陈, 曾召益, 胡翠娥, 陈向荣 2021 70 116301 Google Scholar Wang Y, Chen N D, Chen Y, Zeng Z Y, Hu C E, Chen X R 2021 Acta Phys. Sin. 70 116301 Google Scholar
[16]	Jiang J W, Wang J S, Li B 2011 J. Appl. Phys. 109 014326 Google Scholar
[17]	Pan H, Tang L M, Chen K Q 2022 Phys. Rev. B 105 064401 Google Scholar
[18]	Pan H, Ding Z K, Zeng B W, Luo N N, Zeng J, Tang L M, Chen K Q 2023 Phys. Rev. B 107 104303 Google Scholar
[19]	Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727 Google Scholar
[20]	宗志成, 潘东楷, 邓世琛, 万骁, 杨哩娜, 马登科, 杨诺 2023 72 034401 Google Scholar Zong Z C, Pan D K, Deng S C, Wan X, Yang L N, Ma D K, Yang N 2023 Acta Phys. Sin. 72 034401 Google Scholar
[21]	Markussen T, Jauho A P, Brandbyge M 2009 Phys. Rev. Lett. 103 055502 Google Scholar
[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
[35]	Huang W, Wang J S, Liang G 2011 Phys. Rev. B 84 045410 Google Scholar
[36]	Liang L, Cruz-Silva E, Girão E C, Meunier V 2012 Phys. Rev. B 86 115438 Google Scholar
[37]	Liang L, Meunier V 2013 Appl. Phys. Lett. 102 143101 Google Scholar
[38]	Sevinçli H, Cuniberti G 2010 Phys. Rev. B 81 113401 Google Scholar
[39]	Mazzamuto F, Nguyen V H, Apertet Y, Caër C, Chassat C, Martin J S, Dollfus P 2011 Phys. Rev. B 83 235426 Google Scholar
[40]	Karamitaheri H, Neophytou N, Pourfath M, Faez R, Kosina H 2012 J. Appl. Phys. 111 054501 Google Scholar
[41]	Anno Y, Imakita Y, Takei K, Akita S, Arie T 2017 2D Materials 4 025019 Google Scholar
[42]	Xiao H, Cao W, Ouyang T, Xu X, Ding Y C, Zhong J X 2018 Appl. Phys. Lett. 112 233107 Google Scholar
[43]	Dollfus P, Nguyen V H, Saint-Martin J 2015 J. Phys. Condens. Matter 27 133204 Google Scholar
[44]	Xu Y, Li Z, Duan W 2014 Small 10 2182 Google Scholar
[45]	Li D, Gong Y, Chen Y, Lin J, Khan Q, Zhang Y, Li Y, Zhang H, Xie H 2020 Nano-Micro Lett. 12 36 Google Scholar
[46]	Hippalgaonkar K, Wang Y, Ye Y, Qiu D Y, Zhu H, Wang Y, Moore J, Louie S G, Zhang X 2017 Phys. Rev. B 95 115407 Google Scholar
[47]	Zhu X L, Hou C H, Zhang P, Liu P F, Xie G F, Wang B T 2020 J. Phys. Chem. C 124 1812 Google Scholar
[48]	Zhang G, Zhang Y W 2017 J. Mater. Chem. C 5 7684 Google Scholar
[49]	Zhang G, Zhang Y W 2015 Mech. Mater. 91 382 Google Scholar
[50]	Zeng Y J, Wu D, Cao X H, Zhou W X, Tang L M, Chen K Q 2020 Adv. Funct. Mater. 30 1903873 Google Scholar
[51]	Zhou D, Zhang H, Zheng H, Xu Z, Xu H, Guo H, Li P, Tong Y, Hu B, Chen L 2022 Small 18 2200679 Google Scholar
[52]	Hurtado-Gallego J, Sangtarash S, Davidson R, et al. 2022 Nano Lett. 22 948 Google Scholar
[53]	Reddy P, Jang S Y, Segalman R A, Majumdar A 2007 Science 315 1568 Google Scholar
[54]	Miao R, Xu H, Skripnik M, Cui L, et al. 2018 Nano Lett. 18 5666 Google Scholar
[55]	Famili M, Grace I M, Al-Galiby Q, Sadeghi H, Lambert C J 2017 Adv. Funct. Mater. 28 1703135 Google Scholar
[56]	Bürkle M, Hellmuth T J, Pauly F, Asai Y 2015 Phys. Rev. B 91 165419 Google Scholar
[57]	Wu D, Cao X H, Chen S Z, Tang L M, Feng Y X, Chen K Q, Zhou W X 2019 J. Mater. Chem. A 7 19037 Google Scholar
[58]	Finch C, Garcia-Suarez V, Lambert C 2009 Phys. Rev. B 79 033405 Google Scholar
[59]	Klöckner J C, Cuevas J C, Pauly F 2017 Phys. Rev. B 96 24519 Google Scholar
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