Thermoelectric properties of monolayer Cu<sub>2</sub><i>X</i>

Zheng Jian-Jun; Zhang Li-Ping

doi:10.7498/aps.72.20222015

Abstract

Two-dimensional (2D) materials with lower lattice thermal conductivities and high figures of merit are useful for applications in thermoelectric (TE) devices. In this work, the thermoelectric properties of monolayer Cu₂S and Cu₂Se are systematically studied through first-principles and Boltzmann transport theory. The dynamic stability of monolayer Cu₂S and Cu₂Se through elastic constants and phonon dispersions are verified. The results show that monolayer Cu₂S and Cu₂Se have small lattice constants, resulting in lower phonon vibration modes. Phonon transport calculations confirm that monolayer Cu₂Se has lower lattice thermal conductivity (1.93 W/(m·K)) than Cu₂S (3.25 W/(m·K)) at room temperature, which is due to its small Debye temperature and stronger anharmonicity. Moreover, the heavier atomic mass of Se atom effectively reduces the phonon frequency, resulting in an ultra narrow phonon band gap (0.08 THz) and a lower lattice thermal conductivity for monolayer Cu₂Se. The band degeneracy effect at the valence band maximum (VBM) of monolayer Cu₂S and Cu₂Se significantly increase their carrier effective mass, resulting in higher Seebeck coefficients and lower conductivities under p-type doping. The electric transport calculation at room temperature shows that the conductivity of monolayer Cu₂S (Cu₂Se) under n-type doping about 10¹¹ cm^–2 is 2.8×10⁴ S/m (4.5×10⁴ S/m), obviously superior to its conductivity about 2.6×10² S/m (1.6×10³ S/m) under p-type doping. At the optimum doping concentration for monolayer Cu₂S (Cu₂Se), the n-type power factor is 16.5 mW/(m·K²) (25.9 mW/(m·K²)), which is far higher than p-type doping 1.1 mW/m·K² (6.6 mW/(m·K²)). Through the above results, the excellent figure of merit of monolayer Cu₂S (Cu₂Se) under optimal n-type doping at 700 K can approach to 1.85 (2.82), which is higher than 0.38 (1.7) under optimal p-type doping. The excellent thermoelectric properties of monolayer Cu₂S (Cu₂Se) are comparable to those of many promising thermoelectric materials reported recently. Especially, the figure of merit of monolayer Cu₂Se is larger than that of the well-known high-efficient thermoelectric monolayer SnSe (2.32). Therefore, monolayer Cu₂S and Cu₂Se are potential thermoelectric materials with excellent performances and good application prospects. These results provide the theoretical basis for the follow-up experiments to explore the practical applications of 2D thermoelectric semiconductor materials and provide an in-depth insight into the effect of phonon thermal transport on improvement of TE transport properties.

Keywords:

Authors and contacts

School of Materials and Physics, China University of Mining and Technology, Xuzhou 221116, China

Corresponding author: Zhang Li-Ping, 3391@cumt.edu.cn

FullText HTML : translate this paragraph

References

[1]	Yang J, Stabler F R 2009 J. Electron. Mater. 38 1245 Google Scholar
[2]	Sootsman J, Chung D Y, Kanatzidis M 2009 Angew. Chem. 48 8616 Google Scholar
[3]	Rowe D M 1986 Appl. Energy 24 139 Google Scholar
[4]	Sales B 2002 Science 295 1248 Google Scholar
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[6]	Naghavi S S, He J, Xia Y, Wolverton C 2018 Chem. Mater. 30 5639 Google Scholar
[7]	Sajjad M, Singh N, Sattar S, Wolf S D, Schwingenschlögl U 2019 ACS Appl. Energy Mater. 2 3004 Google Scholar
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[11]	Shafique A, Samad A, Shin Y H 2017 Phys. Chem. Chem. Phys. 19 20677 Google Scholar
[12]	Liu X, Zhang D, Wang H, Chen Y, Wang H, Ni Y 2021 Phys. Chem. Chem. Phys. 23 24039 Google Scholar
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[15]	Pei Y, Wang H, Snyder G J. 2012 Adv. Mater. 24 6125 Google Scholar
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图 1 单层Cu原子和X (X = S, Se)原子晶体结构的俯视图(a)和侧视图(b), 蓝色大球体表示Cu原子, 黄色小球代表X (X = S, Se)原子

Figure 1. Top (a) and side (b) views of the crystal structure of monolayer Cu atoms and X (X = S, Se) atoms. Cu atoms are represented as blue large spheres and X (X = S, Se) atoms are represented as yellow small spheres.

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图 2 单层Cu₂S (a)和Cu₂Se (b)的能带及分波态密度

Figure 2. The electronic band structures and projected density of states of monolayer Cu₂S (a) and Cu₂Se (b).

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图 3 单层Cu₂S (a)和Cu₂Se (b)的声子谱和态密度

Figure 3. Phonon dispersions and phonon density of states of the monolayer Cu₂S (a) and Cu₂Se (b).

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图 4 (a) 单层Cu₂X (X =S, Se)的晶格热导率随温度变化趋势; (b) 300 K下单层Cu₂S和Cu₂Se的晶格热导率随平均自由程分布; (c), (d)声子寿命随频率分布, (e), (f) 声子群速度随频率分布; (g), (h) Grüneisen常数随频率分布

Figure 4. (a) Lattice thermal conductivity as a function of the temperature; (b) lattice thermal conductivity of monolayer Cu₂X (X = S, Se)as a function of the MFP at 300 K; (c), (d) phonon lifetime as a function of the phonon frequency; (e), (f) phonon group velocityas a function of the phonon frequency; (g), (h) the Grüneisen parameter as a function of the phonon frequency.

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图 5 单层Cu₂X (X = S, Se)的塞贝克系数((a), (b))、电导率((c), (d))、功率因数((e), (f))、热电优值((g), (h))与p型和n型掺杂下的载流子浓度的关系

Figure 5. Seebeck coefficient ((a), (b)), conductivity ((c), (d)), power factor ((e), (f)), ZT ((g), (h)) as a function of carrier concentration for p-type and n-type doping of monolayer Cu₂X (X = S, Se).

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表 1 晶格常数α、Cu—X (X = S, Se) 键长l、Cu—X (X = S, Se)—Cu键角 θ₁、Cu—X (X = S , Se)—Cu扭转角θ₂、弹性张量C₁₁, C₁₂和C₆₆、带隙E_PBE, E_HSE06由PBE和HSE06泛函计算实现

Table 1. Lattice parameters α, Cu—X (X = S, Se) bond lengths l, Cu—X (X = S, Se)—Cu bond angle θ₁ , Cu—X (X = S, Se)—Cu twist angle θ₂, elastic tensor C₁₁, C₁₂ and C₆₆, electron bandgap E_PBE, E_HSE06 computed by PBE and HSE06.

α/Å l/Å θ₁/(°) θ₂/(°) C₁₁ (C₂₂)/(N·m^–1) C₁₂/(N·m^–1) C₆₆/(N·m^–1) E_PBE/eV E_HSE06/eV

Cu₂S 5.02 2.22 70.78 21.38 34.7 2.3 19.6 0.23 1.15
Cu₂Se 4.99 2.36 66.16 22.08 37.2 7.8 17.5 0.16 1.05

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表 2 室温下部分2D材料的平均声学支的德拜温度$ {\varTheta }_{{\rm{D}}} $和晶格热导率κ_l

Table 2. The Debye temperature $ {\varTheta }_{{\rm{D}}} $ and lattice thermal conductivity $ {\kappa }_{{\rm{l}}} $ of following 2D materials at room temperature.

Cu₂S Cu₂Se PbI₂^[42] CdS^[43] Stanene^[34] Germanene^[34]

$ {\varTheta }_{{\rm{D}}}/{\rm{K}} $ 111.7 82.8 69 260 198 352
$ {\kappa }_{{\rm{l}}} $/(W·(m·K)^–1) 3.25 1.93 0.09 0.78 5.90 2.40

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表 3 单层Cu₂X (X = S, Se)的弹性模量 C_2D、载流子有效质量$ {m}^{*} $ ($ {m}_{0} $), 形变势常数 $ {E}_{{\rm{l}}} $, 载流子迁移率 μ和弛豫时间 τ

Table 3. Elastic modulus C_2D, effective mass $ {m}^{*} $ ($ {m}_{0} $), deformation potential constant $ {E}_{{\rm{l}}} $, carrier mobility μ and relaxation time τ of monolayer Cu₂X (X = S, Se).

Type C_2D/( N·m^–1) $ {m}^{*} $ ${E}_{{\rm{l}}}$/eV μ/(cm²·(V·s)^–1) τ/(10^–14 s)

Cu₂S h 34.7 8.0 1.68 4.1 1.9
e 0.15 2.1 7.4×10³ 63.1
Cu₂Se h 37.2 6.5 0.8 29.3 10.8
e 0.2 1.56 8.1×10³ 92.1

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[1]	Yang J, Stabler F R 2009 J. Electron. Mater. 38 1245 Google Scholar
[2]	Sootsman J, Chung D Y, Kanatzidis M 2009 Angew. Chem. 48 8616 Google Scholar
[3]	Rowe D M 1986 Appl. Energy 24 139 Google Scholar
[4]	Sales B 2002 Science 295 1248 Google Scholar
[5]	Zhang X, Zhao L D 2015 J. Materiomics 1 92 Google Scholar
[6]	Naghavi S S, He J, Xia Y, Wolverton C 2018 Chem. Mater. 30 5639 Google Scholar
[7]	Sajjad M, Singh N, Sattar S, Wolf S D, Schwingenschlögl U 2019 ACS Appl. Energy Mater. 2 3004 Google Scholar
[8]	Huang H H, Xing G, Fan X, Singh D J, Zheng W T 2019 J. Mater. Chem. C 7 5094 Google Scholar
[9]	Wang Y, Gao Z, Zhou J 2019 E Low dimens. Syst. Nanostruct. 108 53 Google Scholar
[10]	Xu B, Xia Q, Zhang J, Ma S, Wang Y, Xu Q, Li J, Wang Y 2020 Comput. Mater. Sci. 177 109588 Google Scholar
[11]	Shafique A, Samad A, Shin Y H 2017 Phys. Chem. Chem. Phys. 19 20677 Google Scholar
[12]	Liu X, Zhang D, Wang H, Chen Y, Wang H, Ni Y 2021 Phys. Chem. Chem. Phys. 23 24039 Google Scholar
[13]	Heremans J P, Jovovic V, Toberer E S, Saramat A, Kurosaki K, Charoenphakdee A, Yamanaka S, Snyder G J 2008 Science 321 554 Google Scholar
[14]	Tan X, Shao H, Hu T, Liu G Q, Ren S F 2015 J. Phys. Condens. Matter 27 095501 Google Scholar
[15]	Pei Y, Wang H, Snyder G J. 2012 Adv. Mater. 24 6125 Google Scholar
[16]	Reshak A H, Khan S A 2014 J. Magn. Magn. Mater. 354 216 Google Scholar
[17]	Pei Y Z, Shi X Y, Lalonde A, Wang H, Chen L D, Snyder G J 2011 Nature 473 66 Google Scholar
[18]	Yu J, Li T, Nie G, Zhang B P, Sun Q 2019 Nanoscale 11 10306 Google Scholar
[19]	Liu W, Shi X, Hong M, Yang L, Moshwan R, Chen Z G, Zou J 2018 J. Mater. Chem. C 6 13225 Google Scholar
[20]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[21]	Wang V, Xu N, Liu J C, Tang G, Geng W T 2021 Comput. Phys. Commun. 267 108033 Google Scholar
[22]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[23]	Heyd J, Scuseria G E, Ernzerhof M 2006 J. Chem. Phys. 124 8207
[24]	Madsen G K H, Carrete J, Verstraete M J 2018 Comput. Phys. Commun. 231 140 Google Scholar
[25]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 1341
[26]	Li W, Carrete J, Katcho N A, Mingo N 2014 Comput. Phys. Commun. 185 1747 Google Scholar
[27]	Li W, Mingo N, Lindsay L, Broido D A, Stewart D A, Katcho N A 2012 Phys. Rev. B 85 195436 Google Scholar
[28]	Chen X, Wang D, Liu X, Li L, Sanyal B 2020 J. Phys. Chem. Lett. 11 2925 Google Scholar
[29]	Born M, Huang K 1955 Am. J. Phys. 23 474
[30]	Zhang F, Zhu B, Guo H, Qiu J, Zheng K, Chen X, Yu J 2021 Appl. Surf. Sci. 550 149230 Google Scholar
[31]	Gao Z, Tao F, Ren J 2018 Nanoscale 10 12997 Google Scholar
[32]	Zhu X L, Zhang J R, Zhou P, Xie W X, Wang G F, Tian B 2019 Nanoscale 11 19923 Google Scholar
[33]	Guo S D, Wang Y H 2017 J. Appl. Phys. 121 034302 Google Scholar
[34]	Peng B, Zhang H, Shao H, Xu Y, Ni G, Zhang R, Zhu H 2016 Phys. Rev. B 94 245420 Google Scholar
[35]	Zhang W, Zhang X Q, Liu L, Wang Z, Li Z G 2021 Chin. Phys. B 30 526
[36]	Ziman J M 1963 International Series of Monographs on Physics (Oxford: Clarendon) p168
[37]	Carrete J, Li W, Lindsay L, Broido D A, Gallego L J, Mingo N 2016 Mater. Res. Lett. 4 204 Google Scholar
[38]	Slack G A 1973 J. Phys. Chem. Solids 34 321 Google Scholar
[39]	Broido D A, Ward A, Mingo N 2005 Phys. Rev. B 72 014308 Google Scholar
[40]	Lv B, Hu X, Liu X, Zhang Z, Song J, Luo Z 2020 Phys. Chem. Chem. Phys. 22 17833 Google Scholar
[41]	Morelli D T, Heremans J P 2002 Appl. Phys. Lett. 81 5126 Google Scholar
[42]	Bolen E, Deligoz E, Ozisik H 2021 Solid State Commun. 327 114223 Google Scholar
[43]	Mohanta M K, Sarkar A D 2020 ACS Appl. Mater. 12 18123 Google Scholar
[44]	Peng B, Zhang H, Shao H, Xu K, Ni G, Li J, Zhu H, Soukoulis C M 2018 J. Mater. Chem. A 6 2018 Google Scholar
[45]	王宁 2022 博士论文 (成都: 电子科技大学) Wang N 2022 Ph. D Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
[46]	Qiu P, Agne M T, Liu Y, Zhu Y, Chen H, Mao T, Yang J, Zhang W, Haile S M, Zeier W G, Janek J, Uher C, Shi X, Chen L, Snyder G J 2018 Nat. Commun. 9 2910 Google Scholar
[47]	Brown D R, Day T, Caillat T, Snyder G J 2013 J. Electron. Mater. 42 2014 Google Scholar
[48]	Miyatani S Y, Suzuki Y 1953 J. Phys. Soc. Jpn. 8 680 Google Scholar
[49]	Maassen J, Lundstrom M 2013 Appl. Phys. Lett. 102 093103 Google Scholar
[50]	Sun Z H, Yuan K P, Chang Z, Bi S P, Zhang X L, Tang D W 2020 Nanoscale 12 3330 Google Scholar

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Thermoelectric properties of monolayer Cu₂X

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	α/Å	l/Å	θ₁/(°)	θ₂/(°)	C₁₁ (C₂₂)/(N·m^–1)	C₁₂/(N·m^–1)	C₆₆/(N·m^–1)	E_PBE/eV	E_HSE06/eV
Cu₂S	5.02	2.22	70.78	21.38	34.7	2.3	19.6	0.23	1.15
Cu₂Se	4.99	2.36	66.16	22.08	37.2	7.8	17.5	0.16	1.05

	Cu₂S	Cu₂Se	PbI₂^[42]	CdS^[43]	Stanene^[34]	Germanene^[34]
$ {\varTheta }_{{\rm{D}}}/{\rm{K}} $	111.7	82.8	69	260	198	352
$ {\kappa }_{{\rm{l}}} $/(W·(m·K)^–1)	3.25	1.93	0.09	0.78	5.90	2.40

	Type	C_2D/( N·m^–1)	$ {m}^{*} $	${E}_{{\rm{l}}}$/eV	μ/(cm²·(V·s)^–1)	τ/(10^–14 s)
Cu₂S	h	34.7	8.0	1.68	4.1	1.9
Cu₂S	e	34.7	0.15	2.1	7.4×10³	63.1
Cu₂Se	h	37.2	6.5	0.8	29.3	10.8
Cu₂Se	e	37.2	0.2	1.56	8.1×10³	92.1

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Thermoelectric properties of monolayer Cu2X

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Corresponding author: Zhang Li-Ping, 3391@cumt.edu.cn

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Thermoelectric properties of monolayer Cu₂X