First-principles study of thermoelectric performance of monolayer Ge2X4S2 (X = P, As)

Yu Yue; Yang Heng-Yu; Zhou Wu-Xing; Ouyang Tao; Xie Guo-Feng

doi:10.7498/aps.72.20222244

Abstract

Monolayer Ge₂X₄S₂ (X = P, As) are novel two-dimensional (2D) layered materials with suitable optical absorption properties in the visible range and high carrier mobility, so they possess broad application prospects in the photoelectric and thermoelectric fields. In this work, their thermoelectric properties are systematicly evaluated by using the first-principles and Boltzmann transport theory. For monolayer Ge₂As₄S₂ and Ge₂P₄S₂, their smaller phonon group velocities, low relaxation times and the large Grüneisen parameters result in ultra-low lattice thermal conductivities, which are 3.93 W·m^–1·K^–1 and 3.19 W·m^–1·K^–1 in the armchair direction, 4.38 W·m^–1·K^–1 and 3.79 W·m^–1·K^–1 in the zigzag directions at 300 K. Their electronic band structures reveal that the monolayer Ge₂As₄S₂ is a semiconductor with a direct band gap of 1.21 eV, while the single-layer Ge₂P₄S₂ owns an indirect band gap of 1.13 eV. Meanwhile, the twofold degeneracy of valence band provides a large p-type Seebeck coefficient that is 1800 μV·K^–1 for Ge₂P₄S₂ and 2070 μV·K^–1 for Ge₂As₄S₂ in the armchair direction. Obviously, monolayer Ge₂X₄S₂ has smaller lattice thermal conductivity and higher power factor, thus it is worth exploring their thermoelectric properties. The results prove that monolayer Ge₂As₄S₂ and Ge₂P₄S₂ have outstanding thermoelectric performances at 500 K when they are treated by optimal n-type doping. The maximum ZT values of monolayer Ge₂As₄S₂ and Ge₂P₄S₂ are 3.06 (armchair direction) and 3.51 (zigzag direction), as well as 3.21 (armchair direction) and 2.54 (zigzag direction), indicating that monolayer Ge₂X₄S₂ can be a potential candidate in the medium-temperature thermoelectric applications.

Keywords:

Authors and contacts

1.
Hunan Provincial Key Laboratory of Advanced Materials for New Energy Storage and Conversion, School of Materials Science and Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
2.
School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China

Corresponding author: Xie Guo-Feng, xieguofeng@hnust.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874145).

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References

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[7]	Tan Q, Zhao L D, Li J F, Wu C F, Wei T R, Xing Z B, Kanatzidis MG 2014 J. Mater. Chem. A 2 17302 Google Scholar
[8]	Yan X, Poudel B, Ma Y, Liu W S, Joshi G, Wang H, Lan Y C, Wang D Z, Chen G, Ren Z F 2010 Nano Lett. 10 3373 Google Scholar
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[23]	Zeng B W, Long M Q, Zhang X J, Dong Y L, Li M J, Yi Y G, Duan H M 2018 J. Phys. D:Appl. Phys. 51 235302 Google Scholar
[24]	Zhu X L, Liu P F, Zhang J R, Zhang P, Zhou W X, Xie G F 2019 Nanoscale 11 19923 Google Scholar
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[47]	Zhou Z Z, Liu H J, Fan D D, Cao G H, Sheng Y 2019 Phys. Rev. B 99 085410 Google Scholar
[48]	Li W, Carrete J, Mingo N 2013 Appl. Phys. Lett. 103 253103 Google Scholar
[49]	Peng B, Zhang H, Shao H Z, Lu H L, Zhang D W, Zhu H Y 2016 Nano Energy 30 225 Google Scholar
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[51]	Xie G F, Guo Y, Wei X L, Zhang K W, Sun L Z, Zhong J X, Zhang G, Zhang Y W 2014 Appl. Phys. Lett. 104 233901 Google Scholar
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[53]	Wei X L, Wang Y C, Shen Y L, Xie G F, Xiao H P, Zhong J X, Zhang G 2014 Appl. Phys. Lett. 105 103902 Google Scholar
[54]	Zhu L Y, Zhang G, Li B W 2014 Phys. Rev. B 90 214302 Google Scholar
[55]	Li W, Mingo N 2015 Phys. Rev. B 91 144304 Google Scholar
[56]	Pandey T, Polanco C A, Lindsay L, Parker D S 2017 Phys. Rev. B 95 224306 Google Scholar
[57]	Pei Y Z, Wang H, Snyder G J 2012 Adv. Mater. 24 6125 Google Scholar
[58]	Zhu X L, Yang H Y, Zhou W X, Wang T B, Xu N, Xie G F 2020 ACS Appl. Mater. Interfaces 12 36102 Google Scholar
[59]	Cai Y Q, Zhang G, Zhang Y W 2014 J. Am. Chem. Soc. 136 6269 Google Scholar
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Cited By

图 1 (a) 单层Ge₂X₄S₂的几何结构; (b) 对应的布里渊区; (c) 局域电荷密度. 其中紫色、红色以及蓝色球分别是Ge原子、P(As)原子和S原子

Figure 1. (a) The structure of monolayer Ge₂X₄S₂; (b) schematic diagram of the Brillouin zone; (c) electron localization function, where the purple, red and blue balls are Ge atoms, P (As) atoms and S atoms, respectively.

DownLoad: Full-Size Img PowerPoint

图 2 单层Ge₂P₄S₂(a)和 Ge₂As₄S₂(b)的声子色散和对应的声子态密度, 以及它们对应的振动模式(c)

Figure 2. Phonon Spectrum and density of state for monolayer Ge₂P₄S₂ (a) and Ge₂As₄S₂ (b), the corresponding vibration modes of acoustic phonon branches (ZA, TA, and LA) and the lowest optical breach (Opt₁) near and at Г point.

DownLoad: Full-Size Img PowerPoint

图 3 单层Ge₂X₄S₂的晶格热导率与温度的关系(a), 累积晶格热导率与频率的关系(b), 各分支对累积晶格热导率的贡献(c), 累积晶格热导率与声子平均自由程的关系(d)

Figure 3. (a) Lattice thermal conductively with respect to temperature, (b) cumulative lattice thermal conductivity as function of frequency, (c) the contribution of phonon acoustic mode (ZA, TA, LA) and optical modes (Opt) to the total lattice thermal conductivity, (d) cumulative lattice thermal conductivity as a function of mean free path (MFP) of monolayer Ge₂X₄S₂.

DownLoad: Full-Size Img PowerPoint

图 4 单层Ge₂X₄S₂的声子群速度(a), (b), 格林艾森参数(c), (d), 声子弛豫时间和三声子散射相空间(e), (f), 图 (e)和图(f)中的插图为三声子散射相空间

Figure 4. (a), (b) The phonon group velocity, (c), (d) Grüneisen parameters, and (e), (f) phonon relaxation time of monolayer Ge₂X₄S₂. The inset of Fgiure (e) and Figure (f) is three-phonon scattering phase space.

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图 5 单层Ge₂P₄S₂(a) 和Ge₂As₄S₂ (b) 的电子能带结构和对应的电子态密度, 以及价带和导带在费米能级附近的电荷密度 (c)

Figure 5. The electronic band structure and partial density of states for monolayer Ge₂As₄S₂ (a) and Ge₂P₄S₂ (b), the charge density of the valence and conduction bands near the Fermi level (c).

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图 6 单层Ge₂X₄S₂的电子输运参数(a), (b)塞贝克系数; (c), (d)电导率; (e), (f) 电子热导率; (g), (h) 功率因子

Figure 6. Electronic transport parameters of monolayer Ge₂X₄S₂ include the Seebeck coefficient ((a), (b)), electrical conductivity ((c), (d)), electronic thermal conductivity ((e), (f)), and power factor ((g), (h)) as function of the chemical potential.

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图 7 单层Ge₂X₄S₂的ZT值分别与化学势((a)—(d))和载流子浓度((e)—(h))的关系

Figure 7. The ZT values with respect to chemical potential (a)–(d) and carrier concentration (e)–(h) for monolayer Ge₂X₄S₂.

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表 1 弛豫后的结构参数

Table 1. The parameters of optimal structure.

	晶格常数/Å	键长/Å
	晶格常数/Å	Ge—S	Ge—As (P)	As—As (P—P)
Ge₂As₄S₂	7.10	2.48	2.60	2.48
Ge₂P₄S₂	6.77	2.50	2.49	2.21

DownLoad: CSV

表 2 300 K下单层Ge₂X₄S₂的弹性模量C^2D, 形变势常数E_l, 有效质量m^*, 载流子迁移率μ和弛豫时间τ

Table 2. Calculated elastic modulus C^2D, DP constant E_l, effective mass m^*, carrier mobility μ and scattering time τ for electron and hole in monolayer Ge₂X₄S₂ at 300 K.

	方向	类型	C^2D/(J·m^–2)	E_l /eV	m^* /m_e	μ/(cm^–2·V^–1·s^–1)	τ/ps
Ge₂P₄S₂	armchair	electron	55.46	2.04	0.22	3277.22	0.41
	armchair	hole	55.46	3.32	0.65	131.23	0.05
	zigzag	electron	48.44	1.97	0.22	3676.88	0.46
	zigzag	hole	48.44	3.23	0.65	162.32	0.06
Ge₂As₄S₂	armchair	electron	48.94	2.30	0.19	3146.80	0.34
	armchair	hole	48.94	6.56	0.24	220.71	0.03
	zigzag	electron	43.25	2.13	0.19	1943.61	0.21
	zigzag	hole	43.25	6.23	0.24	275.50	0.04

DownLoad: CSV

[1]	Yang J, Xi L L, Qiu W J, Wu L H, Shi X, Chen L D, Yang J H, Zhang W Q, Uher C, Singh D J 2016 npj Comput. Mater. 2 1 Google Scholar
[2]	Ding Z D, An M, Mo S Q, Yu X X, Jin Z L, Liao Y X, Esfarjani K, Lü J T, Shiomi J, Yang N 2019 J. Mater. Chem. A 7 2114 Google Scholar
[3]	Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 16631 Google Scholar
[4]	Hicks L D, Harman T C, Dresselhaus M S 1993 Appl. Phys. Lett. 63 3230 Google Scholar
[5]	Zhao L-D, Chang C, Tan G J, Kanatzidis M G 2016 Energy Environ. Sci. 9 044
[6]	Liu Y C, Wang W X, Yang J, Li S 2018 Adv. Sustainable Syst. 2 1800046 Google Scholar
[7]	Tan Q, Zhao L D, Li J F, Wu C F, Wei T R, Xing Z B, Kanatzidis MG 2014 J. Mater. Chem. A 2 17302 Google Scholar
[8]	Yan X, Poudel B, Ma Y, Liu W S, Joshi G, Wang H, Lan Y C, Wang D Z, Chen G, Ren Z F 2010 Nano Lett. 10 3373 Google Scholar
[9]	Zhao L D, Dravid V P, Kanatzidis M G 2014 Energy Environ. Sci. 7 251 Google Scholar
[10]	Chhowalla M, Shin H S, Eda G, Li L J, Loh K P, Zhang H 2013 Nat. Chem. 5 263 Google Scholar
[11]	Xie W J, He J, Kang H J, Tang X F, Zhu S, Laver M, Wang S Y, Copley J R D, Brown C M, Zhang Q J, Tritt T M 2010 Nano Lett. 10 3283 Google Scholar
[12]	Dresselhaus M S, Dresselhaus G, Sun X, Zhang Z 1999 Phys. Solid State 41 679 Google Scholar
[13]	Rashid Z, Nissimagoudar A S, Li W 2019 Phys. Chem. Chem. Phys. 21 5679 Google Scholar
[14]	Snyder G J, Toberer E S 2008 Nat. Mater. 7 105 Google Scholar
[15]	Guo S D, Li H C 2017 Comput. Mater. Sci. 139 361 Google Scholar
[16]	Zare M, Rameshti B Z, Ghamsari F G, Asgari R 2017 Phys. Rev. B 95 045422 Google Scholar
[17]	Zhang R Q, Zhou Z Z, QI N, Zhao B, Zhang Q K, Zhang Z Y, Chen Z Q 2019 J. Mater. Chem. C 7 14986 Google Scholar
[18]	Ruleova P, Drasar C, Lostak P, Li C-P, Ballikaya S, Uher C 2010 Mater. Chem. Phys. 119 299 Google Scholar
[19]	Yu J B, Sun Q 2018 Appl. Phys. Lett. 112 053901 Google Scholar
[20]	Huang S, Wang Z Y, Xiong R, Yu H Y, Shi J 2019 Nano Energy 62 212 Google Scholar
[21]	Zhu Y L, Yuan J H, Song Y Q, Xue K H, Wang S, Lian C, Li Z N, Xu M, Cheng X M, Miao X S 2019 Int. J. Hydrogen Energy 44 21536 Google Scholar
[22]	Jing Y, MA Y D, LI Y F, Heine T 2017 Nano Lett. 17 1833 Google Scholar
[23]	Zeng B W, Long M Q, Zhang X J, Dong Y L, Li M J, Yi Y G, Duan H M 2018 J. Phys. D:Appl. Phys. 51 235302 Google Scholar
[24]	Zhu X L, Liu P F, Zhang J R, Zhang P, Zhou W X, Xie G F 2019 Nanoscale 11 19923 Google Scholar
[25]	Ouyang T, Jiang E L, Tang C, Li J, He C Y, Zhong J X 2018 J. Mater. Chem. A 6 21532 Google Scholar
[26]	Sun Z H, Yuan K P, Chang Z, Bi S P, Zhang X L, Tang D W 2020 Nanoscale 12 3330 Google Scholar
[27]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[28]	Lee K, Murray É D, Kong L Z, Lundqvist B I, Langreth D C 2010 Phys. Rev. B 82 081101 Google Scholar
[29]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[30]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[31]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106 Google Scholar
[32]	Li W, Lindsay L, Broido D A, Stewart D A, Mingo N 2012 Phys. Rev. B 86 174307 Google Scholar
[33]	Li W, Carrete J, Katcho N A, Mingo N 2014 Comput. Phys. Commun. 185 1747 Google Scholar
[34]	Madsen G K H, Singh D J 2006 Comput. Phys. Commun. 175 67 Google Scholar
[35]	Heyd J, Scuseria G E, Ernzerhof M 2003 J. Chem. Phys. 118 8207 Google Scholar
[36]	Bardeen J, Shockley W 1950 Phys. Rev. 80 72 Google Scholar
[37]	Chaput L, Pécheur P, Scherrer H 2007 Phys. Rev. B 75 045116 Google Scholar
[38]	Price P J 1981 Ann. Phys. 133 217 Google Scholar
[39]	Xi J Y, Long M Q, Tang L, Wanf D, Shuai Z G 2012 Nanoscale 4 4348 Google Scholar
[40]	Becke A D, Edgecombe K E 1990 J. Chem. Phys. 92 5397 Google Scholar
[41]	Nalewajski R F, Köster A M, Escalante S 2005 J. Phys. Chem. A 109 10038 Google Scholar
[42]	Savin A, Nesper R, Wengert S, Wengert S 1997 Angew. Chem. Int. Ed. 36 1808 Google Scholar
[43]	Batsanov S S 2001 Inorg. Mater. 37 871 Google Scholar
[44]	Gao Z B, Tao F, Ren J 2018 Nanoscale 10 12997 Google Scholar
[45]	Gao Z B, Zhang Z F, Liu G, Wang J S 2019 Phys. Chem. Chem. Phys. 21 26033 Google Scholar
[46]	Wee D, Kozinsky B, Marzari N, Fornari M 2010 Phys. Rev. B 81 045204 Google Scholar
[47]	Zhou Z Z, Liu H J, Fan D D, Cao G H, Sheng Y 2019 Phys. Rev. B 99 085410 Google Scholar
[48]	Li W, Carrete J, Mingo N 2013 Appl. Phys. Lett. 103 253103 Google Scholar
[49]	Peng B, Zhang H, Shao H Z, Lu H L, Zhang D W, Zhu H Y 2016 Nano Energy 30 225 Google Scholar
[50]	McGaughey A J H, Landry E S, Sellan D P, Amon C H 2011 Appl. Phys. Lett. 99 131904 Google Scholar
[51]	Xie G F, Guo Y, Wei X L, Zhang K W, Sun L Z, Zhong J X, Zhang G, Zhang Y W 2014 Appl. Phys. Lett. 104 233901 Google Scholar
[52]	Xie G F, Ju Z F, Zhou K K, Wei X L, Guo Z X, Cai Y Q, Zhang G 2018 npj Comput. Mater. 4 1 Google Scholar
[53]	Wei X L, Wang Y C, Shen Y L, Xie G F, Xiao H P, Zhong J X, Zhang G 2014 Appl. Phys. Lett. 105 103902 Google Scholar
[54]	Zhu L Y, Zhang G, Li B W 2014 Phys. Rev. B 90 214302 Google Scholar
[55]	Li W, Mingo N 2015 Phys. Rev. B 91 144304 Google Scholar
[56]	Pandey T, Polanco C A, Lindsay L, Parker D S 2017 Phys. Rev. B 95 224306 Google Scholar
[57]	Pei Y Z, Wang H, Snyder G J 2012 Adv. Mater. 24 6125 Google Scholar
[58]	Zhu X L, Yang H Y, Zhou W X, Wang T B, Xu N, Xie G F 2020 ACS Appl. Mater. Interfaces 12 36102 Google Scholar
[59]	Cai Y Q, Zhang G, Zhang Y W 2014 J. Am. Chem. Soc. 136 6269 Google Scholar
[60]	Zhang L C, Qin G Z, Fang W Z, Cui H J, Zheng Q R, Yan Q B, Su G 2016 Sci. Rep. 6 19830
[61]	Yi W C, Chen X, Wang Z X, Ding Y C, Yang B C, Liu X B 2019 J. Mater. Chem. C 7 7352 Google Scholar
[62]	Heremans J P 2005 Acta Phys. Pol. A 108 609 Google Scholar
[63]	Jonson M, Mahan G D 1980 Phys. Rev. B 21 4223 Google Scholar

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Vol. 72, Issue 7 - 2023-04-05

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First-principles study of thermoelectric performance of monolayer Ge₂X₄S₂ (X = P, As)

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Corresponding author: Xie Guo-Feng, xieguofeng@hnust.cn

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