Thermoelectric transport properties of two-dimensional materials XTe2 (X = Pd, Pt) via first-principles calculations

Wang Yan; Chen Nan-Di; Yang Chen; Zeng Zhao-Yi; Hu Cui-E; Chen Xiang-Rong

doi:10.7498/aps.70.20201939

Abstract

Developing efficient thermoelectric materials has never lost the attraction due to their promising performances in the energy conversion. The different mechanisms of phonon scattering lead to the various outstanding performances of layered materials in thermoelectric properties. So we investigate the structure, electronic and thermoelectric transport properties of Penta-XTe₂ (X = Pd, Pt) layers based on the density functional theory and Boltzmann transport theory. Those monolayers have a beautiful penta-graphene-like buckled structure with a space group of P2_1/c (No.14). The values of optimized lattice constant a (b) are 6.437 Å (6.145 Å) and 6.423 Å (6.12 Å) for PdTe₂ and PtTe₂ monolayers, respectively. In order to assess the stability, we calculate the phonon dispersion along the high symmetry lines in the Brillouin zone. The second-order harmonic and third-order anharmonic interatomic force constants (IFCs) are calculated by using 5 × 5 × 1 supercell and 4 × 4 × 1 supercell based on the relaxed unit cell. All these results indicate that those monolayers are thermodynamically stable. Energy band structure is essential in obtaining reliable transport properties. So we calculate the band structures of penta-XTe₂. Both PdTe₂ and PtTe₂ are semiconductors with indirect band gaps of 1.24 eV and 1.38 eV, respectively, which are in good agreement with previous experimental and theoretical results.The lattice thermal conductivity of XTe₂ decreases with temperature increasing, but the electronic thermal conductivity varies with temperature in the opposite way exactly. It is found that the thermal conductivity comes from the contribution of the lattice thermal conductivity at low temperature. The room-temperature total thermal conductivities in the x (y) direction of the PdTe₂ and PtTe₂ monolayers are 3.95 W/(m·K) (2.7 W/(m·K)) and 3.27 W/(m·K)(1.04 W/(m·K)), respectively. The contribution of low thermal conductivity indicates that the thermoelectric properties of PtTe₂ monolayer may be better than those of PdTe₂ monolayer.The relaxation time (τ) and carrier mobility (μ) are obtained based on the Bardeen-Shockley deformation potential (DP) theory in two-dimensional materials. Remarkably, they have the higher hole mobility than the electron mobility. The anisotropic electronic transport properties of XTe₂ are obtained by solving Boltzmann transport equation. The electrical conductivity over relaxation time (σ/τ) and Seebeck coefficient (S) contribute to the figure of merit ZT. High Seebeck coefficient (S) with the value larger than 400 μV/K can be found in both p-type and n-type cases, suggesting that the TE performance of XTe₂ may be considerable. The room-temperature largest ZT values of penta-XTe₂ (X = Pd, Pt) at p-type are 0.83 and 2.75 respectively. The monolayer PtTe₂ is a potential thermoelectric material.

Keywords:

Authors and contacts

1.
Chongqing Key Laboratory of Photo-Electric Functional Materials, College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
2.
College of Physical Science and Technology, Sichuan University, Chengdu 610065, China

Corresponding author: Hu Cui-E, cuiehu@126.com

Funds: Project supported by the Natural Science Foundation of Chongqing, China (Grant Nos. cstc2019jcyj-msxmX0501, cstc2020jcyj-msxmX0616) and the Science and Technology Research Project of Chongqing Education Committee, China (Grant Nos. KJ1703044, KJ1703062, KJ1600520)

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References

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图 1 XTe₂ (X = Pd, Pt)单层结构的顶视图和侧视图

Figure 1. Top and side views of XTe₂ (X = Pd, Pt) monolayers

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图 2 PdTe₂ (a)和PtTe₂ (b)的声子色散图

Figure 2. Calculated phonon dispersion curves of PdTe₂ (a)and PtTe₂ (b).

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图 3 PdTe₂ (a)和PtTe₂ (b)单层沿布里渊区高对称方向的能带结构

Figure 3. Calculated energy-band structure of layered PdTe₂ (a) and PtTe₂ (b) along high-symmetry directions of the Brillouin zone.

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图 4 单层PdTe₂(a)和PtTe₂ (b)群速度的三支声学分支(LA, TA 和ZA)随频率的变化

Figure 4. Variation of group velocity of three acoustic branches (ZA, TA, LA) with the frequency of PdTe₂ (a) and PtTe₂ (b) monolayers.

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图 5 室温下PdTe₂(a)和PtTe₂ (b)单层的声子色散率随频率的变化关系, LA, TA 和ZA为三支声学分支

Figure 5. Phonon scattering rates of PdTe₂ (a) and PtTe₂ (b) monolayers at room temperature, where ZA, TA and LA are acoustic branches.

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图 6 (a) PdTe₂和PtTe₂层状材料的晶格热导率沿x, y方向随温度的变化率; PdTe₂ (b)和PtTe₂ (c) 晶格热导率, 电子热导率及总热导率随温度变化的关系

Figure 6. (a) Calculated lattice thermal conductivity of monolayer PdTe₂ and PtTe₂ along the x (dark dashed line) and the y (red dashed line) directions and from 200 K to 800 K with the interval of 100 K; thermal conductivity of PdTe₂ (b) and PtTe₂ (c) at different temperatures, where k_e is electron thermal conductivity, k_l is lattice thermal conductivity, and k_e + k_l is total thermal conductivity.

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图 7 p型掺杂时, PdTe₂(a)和PtTe₂ (b)两种材料在不同温度下沿x, y两个方向σ/τ 随载流子浓度的变化. n型掺杂时, PdTe₂ (c)和PtTe₂ (d)两种材料在不同温度下沿x, y两个方向σ/τ 随载流子浓度的变化

Figure 7. Calculated electrical conductivity of p-type (a), (b) and n-type (c), (b) monolayer PdTe₂ and PtTe₂ along the x and the y directions from 300 K to 900 K with the interval of 300 K.

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图 8 p型掺杂时, PdTe₂(a)和PtTe₂ (b)两种材料在不同温度下沿x, y两个方向的塞贝克系数S随载流子浓度的变化. n型掺杂时, PdTe₂ (c)和PtTe₂ (d)两种材料在不同温度下沿x, y两个方向的塞贝克系数S随载流子浓度的变化

Figure 8. Calculated Seebeck coefficient S of p-type (a), (b) and n-type (c), (d) monolayer PdTe₂ and PtTe₂ along the x and the y directions from 300 to 900 K with the interval of 300 K.

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图 9 p型掺杂时PdTe₂(a)和PtTe₂ (b)两种材料在不同温度下沿x, y两个方向ZT值随载流子浓度的变化. n型掺杂时PdTe₂ (c)和PtTe₂ (d)两种材料在不同温度下沿x, y两个方向ZT值随载流子浓度的变化

Figure 9. Calculated ZT values of p-type (a), (b) and n-type (c), (d) monolayer PdTe₂ and PtTe₂ along the x and the y directions from 300 K to 900 K with the interval of 300 K.

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表 1 XTe₂ (X = Pd, Pt) 单层的晶格常数(a, b)

Table 1. The optimized lattice parameters (a, b) of XTe₂ (X = Pd, Pt) monolayers.

Materials	Results	a/Å	b/Å
PdTe₂	Present	6.437	6.145
PdTe₂	Calc.	6.44^[8], 6.439^[35]	6.14^[8], 6.147^[35]
PtTe₂	Present	6.423	6.12
PtTe₂	Calc.	6.44^[36]	—

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表 2 温度为300 K时, PdTe₂和PtTe₂的有效弹性模量C_2D、形变势常量E_l、有效质量m*、载流子迁移率μ及弛豫时间τ

Table 2. Calculated elastic modulus C_{2 D}, DP constant E_l, effective mass (m*), carrier mobility (μ), and relaxation time (τ) at 300 K of PdTe₂ and PtTe₂ monolayers.

PdTe₂	x		y		PtTe₂	x		y
PdTe₂	p	n	p	n	PtTe₂	p	n	p	n
C_2D/(eV·Å^–2)	4.86		3.90			4.75		5.84
E_l/eV	3.6	5.5	3.2	4.6		2.65	3.83	3.9	6.4
m*/m_e	0.88	0.58	0.88	0.58		0.44	0.33	0.46	0.29
μ/(cm²·V^–1·s^–1)	162	157	168	183		1150	1071	630	546
τ/(10^–14 s)	8.2	5.3	8.5	6.1		28.9	20.3	16.6	8.9

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[1]	Jaziri N, Boughamoura A, Müller J, Mezghani B, Tounsi F, Ismail M 2019 Energy Rep. 6 7 Google Scholar
[2]	Zhu T, Liu Y, Fu C, Heremans J P, Snyder J G, Zhao X 2017 Adv. Mater. 29 1605884 Google Scholar
[3]	Zhou W W, Zhu J X, Li D, Hng H H, Boey F Y C, Ma J Zhang H, Yan Q Y 2009 Adv. Mater. 21 3196 Google Scholar
[4]	Zhao L D, Lo S H, Zhang Y S, Sun H, Tan G J, Uher C, Wolverton C, Dravid V P, Kanatzidis M G 2014 Nature 508 7496
[5]	Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451 Google Scholar
[6]	Balandin A, Wang K L 1998 J. Appl. Phys. 84 6149 Google Scholar
[7]	Zhou Y, Zhao L D 2017 Adv. Mater. 29 1702676 Google Scholar
[8]	Lan Y S, Chen X R, Hu C E, Cheng Y, Chen Q F 2019 J. Mater. Chem. A 7 11134 Google Scholar
[9]	Ghosh K, Singisetti U 2015 J. Appl. Phys. 118 135711 Google Scholar
[10]	Jin Z L, Liao Q W, Fang H S, Liu Z C, Liu W, Ding Z D, Luo T F, Yang N 2015 Sci Rep 5 18342 Google Scholar
[11]	Kumar S, Schwingenschlogl U 2015 Chem. Mat. 27 1278 Google Scholar
[12]	Roldán R, Silva-Guillén J A, López-Sancho M P, Guinea F, Cappelluti E, Ordejón P 2014 Ann. Phys. 526 347 Google Scholar
[13]	Chow W L, Yu P, Liu F C, Hong J H, Wang X L, Zeng Q S, Hsu C H, Zhu C, Zhou J D, Wang X W, Xia J, Yan J X, Chen Yu, Wu D, Yu T, Shen Z X, Lin H, Jin C H, Tay B K, Liu Z 2017 Adv. Mater. 29 1602969 Google Scholar
[14]	张贺, 骆军, 朱航天, 刘泉林, 梁敬魁, 饶光辉 2005 物理学报 8 313 Google Scholar Zhang H, Luo J, Zhu H T, Liu Q L, Liang J K, Rao G H 2005 Acta Phys. Sin. 8 313 Google Scholar
[15]	Ahmad S 2017 Mater. Chem. Phys. 198 162 Google Scholar
[16]	Qin D, Yan P, Ding G Q, Ge X J, Song H Y, Gao G 2018 Sci Rep 8 1
[17]	Lan Y S, Lu Q, Hu C E, Chen X R, Chen Q F 2018 Appl. Phys. A-Mater. Sci. Process. 125 33
[18]	Su T Y, Medina H, Chen Y Z, Wang S W, Lee S S, Shih Y C, Chen C W, Kuo H C, Chuang F C, Chueh Y L 2018 Small 14 1800032 Google Scholar
[19]	Wang M J, Ko T J, Shawkat M S, Han S S, Okogbue E, Chung H S, Bae T S, Sattar S, Gil J, Noh C, Oh K H, Jung Y J, Larsson J A, Jung Y 2020 ACS Appl. Mater. Interfaces 12 10839 Google Scholar
[20]	Sun G, Kürti J, Rajczy P, Kertesz M, Hafner J, Kresse G 2003 J. Mol. Struct. 624 37 Google Scholar
[21]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[22]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[23]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
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[25]	Soulard C, Rocquefelte X, Petit P E, Evain M, Jobic S, Itié J P, Munson P, Koo H J, Whangbo M H 2004 Inorg. Chem. 43 1943 Google Scholar
[26]	Oyedele A D, Yang S, Liang L, Puretzky A, Wang K, Zhang J, Yu P, Pudasaini P R, Ghosh A W, Liu Z, Rouleau C M, Sumpter B G, Chisholm M F, Zhou W, Rack P D, Geohegan D B, Xiao K 2017 J. Am. Chem. Soc. 139 1490 Google Scholar
[27]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[28]	Georg K H M, David J S 2006 Comput. Phys. Commun. 175 67 Google Scholar
[29]	Li W, Carrete J, Katcho N A, Mingo N 2014 Comput. Phys. Commun. 185 1747 Google Scholar
[30]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106 Google Scholar
[31]	Bardeen J, Shockley W 1950 Phys. Rev. 80 72 Google Scholar
[32]	Xi J, Long M, Tang L, Wang D, Shuai Z 2012 Nanoscale 4 4348 Google Scholar
[33]	Huang S, Liu H J, Fan D D, Jiang P H, Liang J H, Cao G H, Shi J 2018 J. Phys. Chem. C 122 4217 Google Scholar
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[37]	Carrete J, Li W, Lindsay L, Broido D A, Gallego L J, Mingo N 2016 Mater. Res. Lett. 4 204 Google Scholar
[38]	Peng B, Zhang D, Zhang H, Shao H, Ni G, Zhu Y, Zhu H 2017 Nanoscale 9 7397 Google Scholar

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Thermoelectric transport properties of two-dimensional materials XTe₂ (X = Pd, Pt) via first-principles calculations

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Corresponding author: Hu Cui-E, cuiehu@126.com

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