单层XSe2（X=Zr/Hf）的热电输运特性研究

doi:10.11949/0438-1157.20230622

摘要/Abstract

摘要：

基于第一性原理的密度泛函理论(DFT)结合Boltzmann输运方程(BTE)和形变势理论(DP)系统地研究了单层ZrSe₂和HfSe₂的热电输运特性，分析了二者声子的谐性效应和非谐性效应对其晶格热导率的影响机理，并计算了不同温度下二者的塞贝克系数、功率因数、电导率等热电参数。研究结果表明：在300 K时，单层ZrSe₂和HfSe₂的晶格热导率分别为3.23和4.50 W/(m·K)，且随温升降低；各声子支中横向声学支(TA)对热导率的贡献起主要作用。300 K时n型单层ZrSe₂和HfSe₂的最高ZT分别为1.50和1.95(高于p型)，其中单层HfSe₂表现更佳，因此n型单层HfSe₂是一种良好的热电材料。该研究结果可为基于单层ZrSe₂和HfSe₂的热电设计和应用提供理论指导及借鉴。

关键词: 纳米材料, 计算机模拟, 热传导, 声子, 热电输运特性, 第一性原理

Abstract:

Based on the density functional theory of first-principles, the thermoelectric transport properties of monolayer ZrSe₂ and HfSe₂ are systematically studied by combining Boltzmann transport equation and deformation potential theory. The influence mechanism of phonon harmonic effect and anharmonic effect on lattice thermal conductivity was analyzed, and the thermoelectric parameters such as Seebeck coefficient, power factor and conductivity at different temperatures were calculated. The conclusions indicate that the lattice thermal conductivities of monolayer ZrSe₂ and HfSe₂ are 3.23 and 4.50 W/(m·K) at 300 K respectively, and decrease with the increase of temperature. Meanwhile, the transverse acoustic branch (TA) in phonon branches plays a major role in the thermal conductivity. The highest ZT of n-type single-layer ZrSe₂ and HfSe₂ at 300 K are 1.50 and 1.95 respectively (higher than p-type). Among them, single-layer HfSe₂ performs better, so n-type single-layer HfSe₂ is a good thermoelectric material. Finally, the research results could provide theoretical guidance and reference for thermoelectric design and application based on single-layer ZrSe₂ and HfSe₂.

Key words: nanomaterials, computer simulation, heat conduction, phonon, thermoelectric transport properties, first-principles

中图分类号:

TB 34

刘远超, 关斌, 钟建斌, 徐一帆, 蒋旭浩, 李耑. 单层XSe₂（X=Zr/Hf）的热电输运特性研究[J]. 化工学报, 2023, 74(9): 3968-3978.

Yuanchao LIU, Bin GUAN, Jianbin ZHONG, Yifan XU, Xuhao JIANG, Duan LI. Investigation of thermoelectric transport properties of single-layer XSe₂(X=Zr/Hf)[J]. CIESC Journal, 2023, 74(9): 3968-3978.

图/表 17

图1 单层XSe2 （X=Zr/Hf）的晶体结构

Fig.1 Crystal structure of monolayer XSe2 （X=Zr/Hf）

图2 理论计算流程示意图

Fig.2 Schematic diagram of theoretical calculations process

图3 单层ZrSe2和单层HfSe2的晶格热导率随温度的变化关系

Fig.3 Thermal conductivity of monolayer ZrSe2 and HfSe2 as a function of temperature

图4 不同温度下声子支对单层ZrSe2和HfSe2总热导率的贡献ZA—面外声学支；TA—面内横向声学支；LA—面内纵向声学支；ZO—面外光学支；TO—面内横向光学支；LO—面内纵向光学支

Fig.4 Contribution of phonon branches to the total thermal conductivity of monolayer ZrSe2 and HfSe2 at different temperatures

表1 声子支对单层ZrSe2和单层HfSe2总热导率的贡献情况（300 K）

Table 1 Contributions of phonon branches to the total thermal conductivity of monolayer ZrSe2 and HfSe2 （300 K）

材料	ZA	TA	LA	ZO	TO	LO
ZrSe₂	32.14%	35.40%	23.90%	3.24%	1.30%	0.17%
HfSe₂	31.07%	36.07%	25.62%	2.24%	1.21%	0.15%

图5 单层ZrSe2和单层HfSe2的声子谱

Fig.5 Phonon spectra of monolayer ZrSe2 and HfSe2

图6 300 K时单层ZrSe2和HfSe2的声子群速度随频率的变化关系

Fig.6 Phonon group velocity of monolayer ZrSe2 and HfSe2 as a function of frequency at 300 K

图7 300 K时单层ZrSe2和HfSe2的声子寿命随频率的变化关系

Fig.7 Phonon lifetimes of monolayer ZrSe2 and HfSe2 as a function of frequencyat 300 K

图8 300 K时单层ZrSe2和单层HfSe2的格林艾森参数与频率的变化关系

Fig.8 Grüneisen parameters of monolayer ZrSe2 and HfSe2 as a function of frequency at 300 K

表2 不同温度下各声子支对单层ZrSe2和单层HfSe2的平均格林艾森参数

Table 2 Mean Grüneisen parameters of each phonon branch to monolayer ZrSe2 and HfSe2

材料	平均格林艾森参数
材料	300 K	450 K	600 K	750 K	900 K
ZrSe₂	1.514	1.517	1.518	1.518	1.519
HfSe₂	1.339	1.345	1.347	1.348	1.349

图9 单层ZrSe2和单层HfSe2在300 K时的三声子散射相空间

Fig.9 Three-phonon scattering phase space in monolayer ZrSe2 and HfSe2 at 300 K

图10 单层ZrSe2和单层HfSe2在300 K的声子散射率

Fig.10 Phonon scattering rate of monolayer ZrSe2 and HfSe2 at 300 K

图11 不同温度下单层ZrSe2和单层HfSe2的累积晶格热导率随MFP和频率的变化关系

Fig.11 Cumulative lattice thermal conductivity of monolayer ZrSe2 and HfSe2 as a function of MFP and frequency at different temperatures

图12 单层ZrSe2和HfSe2的能带结构和电子态密度

Fig.12 Energy band structure and electric density of states for monolayer ZrSe2 and HfSe2

图13 单层ZrSe2和HfSe2在300、600和900 K下的电子输运系数

Fig.13 Electron transport coefficient for monolayer ZrSe2 and HfSe2 at 300, 600 and 900 K

图14 单层ZrSe2和HfSe2在不同温度下的ZT随载流子浓度的变化

Fig.14 ZT of monolayer ZrSe2 and HfSe2 as a function of carrier concentration at different temperatures

表3 单层ZrSe2和HfSe2载流子的m* 、El、C2D、 μ和 τ （300 K）

Table 3 m*， El， C2D， μ and τ of carriers in monolayer ZrSe2 and HfSe2 （300 K）

材料	载流子	有效质量		形变势常数E_l/eV	弹性常数C_2D/(J/m²)	载流子迁移率μ/(cm²/(V·s))	弛豫时间τ/(10^-13 s)
材料	载流子	m $Г - M *$ (m_e)	m $M - K *$ (m_e)	形变势常数E_l/eV	弹性常数C_2D/(J/m²)	载流子迁移率μ/(cm²/(V·s))	弛豫时间τ/(10^-13 s)
ZrSe₂	空穴(p-type)	-0.354	-0.331	-7.76	64.24	128.82	0.25
ZrSe₂	电子(n-type)	1.999	0.251	-1.93	64.24	490.33	1.97
HfSe₂	空穴(p-type)	-0.383	-0.368	-7.64	69.11	117.48	0.25
HfSe₂	电子(n-type)	2.231	0.218	-1.40	69.11	1031.54	4.08

表3 单层ZrSe2和HfSe2载流子的m* 、El、C2D、 μ和 τ （300 K）

Table 3 m*， El， C2D， μ and τ of carriers in monolayer ZrSe2 and HfSe2 （300 K）

材料	载流子	有效质量		形变势常数E_l/eV	弹性常数C_2D/(J/m²)	载流子迁移率μ/(cm²/(V·s))	弛豫时间τ/(10^-13 s)
材料	载流子	m $Г - M *$ (m_e)	m $M - K *$ (m_e)	形变势常数E_l/eV	弹性常数C_2D/(J/m²)	载流子迁移率μ/(cm²/(V·s))	弛豫时间τ/(10^-13 s)
ZrSe₂	空穴(p-type)	-0.354	-0.331	-7.76	64.24	128.82	0.25
ZrSe₂	电子(n-type)	1.999	0.251	-1.93	64.24	490.33	1.97
HfSe₂	空穴(p-type)	-0.383	-0.368	-7.64	69.11	117.48	0.25
HfSe₂	电子(n-type)	2.231	0.218	-1.40	69.11	1031.54	4.08

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单层XSe₂（X=Zr/Hf）的热电输运特性研究

Investigation of thermoelectric transport properties of single-layer XSe₂(X=Zr/Hf)

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