CuBiI三元化合物晶体结构预测及光电性能第一性原理研究

王兰; 程思远; 曾航航; 谢聪伟; 龚元昊; 郑植; 范晓丽

doi:10.7498/aps.70.20210145

摘要

作为潜在的新型光电材料, 三元金属卤化物一直以来广受关注. 本文通过基于遗传算法的晶体结构预测软件USPEX, 对三元CuBiI化合物(CuBi₂I₇, Cu₂BiI₅, Cu₂BiI₇, Cu₃BiI₆, Cu₃Bi₂I₉, CuBi₃I₁₀, Cu₄BiI₇)在常压、绝对零度下的稳定晶体结构进行了全局搜索. 采用基于密度泛函理论的第一性原理计算方法, 计算了所发现结构的形成能、弹性系数和声子色散谱, 确定了12个具有良好的热力学、弹性力学及晶格动力学稳定性的CuBiI化合物结构. 这12个潜在稳定结构的理论带隙为1.13—3.09 eV, 其中CuBi₂I₇, Cu₂BiI₅, Cu₂BiI₇和Cu₄BiI₇在可见光区域表现出极强的光吸收能力(光吸收系数高于4 × 10⁵ cm^–1), 光电转换效率最高可达31.63%. 计算结果表明三元金属卤化物CuBiI具有成为高性能太阳能电池吸收层材料的潜力.

关键词:

Abstract

Ternary metal halides have attracted much attention as a new potential photoelectric material due to their ultra-high photoelectric conversion efficiencies. In this paper, USPEX, a crystal structure prediction software based on genetic algorithm, is used to investigate the potential crystal structures of ternary CuBiI compounds (CuBi₂I₇, Cu₂BiI₅, Cu₂BiI₇,Cu₃BiI₆, Cu₃Bi₂I₉, CuBi₃I₁₀, and Cu₄BiI₇) at atmospheric pressure and absolute zero temperature. Based on the density functional theory, the formation energies, elastic coefficients, and phonon dispersion curves of the predicted structures are calculated. The twelve stable CuBiI compounds with good thermodynamic, dynamical and mechanical stabilities are identified. The twelve crystal structures of CuBiI compound feature mainly the co-existence of Cu—I and Bi—I bonds and coordination polyhedrons of I atoms. The band gaps of twelve structures, calculated by HSE06 method, are 1.13–3.09 eV, indicating that the stoichiometric ratio affects the band gap obviously. Among them, the band gaps of Cu₂BiI₅-P1, Cu₂BiI₇-P1 and Cu₂BiI₇-P1-II are relatively small, close to the optimal band gap value for light absorption (1.40 eV), demonstrating that these compounds are suitable for serving as light absorbing materials in solar cells. The distribution of density of state (DOS) indicates that the top of the valence band of CuBiI compound is attributed to the hybridized Cu-3d and I-5p orbitals; the bottom of the conduction band of Cu₃BiI₆-R3 comes mainly from the Bi-6p and I-5p orbitals, and Cu-3d contributes little; the conduction band bottom of Cu₂BiI₇ is mainly from the I-5p orbital, and the Cu-3d has little contribution. The bottoms of the conduction band of other structures originate mainly from the hybridized Bi-6p and I-5p orbitals. Electronic localization function and Bader charge analysis show that the Cu—I and Bi—I bonds have more ionic features and less covalent natures. The DOS distribution also confirms the covalent interaction of Cu/Bi-I. In addition, the CuBiI ternary compounds have extremely strong light absorption capacities (light absorption coefficient higher than 4 × 10⁵ cm^–1) in the high-energy region of visible light and high power conversion efficiency (31.63%), indicating that the CuBiI ternary compounds have the potential to be an excellent photoelectric absorption material. Our investigation suggests the further study and potential applications of CuBiI ternary compound as absorber materials in solar cell.

Keywords:

作者及机构信息

1.
西北工业大学材料学院, 凝固技术国家重点实验室, 西安　710072

2.
西北工业大学玛丽女王工程学院, 西安　710127

3.
许昌大学先进材料与能源学院, 表面微纳米材料研究所, 河南省微纳米储能与转换材料重点实验室, 许昌　461000

通信作者: 范晓丽, xlfan@nwpu.edu.cn

基金项目: 国家重点研发计划(批准号: 2018YFB0703800)、陕西省杰出青年自然科学基金(批准号: 2019JC-10)和西北工业大学研究生创新创造种子基金(批准号: CX2020083)资助的课题

Authors and contacts

1.
State Key Laboratory of Solidification Processing, School of Material Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China

2.
Queen Mary University of London Engineering School, Northwestern Polytechnical University, Xi’an 710127, China

3.
Key Laboratory for Micro-Nano Energy Storage and Conversion Materials of Henan Province, Institute of Surface Micro and Nano Materials, College of Advanced Materials and Energy, Xuchang University, Xuchang 461000, China

Corresponding author: Fan Xiao-Li, xlfan@nwpu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2018YFB0703800), the Natural Science Fund for Distinguished Yong Scholars of Shaanxi Province, China (Grant No. 2019JC-10), and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University, China (Grant No. CX2020083)

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施引文献

图 1 12个CuBiI三元化合物结构的声子色散谱图　(a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II

Fig. 1. Phonon dispersion spectra for the 12 structures of CuBiI ternary compound: (a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II.

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图 2 CuBi₂I₇-P1的晶体结构　(a) 主视图; (b) 俯视图. CuBi₂I₇-P1-II的晶体结构 (c) 主视图; (d) 俯视图

Fig. 2. Crystal structure of CuBi₂I₇-P1: (a) Front view; (b) top view. Crystal structure of CuBi₂I₇-P1-II: (c) Front view; (d) top view

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图 3 Cu₂BiI₅-P1的晶体结构　(a) 主视图; (b) 俯视图. Cu₂BiI₅-Cm的晶体结构 (c) 主视图; (d) 俯视图

Fig. 3. Crystal structure of Cu₂BiI₅-P1: (a) Front view; (b) top view. Crystal structure of Cu₂BiI₅-Cm: (c) Front view; (d) top view.

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图 4 Cu₃BiI₆-P3的晶体结构　(a) 主视图; (b) 俯视图. Cu₃BiI₆-R3的晶体结构 (c) 主视图; (d) 俯视图

Fig. 4. Crystal structure of Cu₃BiI₆-P3: (a) Front view; (b) top view. Crystal structure of Cu₃BiI₆-R3: (c) Front view; (d) top view.

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图 5 Cu₄BiI₇-P1的晶体结构　(a) 主视图; (b) 俯视图. Cu₄BiI₇-P3的晶体结构 (c) 主视图; (d) 俯视图

Fig. 5. Crystal structure of Cu₄BiI₇-P1: (a) Front view; (b) top view. Crystal structure of Cu₄BiI₇-P3: (c) Front view; (d) top view.

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图 6 Cu₃Bi₂I₉-P1的晶体结构　(a) 主视图; (b) 俯视图. CuBi₃I₁₀-P1的晶体结构 (c) 主视图; (d) 俯视图

Fig. 6. Crystal structure of Cu₃Bi₂I₉-P1: (a) Front view; (b) top view. Crystal structure of CuBi₃I₁₀-P1: (c) Front view; (d) top view

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图 7 Cu₂BiI₇-P1的晶体结构　(a) 主视图; (b) 俯视图. Cu₂BiI₇-P1-II的晶体结构 (c) 主视图; (d) 俯视图

Fig. 7. Crystal structure of Cu₂BiI₇-P1: (a) Front view; (b) top view. Crystal structure of Cu₂BiI₇-P1-II: (c) Front view; (d) top view

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图 8 12个CuBiI三元化合物结构的能带结构图 (红色, HSE06方法计算结果; 蓝色, PBE方法计算结果)　(a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II

Fig. 8. Band structure for the 12 structures of CuBiI ternary compound calculated by the PBE (blue lines) and HSE06 (red lines) methods: (a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II.

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图 9 12个CuBiI三元化合物结构的总态密度、投影态密度图以及价带顶、导带底(从左到右或从上到下)的电荷密度分布图　(a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II

Fig. 9. Total density of state (TDOS), projection density of state (PDOS) and charge density distribution (Left to right or top to bottom) at CBM and VBM for the 12 structures of CuBiI ternary compound: (a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II.

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图 10 12个CuBiI三元化合物结构的电子局域函数分布图　(a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II

Fig. 10. Electron localization function (ELF) for the 12 structures of CuBiI ternary compound: (a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P3; (h) Cu₄BiI₇-P1; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II.

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图 11 12个CuBiI三元化合物结构的光吸收谱, 灰色区域代表可见光能量范围(1.64—3.19 eV)　(a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II; (c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II

Fig. 11. Optical absorption spectrum for the 12 structures of CuBiI ternary compound. The gray area represents the Visible energy range (1.64–3.19 eV): (a) CuBi₂I₇-P1; (b) CuBi₂I₇-P1-II;(c) Cu₂BiI₅-P1; (d) Cu₂BiI₅-Cm; (e) Cu₃BiI₆-P3; (f) Cu₃BiI₆-R3; (g) Cu₄BiI₇-P1; (h) Cu₄BiI₇-P3; (i) Cu₃Bi₂I₉-P1; (j) CuBi₃I₁₀-P1; (k) Cu₂BiI₇-P1; (l) Cu₂BiI₇-P1-II.

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图 12 SLME方法预测的12个CuBiI三元化合物结构的光电转换效率与吸收层厚度的关系

Fig. 12. Photoelectric conversion efficiency of 12 structures of CuBiI ternary compound with respect to the absorption layer thickness predicted by SLME method.

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表 1 12个CuBiI三元化合物结构的结构名称、空间群、晶胞内原子数、体积及形成能

Table 1. Structure name, space group, number of atoms per unit cell, volume of the unit cell and formation energy for the 12 structures of CuBiI ternary compound.

Structure name	Space group	Number of/ (atoms·unit cell^–1)	Volume/ (Å³·unit cell^–1)	${{E} }_{\rm{form} }$/ (eV·atoms^–1)	Structure name	Space group	Number of/ (atoms·unit cell^–1)	Volume/ (Å³·unit cell^–1)	${{E} }_{\rm{form} }$/ (eV·atoms^–1)
CuBi₂I₇-P1	P1	10	474.24	–0.362	CuBi₂I₇-P1-II	P1	10	465.35	–0.385
Cu₂BiI₅-P1	P1	8	295.03	–0.287	Cu₂BiI₅-Cm	Cm	16	742.54	–0.290
Cu₃BiI₆-P3	P3	10	404.63	–0.265	Cu₃BiI₆-R3	R3	30	1318.62	–0.244
Cu₄BiI₇-P1	P1	12	428.29	–0.237	Cu₄BiI₇-P3	P3	12	451.33	–0.231
Cu₃Bi₂I₉-P1	P1	14	645.41	–0.294	CuBi₃I₁₀-P1	P1	14	691.08	–0.402
Cu₂BiI₇-P1	P1	10	420.79	–0.225	Cu₂BiI₇-P1-II	P1	10	420.68	–0.226

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表 2 12个CuBiI三元化合物结构的弹性系数(C_ij)

Table 2. Calculated elastic constants for the 12 structures of CuBiI ternary compound.

C_ij/GPa	CuBi₂I₇-P1	CuBi₂I₇-P1-II	Cu₂BiI₅-P1	Cu₂BiI₅-Cm	Cu₃BiI₆-P3	Cu₃BiI₆-R3	Cu₄BiI₇-P1	Cu₄BiI₇-P3	Cu₃Bi₂I₉-P1	CuBi₃I₁₀-P1	Cu₂BiI₇-P1	Cu₂BiI₇-P1-II
C₁₁	8.34	9.03	39.90	4.76	11.99	17.59	23.63	32.25	17.16	2.82	9.71	3.12
C₂₂	12.61	14.16	29.93	35.09	—	—	18.34	—	20.42	9.34	14.12	10.34
C₃₃	8.35	9.00	35.71	5.64	5.92	5.05	23.61	8.90	11.86	8.62	14.43	26.51
C₄₄	3.52	3.62	10.18	1.73	1.01	3.53	6.87	1.41	3.91	3.27	6.46	7.16
C₅₅	3.74	2.99	9.96	—	—	—	7.83	—	3.56	1.91	3.73	4.52
C₆₆	2.41	4.43	6.77	1.24	4.42	6.13	8.72	11.26	6.01	1.93	3.13	3.18
C₁₂	4.73	4.45	9.13	1.63	3.01	5.22	4.56	9.71	6.13	1.96	4.71	3.19
C₁₃	2.61	2.57	14.13	2.77	1.33	2.99	7.76	3.30	3.14	2.11	5.61	6.45
C₁₄	–2.07	–0.04	4.02	—	0.04	1.7	–1.84	0.28	0.51	–0.63	–0.17	–0.32
C₁₅	0.18	0.21	0.18	–0.67	–0.15	–0.38	2.85	0.06	–0.79	–0.21	–2.11	0.54
C₁₆	0.79	2.27	0.12	—	—	—	–0.27	—	–0.51	0.86	–1.73	–0.32
C₂₃	2.69	2.76	14.94	2.42	—	—	5.49	—	6.79	2.98	7.51	7.18
C₂₄	–2.53	0.12	5.64	—	—	—	–0.99	—	2.280	–0.05	–2.43	2.11
C₂₅	0.28	0.16	0.17	–0.12	—	—	2.68	—	0.49	–0.09	–3.12	1.54
C₂₆	0.49	1.72	–0.02	—	—	—	0.04	—	0.41	1.47	1.35	1.01
C₃₄	–1.69	–0.27	5.74	—	—	—	–0.56	—	2.53	–0.89	–1.51	0.36
C₃₅	–1.76	0.39	0.12	–0.90	—	—	3.43	—	–0.21	–2.38	–3.43	1.76
C₃₆	1.47	1.17	–0.04	—	—	—	1.72	—	0.80	0.81	0.13	–0.48
C₄₅	–0.41	0.83	0.13	—	—	—	–0.47	—	0.21	0.85	1.26	0.19
C₄₆	–0.10	0.42	0.01	0.12	—	—	1.75	—	0.34	–0.62	–2.13	–0.69
C₅₆	–0.58	–0.29	1.485	—	—	—	–1.07	—	0.94	–0.53	0.82	0.72

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表 3 12个CuBiI三元化合物结构的晶格常数以及Cu/Bi—I键长

Table 3. Lattice constants and Cu/Bi—I bond length for the 12 structures of CuBiI ternary compound.

Structure name	a/Å	b/Å	c/Å	α/(°)	β/(°)	γ/(°)	Cu—I/Å	Bi—I/Å
CuBi₂I₇-P1	7.93	7.94	7.92	97.67	82.58	76.98	2.53—2.55	3.02—3.32
CuBi₂I₇-P1-II	8.05	7.85	7.75	97.64	100.86	100.78	2.54—2.55	3.03—3.22
Cu₂BiI₅-P1	4.42	7.62	9.57	95.94	103.35	106.82	2.59—2.67	3.09—3.18
Cu₂BiI₅-Cm	16.64	4.33	12.22	90.00	122.51	90.00	2.57—2.72	2.84—3.50
Cu₃BiI₆-P3	7.89	7.89	7.54	90.00	90.00	120.00	2.54—2.61	3.02—3.29
Cu₃BiI₆-R3	11.40	11.40	11.72	90.00	90.00	120.00	2.52—2.56	3.05—3.35
Cu₄BiI₇-P1	7.61	7.79	7.64	101.68	100.50	98.22	2.56—2.74	3.06—3.22
Cu₄BiI₇-P3	8.32	8.32	7.52	90.00	90.00	120.00	2.64—2.68	3.09—3.22
Cu₃Bi₂I₉-P1	7.67	8.59	9.85	84.58	88.98	86.74	2.55—2.70	2.99—3.28
CuBi₃I₁₀-P1	9.46	10.12	7.85	103.09	106.70	77.25	2.53—2.54	2.99—3.32
Cu₂BiI₇-P1	7.33	7.90	7.92	104.09	108.49	81.74	2.59—2.64	3.05—3.34
Cu₂BiI₇-P1-II	9.00	7.78	7.20	109.91	89.24	64.61	2.58—2.70	2.98—3.34

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表 4 12个CuBiI三元化合物结构的带隙值(HSE06和PBE方法计算结果), 价带顶与导带底位置, Bader电荷转移以及SLME (spectroscopic limited maximum efficiency)值

Table 4. Band gaps (E_g) calculated by the HSE06 and PBE method, positions of VBM and CBM, Bader charge and the spectroscopic limited maximum efficiency (SLME) values for the 12 structures of CuBiI ternary compound.

Structure name	E_g/eV		VBM	CBM	Bader charge			SLME/%
Structure name	HSE06	PBE	VBM	CBM	Cu/(e·atom^–1)	Bi/(e·atom^–1)	I/(e·atom^–1)	SLME/%
CuBi₂I₇-P1	2.39	1.48	0 0 0	0 0 0	0.33	1.08	–0.36	10.75
CuBi₂I₇-P1-II	2.13	1.21	0 0 0	0 0.5 0	0.33	1.09	–0.36	9.50
Cu₂BiI₅-P1	1.56	0.84	0 0 0.5	0 0.5 0	0.34	1.04	–0.34	22.20
Cu₂BiI₅-Cm	1.87	0.89	0 0 0	0 0 0	0.29	1.07	–0.33	7.50
Cu₃BiI₆-P3	3.09	1.97	0.05 0 0	0 0 0.5	0.29	1.08	–0.33	2.86
Cu₃BiI₆-R3	2.81	1.85	0 0 0	0.5 0 0.5	0.31	1.01	–0.32	5.49
Cu₄BiI₇-P1	2.19	1.22	0 0 0	0 0.5 0	0.30	1.03	–0.32	15.77
Cu₄BiI₇-P3	2.21	1.21	0 0 0.06	0 0 0.5	0.32	1.06	–0.33	13.61
Cu₃Bi₂I₉-P1	2.03	1.17	0 0 0.5	0 0 0.5	0.34	1.02	–0.34	19.02
CuBi₃I₁₀-P1	2.36	1.41	0 0.5 0	0 0.5 0	0.33	1.09	–0.36	4.17
Cu₂BiI₇-P1	1.13	0.50	0 0 0	0 0.5 0	0.37	1.09	–0.26	31.63
Cu₂BiI₇-P1-II	1.40	0.60	0 0 0	0 0.5 0.5	0.35	1.06	–0.25	28.30

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