杂化泛函HSE和PBE0计算CsPbI3缺陷性质的比较研究

doi:10.15541/jim20220756

无机材料学报 ›› 2023, Vol. 38 ›› Issue (9): 1110-1116.DOI: 10.15541/jim20220756 CSTR: 32189.14.10.15541/jim20220756

所属专题：【材料计算】计算材料(202409)；【能源环境】钙钛矿(202409)；【能源环境】太阳能电池(202409)

• 研究快报 • 上一篇

杂化泛函HSE和PBE0计算CsPbI₃缺陷性质的比较研究

吴晓维¹(), 张涵¹^,², 曾彪¹^,², 明辰¹^,², 孙宜阳¹^,²()

1.中国科学院上海硅酸盐研究所, 上海 201899
2.中国科学院大学材料科学与光电工程中心, 北京 100049

收稿日期:2022-12-17 修回日期:2023-05-11 出版日期:2023-09-20 网络出版日期:2023-06-01
通讯作者: 孙宜阳, 研究员. E-mail: yysun@mail.sic.ac.cn
作者简介:吴晓维(1993-), 女, 硕士. E-mail: wxw_xiaowei@163.com

Comparison of Hybrid Functionals HSE and PBE0 in Calculating the Defect Properties of CsPbI₃

WU Xiaowei¹(), ZHANG Han¹^,², ZENG Biao¹^,², MING Chen¹^,², SUN Yiyang¹^,²()

1. Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 201899, China
2. Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2022-12-17 Revised:2023-05-11 Published:2023-09-20 Online:2023-06-01
Contact: SUN Yiyang, professor. E-mail: yysun@mail.sic.ac.cn
About author:WU Xiaowei (1993-), female, Master. E-mail: wxw_xiaowei@163.com
Supported by:
National Key R&D Program of China(2021YFB3500501)

摘要/Abstract

摘要：

在卤族钙钛矿材料的缺陷研究中, 密度泛函理论计算发挥着重要作用。传统的半局域泛函(如PBE)虽然能够得到与实验接近的禁带宽度, 但是已有研究表明其不能准确描述材料的带边位置。采用更准确的杂化泛函, 结合自旋轨道耦合(SOC)效应与充分的结构优化开展缺陷研究十分必要。可以选择两种杂化泛函, 即屏蔽的杂化泛函HSE和非屏蔽的杂化泛函PBE0。本研究以正交相CsPbI₃为例, 系统比较了两种方法在缺陷性质计算上的差异。计算结果表明, 对于体相性质, 两种杂化泛函并无明显的差别。但是, 对于缺陷性质, 两种泛函出现定性的差别。HSE计算中预测的浅能级缺陷, 在PBE0计算中大部分变为深能级缺陷, 且缺陷转变能级和Kohn-Sham能级均出现定性差别。上述差别的本质在于, Hartree-Fock交换势具有长程作用特征, 因而普通的杂化泛函如PBE0在计算量允许的超胞尺寸上无法得到收敛的结果, 而HSE对上述交换势具有屏蔽作用, 可采用相对小尺寸的超胞得到收敛的缺陷能级。本研究结果表明, 尽管HSE杂化泛函需要较大的Hartree-Fock混合参数(约0.43), 其仍是准确计算卤族钙钛矿缺陷性质的有效方法。

关键词: 钙钛矿, 本征缺陷, CsPbI₃, 杂化泛函, 第一性原理计算

Abstract:

Density functional theory calculations play an important role in the study of defects in halide perovskites. Although the traditional semi-local functionals (such as PBE) can obtain the band gaps close to the experiments, they fail to accurately describe the positions of the band edges. Utilizing more accurate hybrid functionals combined with the spin-orbit coupling (SOC) effect with full structure relaxation is considered to be necessary for the prediction of defect properties. There are two types of hybrid functionals in the literature, namely the screened HSE and the unscreened PBE0. In this study, taking the orthorhombic phase CsPbI₃ as an example, these methods were compared for the calculation of defect properties. The results show that there is no obvious difference between two methods for bulk properties, but qualitative differences appear for the defect properties. Most of the shallow-level defects predicted in the HSE calculations become deep-level defects in the PBE0 calculations. Meanwhile, there are qualitative differences between the defect transition levels and the Kohn-Sham levels. The origin of above differences lies in the fact that the Hartree-Fock exchange potential has long-range interaction. Therefore, in unscreened hybrid functionals, such as PBE0, it is more difficult to obtain convergent results with a manageable supercell size. In contrast, HSE exhibits a screening effect on the Hartree-Fock exchange potential and can obtain accurate defect energy levels using relatively small supercell sizes. Therefore, all results here demonstrate that the HSE hybrid functional owns a significant advantage in dealing with this problem even though a large Hartree-Fock mixing parameter (about 0.43) is needed.

Key words: perovskites, intrinsic defect, CsPbI₃, hybrid functional, first-principles calculation

中图分类号:

TQ174

吴晓维, 张涵, 曾彪, 明辰, 孙宜阳. 杂化泛函HSE和PBE0计算CsPbI₃缺陷性质的比较研究[J]. 无机材料学报, 2023, 38(9): 1110-1116.

WU Xiaowei, ZHANG Han, ZENG Biao, MING Chen, SUN Yiyang. Comparison of Hybrid Functionals HSE and PBE0 in Calculating the Defect Properties of CsPbI₃[J]. Journal of Inorganic Materials, 2023, 38(9): 1110-1116.

图/表 9

Fig. 1 Fitting Murnaghan equation of state to obtain the equilibrium volume and bulk modulus with inset showing the atomic structure of γ-phase CsPbI3

Table 1 Lattice constants and internal parameters of orthorhombic CsPbI3 calculated by two different hybrid functionals

	HSE-0.43			PBE0-0.20
	X/a	Y/b	Z/c	X/a	Y/b	Z/c
	a/nm 0.9008	b/nm 1.2525	c/nm 0.8632	a/nm 0.9061	b/nm 1.2589	c/nm 0.8674
Cs	0.4312	0.25	0.0228	0.4294	0.25	0.0238
Pb	0	0	0	0	0	0
I₁	0.5110	0.25	0.5783	0.5104	0.25	0.5804
I₂	0.2021	0.0387	0.3017	0.2017	0.0395	0.3021

Fig. 2 Band structures of γ-CsPbI3 calculated by two hybrid functionals HSE-0.43 (a) and PBE0-0.2 (b) including the SOC effect

Fig. 3 Atomic structures of 12 intrinsic defects after relaxation in neutral charge state As two functionals yield similar structures, only the structures from PBE0-0.2 calculations are shown here

Fig. 4 Defect transition levels in γ-CsPbI3 calculated by HSE-0.43 (a) and PBE0-0.2 (b) Blue lines: acceptor levels; Red lines: donor levels

Fig. 5 Kohn-Sham energy levels of vCs, vI, Csi, Ii, CsPb and PbCs defects calculated by HSE-0.43 (a) and PBE0-0.2 (b) For acceptor defects, the left half is for −1 state, while the right half is for the neutral state. For donor defects, the left half is for neutral state, while the right half is for +1 state. Open and solid circles represent holes and electrons, respectively.

Fig. S1 Total and projected density of states of γ-CsPbI3 calculated by two hybrid functionals HSE-0.43 (a) and PBE0- 0.2 (b) including the SOC effect

Fig. S2 Parabolic fitting of the band near Γ point to obtained the effective masses of electrons and holes. For clarity, the electron and hole bands are referenced to the CBM and VBM, respectively; SOC effect is included here; (a) HSE-0.43; (b) PBE0-0.2

Fig. S3 Comparison of dielectric constants calculated by two hybrid functionals (a) Real part ε1; (b) Imaginary part ε2; Calculations considered SOC effect and employed 5×4×5 k-grid and 544 empty bands

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杂化泛函HSE和PBE0计算CsPbI₃缺陷性质的比较研究

Comparison of Hybrid Functionals HSE and PBE0 in Calculating the Defect Properties of CsPbI₃

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