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。

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.