Calculations on shallow defect levels in CsPbBr₃

It is well known that in metal-halide perovskite the dominant defects are shallow. However, accurately prediction of the shallow defect level from DFT calculation is still challenging due to two reasons. One is that the defect state wave function could be quite delocalized, thus a very large supercell is necessary to get converged results, which is beyond the capacity of traditional DFT method. The other one is that the band gap error of DFT would also affect the accuracy. Here we proposed a method to calculate the shallow defect levels combining the potential patching and the LDA-1/2 approaches (PP+LDA-1/2). The potential patching method allows the calculation of 10⁵-atom supercells, and the LDA-1/2 method overcomes the band gap problem. We apply this method to calculate the shallow levels of the dominant intrinsic defects (V_Pb, V_Cs, V_Br) in CsPbBr₃. It is found supercells with over 10⁴-atom needed to get converged energy. The predicted defect levels are only 15-70 meV away from the band edge, much smaller than previously reported results obtained from small supercell calculations. These results highlights the importance of large-supercell calculations in predicting shallow defect levels.