Electronic properties of Pb-I deficient lead halide perovskites

The electronic structure evolution of deficient halide perovskites with a general formula $(A,A')_{1+x}M_{1-x}X_{3-x}$ was investigated using the density functional theory. The focus is placed on characterization of changes in the band gap, band alignment, effective mass, and optical properties of deficient perovskites at various concentrations of defects. We uncover unusual electronic properties of the defect corresponding to a $M\!-\!X$ vacancy filled with an $A'$ cation. This defect "repels" electrons and holes producing no trap states and, in moderate quantities ($x\le0.1$), does not hinder charge transport properties of the material. This behavior is rationalized using a confinement model and provides an additional insight to the defect tolerance of halide perovskites.