Formation of Bi−Bi Dimers in Heavily Bi-Doped Lead Halide Perovskites: Origin of Carrier Density Saturation

Heterovalent $\mathrm{Bi}$ doping in lead halide perovskites (LHPs) is of particular interest in recent research to improve the electronic and optoelectronic properties. In experiments, the incorporation of $\mathrm{Bi}$ not only converts the conductivity type of crystals from p type to n type, leading to the significant enhancement of charge-carrier concentration, but also results in the appearance of near-infrared photoluminescence (NIR PL) along with the decrease of band-edge PL intensity. However, with a high concentration of $\mathrm{Bi}$ doping, the carrier concentration exhibits a saturated tendency and the intensity of NIR PL decreases abnormally. The origins behind these interesting phenomena are not yet well understood. Herein, based on first-principles calculations, we demonstrate that $\mathrm{Bi}$ dimers form n type and intrinsic LHPs with a high concentration of $\mathrm{Bi}$ doping. They act as effective n-type limiting defects, and hence, cause carrier saturation in experiments. Moreover, the NIR PL arising from the ${\mathrm{Bi}}_{\mathrm{Pb}}$ defect is suppressed due to the density conversion of isolated ${\mathrm{Bi}}_{\mathrm{Pb}}$ defects to $\mathrm{Bi}$ dimers when $\mathrm{Bi}$ is heavily doped. Meanwhile, nonradiative recombination is also promoted due to the deep charge-state transition level introduced by the $\mathrm{Bi}$ dimer. Our work not only reveals the mechanism of highly concentrated $\mathrm{Bi}$ limiting the electronic and optical properties of LHPs, but also suggests the precise control of $\mathrm{Bi}$ doping in electronic and photovoltaic applications.