A carrier density dependent diffusion coefficient, recombination rate and diffusion length in MAPbI and MAPbBr crystals measured under one- and two-photon excitations

Applications of lead halide perovskites in solar cells and photo- and ionising radiation detectors are based on effective charge carrier generation and transport. The perovskites exhibit large carrier recombination lifetimes and diffusion coefficients leading to exceptionally long carrier diffusion lengths for solution processed materials. However, carrier density dependences of these parameters are not very well established. Therefore, in this work, we have used non-destructive optical techniques such as time-resolved differential absorption, time-resolved photoluminescence and light induced transient gratings (LITG) for the simultaneous determination of carrier density dependent recombination and diffusion rates as well as diffusion length in MAPbI 3 and MAPBr 3 crystals in a wide range of excitation densities upon single and two photon injections. At low carrier densities, recombination processes on bulk and surface traps were found to be dominant providing 1-2 μs lifetime, and 6 × 10 3 ; ∼30 cm s −1 surface recombination velocities in MAPbI 3 and MAPbBr 3 crystals, respectively. For higher carrier densities, an enhancement in carrier recombination rate as well as an increase in carrier diffusivity is observed. We related the lifetime reduction with excitation to the bimolecular and Auger recombination processes with B 0 = 1.0 (4) × 10 −10 cm 3 s −1 and C = 1.5 (1.2) × 10 −29 cm 6 s −1 coefficients in MAPbI 3 and MAPbBr 3 , respectively. The LITG measurements provide a direct increase in the carrier density dependent diffusion coefficient from 1.35 to 3 cm 2 s −1 in MAPbI 3 and from 0.45 cm 2 s −1 to 1.7 cm 2 s −1 in MAPbBr 3 due to the carrier plasma degeneracy and saturation of localized states. A high carrier density related diffusion length drop from 10 to 0.1 μm in the 10 16 -10 19 cm −3 carrier density range was observed. Recombination, diffusion rates and diffusion length in MAPbI 3 and MAPBr 3 crystals in a wide carrier density range: experiment and theory.