Limits of Carrier Diffusion in n-Type and p-Type CH₃NH₃PbI₃ Perovskite Single Crystals

Using a combination of scanning photocurrent microscopy (SPCM) and time-resolved microwave conductivity (TRMC) measurements, we monitor the diffusion and recombination of photoexcited charges in CH₃NH₃PbI₃ perovskite single crystals. The majority carrier type was controlled by growing crystals in the presence or absence of air, allowing the diffusion lengths of electrons (L_D ^e-) and holes (L_D ^h+) to be directly imaged with SPCM (L_D ^e- = 10-28 μm, L_D ^h+ = 27-65 μm). TRMC measurements reveal a photogenerated carrier mobility (μ_h + μ_e) of 115 ± 15 cm² V^-1 s^-1 and recombination that depends on the excitation intensity. From the intensity dependence of the recombination kinetics and by accounting for carrier diffusion away from the point of photogeneration, we extract a second-order recombination rate constant (k_rad = 5 ± 3 × 10^-10 cm³/s) that is consistent with the predicted radiative rate. First-order recombination at low photoexcited carrier density (k_nr ^p-type = 1.0 ± 0.3 × 10⁵ s^-1, k_nr ^n-type = 1.5 ± 0.3 × 10⁵ s^-1) is slower than that observed in CH₃NH₃PbI₃ thin films or in GaAs single crystals with AlGaAs passivation layers. By accounting for the dilution of photogenerated carriers upon diffusion, and by combining SPCM and TRMC measurements, we resolve disagreement between previous reports of carrier diffusion length.