Impact of Trap Filling on Carrier Diffusion in MAPbBr$_3$ Single Crystals

We present experimental evidence showing that the effective carrier diffusion length ($L_d$) and lifetime ($\tau$) depend on the carrier density in MAPbBr$_3$ single crystals. Independent measurements reveal that both $L_d$ and $\tau$ decrease with an increase in photo-carrier density. Scanning photocurrent microscopy is used to extract the characteristic photocurrent $I_{ph}$ decay-length parameter, $L_d$, which is a measure of effective carrier diffusion. The $L_d$ magnitudes for electrons and holes were determined to be ~ 13.3 $\mu$m and ~ 13.8 $\mu$m respectively. A marginal increase in uniform light bias ($\leq 5 \times 10^{15}$ photons/cm$^2$) increases the modulated photocurrent magnitude and reduces the $L_d$ parameter by a factor of two and three for electrons and holes respectively, indicating that the recombination is not monomolecular. The $L_d$ variations were correlated to the features in photoluminescence lifetime studies. Analysis of lifetime variation shows intensity-dependent monomolecular and bimolecular recombination trends with recombination constants determined to be ~ 9.3 $\times 10^6$ s$^{-1}$ and ~ 1.4 $\times 10^{-9}$ cm$^{3}$s$^{-1}$ respectively. Based on the trends of $L_d$ and lifetime, it is inferred that the sub-band-gap trap recombination influences carrier transport in the low-intensity excitation regime, while bimolecular recombination and transport dominate at high intensity.