Organic-inorganic perovskites have earned the reputation of materials suitable for cheap and scalable production of not only the solar cells, but also the thin film transistors, light emitting diodes, and even lasers. Mobility and lifetime of charge carriers play a crucial role in these devices; however, some internal processes governing these parameters remain understudied. In particular, little is known about the diffusivity of holes and its dependence on carrier density or carrier localization parameters, mostly due to experimental difficulties.

In this presentation, we demonstrate the applicability of all-optical light-induced transient grating (LITG) technique for measurements of carrier diffusion coefficient in various perovskite samples. This method has several advantages, like no need for electrical contacts, the possibility to extract the mobility of holes in both doped and intrinsic semiconductor, and the ability to study the dependence of carrier diffusivity and lifetime on carrier density, especially at high excitations. 

Based on LITG results in bulk CH₃NH₃Pb(Sn)X₃ layers deposited by vapor deposition or spin-coating techniques, we demonstrate two distinct regimes of carrier transport in the perovskites, namely band-like or localization-limited carrier diffusion [1]. Band-like diffusion with typical ambipolar diffusion coefficient of ~1 cm²/s takes place in high structural quality layers. This value is determined by the fundamental material properties and is controlled by polar-optical electron-phonon scattering. It increases weakly with carrier density due to degeneracy of carriers and is limited by screened electron-hole scattering at high carrier densities. In contrast, the trap-limited diffusion varies a lot from 10^-4 to 1 cm²/s, due to strong dependence on densities of traps and charge carriers. In the latter case, the diffusivity is very sensitive to layer deposition technology. It can be enhanced, e.g., by using chemical additives during MAPbX₃ layer formation [2]. On the other hand, wet cast MASnI₃ layers show intrinsically high diffusivity of carriers comparable to that of vapor deposited layers or crystalline MAPbX₃ samples, despite very high background p-type doping [3].

Finally, we show that diffusion coefficient in quasi-2D PEA₂FA_n-1Pb_nBr_3n+1 samples depends on the number n of perovskite layers. We observe that diffusion coefficient is by order of magnitude larger in the thinnest layers with n = 1 and 2 at lower carrier densities, which points out to the two-dimensional nature of these structures. The thicker layers with more periods demonstrate the trap-limited diffusion regime, quite resembling that in bulk CH₃NH₃PbX₃.