Classical modelling of grain size and boundary effects in polycrystalline perovskite solar cells

A theoretical approach based on the Matthiessen rule for scattering lifetime is presented to formulate the effective characteristics of polycrystalline solar cells. Application of this method to Perovskite solar cells obtains polycrystalline bulk defect density for diverse grain sizes along with the determination of surface recombination velocity at grain boundaries. Unlike previous works on Silicon based solar cells that use an independently weighted average equation for extracting mobility, we introduce a variation of Drude-Smith model for calculating the mobility from carrier lifetime and defect density. In agreement with the experiments, introduced method reveals sub-picosecond background scattering times associated with phonon-lattice vibrations. Obtained carrier diffusion length spans over multi-micron to multi-millimeter scale for grain sizes ranging from 100 nm to 1 mm. Calculated monomolecular recombination lifetimes explains elevated Photoluminescence Yield and peak position in larger grain sizes. Presented method is verified by feeding extracted parameters into Drift-Diffusion equations and fitting with reported experimental photovoltaic conversion efficiency data. Finally, through employing a Gaussian distribution for grain sizes, we also study the reduction of device efficiency caused by non-uniform grain size distribution as a more realistic case.