Comprehensive analytical modeling of perovskite (MAPbI3) solar cells: A rigorous validation via simulations and experiments

This study proposes an innovative analytical model for perovskite solar cells (PSCs) with an n-i-p structure (FTO/TiO${}_2$/MAPbI${}_3$/HTM), based on an experimentally validated design. Unlike conventional approaches, our work establishes a triple comparison between numerical simulation, experimental data and analytical modeling, which enables rigorous cross-validation. First, we used Silvaco software to reproduce the structure and extract key parameters such as a short-circuit current density (J${}_{\mathrm{SC}}$) of 22.057 mA/cm${}^2$, an open-circuit voltage (V${}_{\mathrm{OC}}$) of 1.15 V, a power conversion efficiency (PCE) of 12.68%, and a fill factor (FF) of 50.03%, all in good agreement with the experimental results. Next, an analytical model based on the continuity equation was developed, incorporating interface conditions, the internal electric field, and the carrier generation profile. This model, implemented in MATLAB, allows the J-V curve to be plotted by combining the photogenerated and dark currents. This curve facilitates the extraction of key parameters, including J${}_{\mathrm{SC}}$ of 22.82 mA/cm${}^2$, V${}_{\mathrm{OC}}$ of 1.1147 V and a PCE of 12.74%, which shows a high compatibility between experimental data, the Silvaco program simulation and the analytical model. By varying the thickness of the perovskite layer through the model simulations (around 0.26 to 0.35 $\mu$m), we observed a corresponding variation in the PCE of 15.678% (0.35 $\mu$m). This work not only demonstrates that the analytical model is consistent with the Silvaco simulation and experimental data, but also evaluates its utility for optimizing the performance and design of PSC.