Current-voltage curves of planar heterojunction perovskite solar cells – Novel expressions based on Lambert W function and Special Trans Function Theory

INTRODUCTION: At the present time, much attention has been focused on new types of solar cells, called perovskite solar cells. They are highly efficient devices with more than 25% power conversion efficiency. However, perovskite solar cell performance has not yet been fully explored. OBJECTIVES: We aimed to mathematically investigate the analytical modeling of current–voltage curves of planar heterojunction perovskite solar cells using Perovich Special Trans Function Theory (STFT). Furthermore, we proposed novel analytical closed-form solutions for short-circuit current and open-circuit voltage of these cells in terms of STFT. We evaluated the safety for laying the theoretical foundation by comparing the accuracy of the proposed expressions by the known methods. METHODS: A novel hybrid metaheuristic algorithm, called particle swarm optimization (PSO) – evaporation rate water cycle algorithm (ERWCA), is proposed to determine equivalent circuit parameters of the perovskite solar cell. A novel objective function is introduced for estimating the parameters for that purpose too. RESULTS: It was shown that STFT is very applicable and efficient for representing current–voltage expressions of perovskite solar cells. STFT provides a more accurate solution and requires fewer order members than the solutions provided by the conventional Taylor series. Based on these expressions and numerical calculations, it is verified that the characteristic values ​​of variables (short-circuit current, no-load voltage, efficiency, and fill factor) were not accurately calculated in the literature. Also, parameters of equivalent circuits of these cells were not accurately estimated. The equivalent circuit parameters were determined using the algorithm proposed in this work, which fit the verified values ​​of characteristic quantities much better than the literature. CONCLUSION: This work lays the foundation for developing the planar-structured perovskite solar cell models, in which the proposed estimation method and expressions are highly effective and provide excellent results.