Analytical investigation of electric power in 3D bifacial polycrystalline silicon solar cells: impact of grain size and microstructural insights via digital microscopy

Abstract

This study presents a three-dimensional analytical model to evaluate the electrical performance of bifacial polycrystalline silicon solar cells, focusing on the effects of grain size and surface recombination velocities (Sf, Sb, Sgb). The continuity equation for minority carriers is solved using the method of separation of variables to derive closed-form expressions for excess carrier density, photocurrent, photovoltage, I–V characteristics, and power output. Power is expressed as a function of Sf, and the maximum power point (Pm) is determined through graphical analysis. Microstructural parameters such as grain size and grain boundary density obtained via digital microscopy are directly integrated into the model through their impact on grain boundary recombination velocity (Sgb). Additionally, frit thickness and uniformity are incorporated by adjusting the rear surface recombination velocity (Sb). Simulation results show that increasing grain size significantly improves carrier lifetime, photovoltage, and power output, particularly under both-sided illumination. Compared to traditional numerical approaches, the proposed analytical model offers lower computational cost and seamless integration of microscopy data, enabling rapid parametric optimization. This modeling microscopy framework provides a robust and scalable tool for the industrial optimization of high-efficiency bifacial polycrystalline silicon solar cells.