Analytical solutions for the photocurrent and dark diffusion current of preferentially doped polysilicon solar cells

Abstract

A two-dimensional physical model is used in the analysis of the photovoltaic properties of a preferentially doped polycrystalline silicon solar cell along the grain boundaries. The cell is assumed to have an oriented columnar structure formed by a juxtaposition of silicon grains. A mathematical analysis, based on the superposition principle and the technique of separation of variables, is presented. This analysis has allowed us to obtain analytical expressions for the photocurrents and dark diffusion currents of the horizontal junction and vertical junctions of the base region. These expressions are valid for any arbitrary value of the recombination velocity at the grain boundaries. The results show that the preferential doping significantly improves the performance of polycrystalline silicon solar cells especially in those formed by fine grains and with high recombination at the grain boundaries. In fact, with a grain size W = 20 μm, the preferential doping makes possible an increase of 62% in the short-circuit current, a decrease in the dark diffusion current which can reach 58.5% and an enhancement in the conversion efficiency more than 3%.