Development of a solar element model using the method of fractal geometry theory

It is shown that in the existing models of the solar cell, assumptions were made about the ideally smooth surface topography, which had a significant impact on the calculation of the output parameters. It is proposed to take into account the real working area of the receiving surface of the solar cell to improve the accuracy, linearity and stability of the current-voltage characteristics. A geometric model of the structure of the receiving surface of a solar cell has been developed, which describes and takes into account geometric changes in the structure of a semiconductor conducting layer, in the presence of damaging defects in the form of local inhomogeneities, micropores and macrocracks. It was found that the receiving surface with damaging defects is a porous inhomogeneous structure and has fractal properties: self-similarity, invariance, scalability. It is proposed to determine the real working area, to use the method of the theory of fractal geometry and, as an effective quantitative parameter for assessing the change in fractal structure, to choose the value of the fractal dimension. The obtained analytical expressions for the improved model establish the relationship between the output parameters and determine the degree of filling of the current-voltage characteristic for the output power and efficiency. The computational experiment showed that the real area can be much less than the geometric area of the topological relief and is quantitatively related to the change in fractal dimension in the range from 2.31 to 2.63. The obtained data on the real area, when solving analytical expressions for the solar cell model, play an important role in ensuring the stability and linearity of the current-voltage characteristic, increasing its accuracy up to 5 %.