Constructal design of top metallic contacts on a disc-shaped solar cell

Trends in crystalline silicon photovoltaic improvements demonstrate that some of the key factors that have contributed to reaching efficiency values up to 23 % are the introduction of the passivated emitter and rear cell structure with local rear contacts in low-cost large-volume fabrication; the reduction of the width of the front metallization fingers, from about 100 microm to less than 30 micro m in large volume production, and the re-emergence of mono-crystalline silicon wafers as a consequence of cost reduction in the Czochralski silicon ingot fabrication process. In the present work, we have developed a theoretical model that defines the geometric arrangement of a branched top metallic contacts network over a solar cell with a disc-shaped body. The solar cell considers two main regions: the solar cell material and an insert of metallic material for the collection of the photogenerated electrical current. The geometric characteristics of the network are defined from the minimization of the resistive power losses applying the constructal design method. As a fundamental result, the optimal lengths, branching angles, and geometrical relationships of the n-branched network are determined. The numerical results show that the dimensionless power losses of the branched arrangement of contacts present minimum values for the allocation of the metallic material and the disc size of the solar cell.