Geometry Optimization of Top Metallic Contacts in a Solar Cell Using the Constructal Design Method

Sunlight is a natural resource that can be harnessed by the photovoltaic conversion of sunlight into electricity-utilizing solar cells. The production of most common solar cells consists of a homojunction of a p-type and n-type silicon. The p—n junction is realized by the diffusion of impurities through one surface of the wafer. Silicon wafers have a typical dimension of 156 × 156 mm2 and a thickness of 0.15–0.2 mm. Groups of 50–100 solar cells are electrically connected and encapsulated to form a module. The required area for interconnection does not contribute to power generation, and the performance of larger area devices usually suffers from higher resistive losses. In the present work, a theoretical model of the geometric arrangement of the top contact metallic electrodes branched network in a photovoltaic cell is developed. The network structure of the electrodes is obtained from applying the constructal design methodology by the minimization of the overall resistance. As a result, the optimal lengths and geometrical relationships of an electrode branching network with a branching angle are determined. A geometric distribution of the electrode network on the solar cell analyzed by the total resistance of every level of branching is defined. The top metallic contact network presents a tree-shaped geometric arrangement with the main objective of covering a generation area for an enhanced collection of the generated electrical current. The theoretical results obtained are expressed as the total voltage of the arrangement and the lengths of the branched electrode network.