A model for screen utility to predict the future of printed solar cell metallization

Fine line screen printing for solar cell metallization is one of the most critical steps in the entire production chain of solar cells, facing the challenge of providing a conductive grid with a minimum amount of resource consumption at an ever increasing demand for higher production speeds. The continuous effort of the industrial and scientific community has led to tremendous progress over the last 20 years, demonstrating an average reduction rate for the finger width of approximately 7 µm per year with the latest highlight of achieving widths of 19 µm. However, further reductions will become a major challenge because commonly used metal pastes are not able to penetrate arbitrary small screen opening structures. Therefore, this study introduces the novel dimensionless parameter screen utility index SUI which quantifies the expected printability of any 2-dimensional screen architecture in reference to a given paste. Further, we present a full theoretical derivation of the SUI, a correlation to experimental results and an in-depth simulation over a broad range of screen manufacturing parameters. The analysis of the SUI predicts the point when commonly used wire materials will fail to provide sufficient meshes for future solar cell metallization tasks. Therefore, novel wire materials (e.g. the use of carbon nanotubes) with very high ultimate tensile strengths are discussed and suggested in order to fulfill the SUI requirements for printing contact fingers with widths below 10 µm. We further analyze economic aspects of design choices for screen angles by presenting an analytical solution for the calculation of mesh cutting losses in industrial screen production. Finally, we combine all aspects by presenting a generalized approach for designing a 2-dimensional screen architecture which fulfills the task of printing at a desired finger width.