Silver (Ag) pastes are widely used in the global market for most solar cell architectures. Thereby, lead (Pb) is no longer wanted in productions for environmental reasons. In this work, a model for the contact formation between Pb-free, tellurium oxide (TeO2) containing screen-printable Ag pastes and silicon is presented. It is shown that Te plays a key role in this model. Te is not only an important part in etching the surface passivation layers with TeO2 dissolving the dielectric layer but also for a formation of the contacts with Te forming a compound consisting of Ag2Te. Using EDX mapping, local contact regions can be examined and interpreted for contact formation. The used paste system enables far more flexible paste mixturing leading to a novel developed commercial paste which is on a par with other pastes used in industry concerning the resulting contact properties. This is also demonstrated in this work by the very low contact resistivity of less than 1 mΩcm2 over a wide range of firing peak temperatures. It is additionally shown that good resistivities can be achieved on both n+- and p+-doped regions.