As screen printed contacts are the predominant metallisation technique in industrial production of Si solar cells, a better understanding of their properties is necessary. In this work, we show that high-quality cross-sectional samples can be prepared, whose study by transmission electron microscopy (TEM) reveals precisely the structure of the contact between the silver fingers and the Si. On diffused  Si wafers, direct firing of an Ag paste results in interfaces which are mainly composed of shaped Ag crystallites penetrating the emitter up to 120 nm. These crystallites are in epitaxial relation with the Si substrate. When firing the contacts through a SiNx layer, larger Ag crystallites are present at the interface with Si and the orientation relation is lost. In both cases, high resolution TEM imaging and EDX analyses reveal a crystalline Ag/Si interface, where neither oxide nor glass frit can be detected. The presence of a significant glass frit l ayer between the Ag crystallites contacting the Si and the large Ag grains forming the bulk of the fingers can partly explain why lowly doped emitters are difficult to contact by screen-printing.