The paper presents a detailed model of the contacting interface of c-Si solar cells. A finite 3D element model is used as a framework to determine the contact resistivity of the front contacts. It is based on detailed microstructural characterization of experimental geometries and further parameters obtained from quantum mechanical calculations. It includes experimentally obtained emitter doping profiles, corresponding to sheet resistances of 50, 60, 65 and 95 Ohm sq, the microscopic contact resistivities based on ab initio calculated Schottky barriers, as well as the conductivity of the emitter layer, including effect of local variations related to the doping profiles. The typical size and shape of the Ag crystallites is accounted for, and also the presence of a glass phase. The model results agrees very well with experimental results of the contact resistivity obtained at various temperatures, and to measurements performed after selective removal of layers in the front contact, and is thus able to quantify the impact of the various microstructural features. The model is used to consider the effects of emitter layer etching, which commonly occurs during fabrication processes, providing insight and direction for future development of large scale processing and manufacture of c-Si photovoltaics.