Molecular junctions were fabricated with the combined use of electrochemistry and conventional CMOS tools. They consist of a 5-10 nm thick layer of oligo(1-(2-bisthienyl)benzene) between two gold electrodes. The layer was grafted onto the bottom electrode using diazonium electroreduction, which yields a stable and robust gold-oligomer interface. The top contact was obtained by direct electron-beam evaporation on the molecular layers through masks defined by electron-beam lithography. Transport mechanisms across such easily p-dopable layers were investigated by analysis of current density-voltage (J-V) curves. Application of a tunneling model led to a transport parameter (thickness of similar to 2.4 nm) that was not consistent with the molecular thickness measured using AFM (similar to 7 nm). Furthermore, for these layers with thicknesses of 5-10 nm, asymmetric J-V curves were observed, with current flowing more easily when the grafted electrode was positively polarized. In addition, J-V experiments at two temperatures (4 and 300 K) showed that thermal activation occurs for such polarization but is not observed when the bias is reversed. These results indicate that simple tunneling cannot describe the charge transport in these junctions. Finally, analysis of the experimental results in term of "organic electrode" and redox chemistry in the material is discussed.