Molecular electronics on silicon substrates hold promise for new functional possibilities on silicon. One such possibility is a hybrid silicon-molecule device that shows negative differential resistance (NDR) when conduction through the molecular levels are cut-off as the levels are driven into the silicon band-gap region. We demonstrate through a self-consistent solution based on Non-equilibrium Green’s Function (NEGF) formalism that the NDR peaks show a clear polarity dependence, appearing for only positive bias on a p-doped substrate. We further discuss what determines the position of the NDR peaks and how the locations are affected by self-consistency.