The properties are discussed of organic-on-inorganic (OI) semiconductor contact barrier diodes, where the 3, 4, 9, 10 perylenetetracarboxylic diimide (PTCDI) and the copper phthalocyanine (CuPc) serve as the organic thin film. The results presented can be fully understood in terms of the thermionic emission-space-charge-limited (TE-SCL) current model introduced for OI structures with prototypical aromatic compound; 3, 4, 9, 10 perylenetetracarboxylic dianhydride (PTCDA) vapour-deposited onto n- and p-Si substrates. Also, under moderate and high reverse bias voltages the results obtained can be understood in terms of the organic-on-inorganic heterojunction (OI-HJ) model. Comparisons between diode performances and theory are made. The contact barrier diodes exhibit high breakdown voltages and reverse dark currents limited by generation and recombination of carriers in the Si bulk. From the forward current-voltage characteristics at several temperatures, apparent OI contact barriers of PHI-bp = (0.63 +/- 0.01) V for PTCDI and PHI-bp = (0.59 +/- 0.02) V for CuPc, are formed with p-Si substrates. Studies of the I-U characteristics suggest the presence of an exponential trap distribution in the band-gap of the organic semiconductors used. The resulting diodes are superior in many respect to conventional Schottky diodes due to enhanced contact barriers and reduced edge effects.