We discuss the effects of organic film thickness, film crystalline texture, contact metal, and temperature on the current‐voltage characteristics (I‐V) of organic‐on‐inorganic (OI) semiconductor contact barrier diodes, where the prototypical compound; 3, 4, 9, 10‐perylenetetracarboxylic dianhydride (PTCDA) serves as the organic thin film. The results presented can be fully understood in terms of ... [Show full abstract] the thermionic emission‐space‐charge‐limited (TE‐SCL) current model introduced in previous papers. Studies of the I‐V characteristics suggest the presence of a trap distribution centered at Δϵ=0.20 eV above the PTCDA valence band edge. Also, we have found a correlation between the hole mobility (μ eff ) and PTCDA crystalline texture, and obtain a mobility as high as μ eff =1.4 cm<sup>2</sup>/V s for highly ordered crystalline thin films. Finally, the general criteria which must be fulfilled by an organic compound used to achieve high‐performance OI devices are outlined. The properties of several such devices using various organic thin films are described.