Injection barrier at metal/organic semiconductor junctions with a Gaussian density-of-states

We physically model the injection characteristics at the metal/organic semiconductor (M/O) junctions with a Gaussian density-of-states (GDOS). By both analytical and numerical modelling, the charge carrier concentrations at the M/O junctions in an organic rectifying diode (ORD) are calculated. The results demonstrate a special attention required in the application of the Schottky–Mott rule, which defines the injection barrier (IB) for ideal metal/semiconductor junctions, to M/O junctions. By systematically changing the width of the GDOS that describes the energetic disorder in the organic semiconductor, we show that the edge of the highest-occupied molecular orbitals (HOMO) should be defined as σ 2 / 2 k B T higher rather than 2 σ from the maximum of the HOMO to keep the consistency of the Schottky–Mott rule. A simple analytical expression for the IB is presented which contains the effect of the disorder in facilitating the charge carrier injection. Simulated current density-voltage characteristics of the ORDs are also presented to support the arguments.