We present a unified device model for single layer organic light emitting diodes (LEDs) which includes charge injection, transport, and space charge effects in the organic material. The model can describe both injection limited and space charge limited current flow and the transition between them. We specifically considered cases in which the energy barrier to injection of electrons is much larger than that for holes so that holes dominate the current flow in the device. Charge injection into the organic material occurs by thermionic emission and by tunneling. For Schottky energy barriers less than about 0.3–0.4 eV, for typical organic LED device parameters, the current flow is space charge limited and the electric field in the structure is highly nonuniform. For larger energy barriers the current flow is injection limited. In the injection limited regime, the net injected charge is relatively small, the electric field is nearly uniform, and space charge effects are not important. At smaller bias in the injection limited regime, thermionic emission is the dominant injection mechanism. For this case the thermionic emission injection current and a backward flowing interface recombination current, which is the time reversed process of thermionic emission, combine to establish a quasi-equilibrium carrier density. The quasi-equilibrium density is bias dependent because of image force lowering of the injection barrier. The net device current is determined by the drift of these carriers in the nearly constant electric field. The net device current is much smaller than either the thermionic emission or interface recombination current which nearly cancel. At higher bias, injection is dominated by tunneling. The bias at which tunneling exceeds thermionic emission depends on the size of the Schottky energy barrier. When tunneling is the dominant injection mechanism, a combination of tunneling injection current and the backflowing interface recombination current combine to establish the carrier density. We compare the model results with experimental measurements on devices fabricated using the electroluminescent conjugated polymer poly[2-methoxy, 5-(2′-ethyl-hexyloxy)-1,4-phenylene vinylene] which by changing the contacts can show either injection limited behavior or space charge limited behavior.

Davids, P. S., Campbell, I. H., & Smith, D. L. (1997). Device model for single carrier organic diodes. Journal of Applied Physics, 82(12), 6319–6325.