Charge-carrier injection and transport in organic light-emitting diodes: Single-particle versus mean-field approach

In the framework of the one-dimensional mean-field (MF) drift-diffusion approach the well-defined boundary conditions far away from the metal/insulator contacts of a planar metal/insulator/metal system are used to determine the boundary condition at the interface itself. The novel self-consistent boundary condition linking the carrier density and the electric field at the interface enables a straightforward description of the current voltage (IV) characteristics in forward and reverse bias bridging space charge and injection-limited regimes and accounting for barrier lowering from the potential drop in the used contact materials. Yet, because of the low carrier density in the insulator under injection limitation, single-particle phenomena, such as the Schottky effect, must be considered. We reconsider the validity of the MF approach, depending on the external bias and the prevailing injection barriers. For the crucial parameter window where the MF approach fails and single-particle phenomena become important, a modification of the boundary conditions at the insulator/metal interface is proposed to account for the discrete nature of carriers. The difference between the thus modified MF and the unmodified MF approach is illustrated by several examples