sity of states. The electron-hole recombination process is thus simulated without free parameters. Within the version of the model described in this work, exciton forma tion is assumed to be followed by immediate radiative decay. However, the model is expected to provide a basis for efficient full 3D-ME device models that also include ex citon transfer and exciton loss processes. We hnd that the use of the 3D-ME method developed in this work enables efficient simulations at voltages below . Fig. IB gives the simulation time for a single-layer bipolar device with ; = 1.2 V and shows a comparison with the time required for KMC simulations for the same device. We note that the same overall conclusions concerning the simulation time also hold for devices with larger values of 14;. The structure of this description is as follows. In Sec. II, the bipolar 3D-ME model is formulated by describing the simulation approach and the method for de riving the recombination rate used in the model. In Sec. Ill, we apply the model to single-layer and realistic three-layer devices. The current density-voltage J(V) characteristics, carrier concentration profile and recombination prohle are compared with the results of 3D-KMC simulations, as well as the detailed site-resolved charge- carrier concentrations and recombination rates. Next, we compare the “local” versus “nearest neighbor”descriptions of recombination. Finally, we discuss, based on the simulations, the so-called ideality factor of bipolar devices, obtained from the simu lated J(V) curves below 4 i• I the literature, measurements of the ideality factor have been used to deduce information about the nature of the recombination pro cess. Sec. IV contains a brief summary and an outlook. Sec. V is supplementary information providing further details on the derivation of this approach. In this section, the bipolar 3D-ME model is formulated. As in unipolar 3D-ME models for the charge transport in disordered organic semiconductors, we assume that the charge carriers occupy localized molecular states and that the charge transport is due to incoherent hopping between these states. The disordered organic semiconductor is described as a cubic lattice with a lattice constant a (typically a ~ 1 nm), representing the actual molecular sites. All quantities referring to holes or electrons are denoted II) The bipolar 3D master-equation model A . SIMULATION APPROACH