characteristics, the choice of voltage point affects the extracted ideality factor (see above) (c) In reality, there is usually a leakage current in the low voltage regime which is not included in the simulation. The leakage current is expected t o influence the ideality factor. Hence, one needs t o be careful regarding the physical interpretation of the ideality factor. 

In Fig. 8, the disorder energy σ is varied while the temperature T is hxed at 290 K. Fig. 8 part (a) shows that for large σ and low voltages, the current density is larger than that for the small σ case. This is, at least in part, due to the easier injection from the electrodes into a wider DOS. Fig. 8 part (b) shows that the ideality factor is indeed voltage dependent. For small σ and low voltages, the ideality factor approaches unity. In the voltage range studied, it increases with σ . This effect can be explained from the increasing charge carrier concentration, at any point in the device, with increasing σ , combined with the increase with σ of the diffusion coefficient enhancement factor at any given carrier concentration. 

In Fig. 9, the disorder energy σ is hxed at 0.10 eV while the temperature T is varied. We observe that the ideality factor is almost independent of temperature, which agrees with experimental results. We also hnd that for a series of symmetric 100 nm devices with varying EML layer thicknesses the ideality factor, evaluated at a hxed low voltage, is not significantly dependent on the voltage. We remark that accurate calculation of the ideality factor requires high precision in the current density-voltage calculation. To run the 3D-ME simulations with a sufficiently high precision for a current density as low as 1C 6 A/m $^{2}$, the simulation time is significantly larger than those shown in Figs. 1A-B. 

## IV) Conclusions and outlook 

In this work, we have presented a bipolar 3D-ME simulation model that can be used to predictive!y model electron-hole recombination in disordered organic sem i conductor devices at low voltages. For voltages close t o or smaller than the built-in voltage $_{bi}$, the simulation method is numerically much more efficient than 3D-KMC simulations. The model has been validated by comparing the simulation results for a wide range of parameters with those obtained from 3D-KMC simulations. From the development of a theoretical expression for the recombination prefactor (Eq. (13)), 

