(HTL/EML/ETL σ = 0.05/0.10/0.05 eV or 0.10/0.05/0.10 eV), hopping attempt frequency of electrons and holes z/ , e.g., zq = lOzz fi in HTL and EML), hopping attempt frequency zq in different layers and z 1 in HTL and ETL are 10, 100, or 1000 times larger than those in EML), device thicknesses or layer thicknesses L (HTL/EML/ETL thickness = 10/30/10 nm, 5/90/5 nrn, 10/80/10 nm, 30/40/30 nm, or 40/20/40 nm), temperature (T = 250, 320, or 387 K), injection barrier ( Φ = 0.2, 0.3, 0.5, or 0.6 eV), and dielectric constant ( ε Γ = 4 or 6). At low voltages (V < 4 V), the 3D-ME simulation results agree in most cases well with the results from 3D-KMC simulations. There exist a few cases where deviations in the carrier concentration profiles are observed. However, in these cases the agreement in the current density-voltage characteristics and the recombination profile (which are more important for device characteristics) is still good. In addition to model validation, these simulation data sets also provide physical insight into device optimization. For example, a possible approach to obtain a uniform emission profile in the EML is to set the disorder energy σ in the EML to be larger than those in ETL and HTL. 

## B . SITE- RESOLVED CHARGE-CARRIER CONCENTRATIONS AND R E COMBINATION RATES 

In Sec. IIIA, the 3D-ME and 3D-KMC charge carrier and recombination profiles were compared in a layer-averaged way. However, due to the energetic disorder, the charge carrier occupation probability and the recombination rate associated with each molecular site are highly inhomogeneous. A more strict test of the 3D-ME model is to compare the site-resolved concentration and recombination rates with the 3D-KMC results. In Fig. 5 parts (a) through (e), such a comparison is shown for the device in Fig. 3A with σ = 0.10 eV, at V = 3 V. The disorder configurations are taken to be the same for the ME and KMC simulations. In the figure, the molecular sites are labeled with a site number by descending order of carrier concentration (or recombination rate), as calculated from the 3D-ME simulations. The same site numbers are assigned to the KMC simulation results. The KMC-calculated and ME-calcu!ated site-resolved concentrations or rates are both shown as a function of the site number. To obtain better statistics, the results are binned for every 100 sites. 

The results in Fig. 5 parts (a) through (e) show that the site-resolved electron and hole concentrations calculated using the 3D-ME simulations can very well reproduce 

