and in the expression of A , they approximately cancel each other. Furthermore, µ increases with σ and c, while r$_{v}$ decreases with σ and c. Hence, their product in the expression of A also becomes almost σ and c independent, except for the case of c = 10 $^{3}$. I Sec. Ill, we show from a comparison of 3D-ME and 3D-KMC simulation results for a large number of devices with varying materials parameters and layer thicknesses, studied for a wide application-relevant voltage and temperature range, that a satisfactory agreement is obtained when simply using a constant value A = 0.024 – 0.005, combined with B 0.154. This finding significantly reduces the computational cost in 3D-ME modeling, because instead of updating for all molecular sites during each iteration step, it is t o a good approximation allowed t o use a single value for the entire device. 

In realistic devices, it is possible that the DOS of the HOMO and LUMO have different widths, i.e. e . In this case, by benchmarking the 3D-ME results with 3D-KMC, we find that using an effective e = min(u $^{e}$, u ) in Eq. (14) yields a good agreement. We ew this as a result of the different roles of the two carriers: the carriers on molecules with the larger σ will be “trapped” and the recombination is most likely due t o capture of the more mobile other type of carrier, on molecules with a smaller σ . 

## Ill) 3D bipolar device simulations 

In this section, the results of device simulations using the bipolar 3D-ME model are compared with the results of 3D-KMC simulation results. We also show simulation results for V < where only the 3D-ME model can be used. The simulations were carried out using a constant recombination prefactor 7 , of the form given by Eq. (14), and with the optimized parameters A = 0.024 and B = 0.154 as explained in the previous section. 

## A . CURRENT DENSITY- VOLTAGE CHARACTERISTICS AND PROFILES OF THE CHARGE CARRIER CONCENTRATION, RECOMBINATION RATE, AND ELECTRIC FIELD 

As an example, we study 100 nm thick devices, with the layer structure shown in Fig. 3A. We assume a lattice constant a = 1 nm, hopping attempt frequency = 3.3 x 10 10 s _ , relative dielectric constant ε Γ = 3, and temperature T = 290 K. The HOMO 

