Three-Dimensional Modeling of Organic Light-Emitting Diodes Containing Molecules with Large Electric Dipole Moments

We present the results of a three-dimensional kinetic Monte Carlo (3D KMC) simulation study of the current density and efficiency of a prototypical green phosphorescent organic light-emitting diode within which the TPBi [2,$2^{\prime }$,$2^{″}$-(1,3,5-benzinetriyl)-tris(1-phenyl-1-H-benzimidazole)] molecules that comprise the electron transport layer have a large (7 D) static dipole moment. By explicitly calculating the dipole-induced electrostatic field distribution the additional energetic disorder and the additional internal electrostatic field due to the small net dipole-moment orientation in TPBi are included in a mechanistic manner. The simulation results are compared with the results of an experimental study by B. Sim et al. [ACS Appl. Mater. Interf. 8, 33010 (2016)]. Using a set of simulation parameters that provides a fair agreement with the experimental voltage-dependent current density, external quantum efficiency, and emission profiles, the simulations are used to study the sensitivity to the size and net orientation of the dipole moments. We show how the dipole-induced disorder and the dipole orientation affect the current density, the electron injection efficiency, the blocking of holes by the TPBi layer, the shape of the emission profile, and the quantum efficiency. A key element of the validation of the simulations is a comparison with measured emission profiles, which Sim et al. obtained from sense layer experiments. Explicit KMC simulations of these experiments are used to investigate the expected accuracy with which the emission profiles are probed.

Figure 1

Molecular structure of TPBi (a) and angular dependence of the normalized orientation probability distribution function for TPBi, obtained from quantum-chemical calculations in Ref. [12] (b) and obtained from a fit to these data using the approach described in Sec. 2b (c). A three-dimensional representation of the structure of TPBi has been given in Fig. 2 of Ref. [12].

Figure 2

Energy-level and layer structure of the phosphorescent OLEDs studied. The CBP:Ir(ppy)${}_2$(acac)(6.5 mol%) emissive layer is sandwiched in between a CBP hole transport layer and a TPBi electron transport layer. ITO(70 nm)/${\mathrm{Mo}\mathrm{O}}_3$(1 nm) and $\mathrm{Li}\mathrm{F}$(0.7 nm)/$\mathrm{Al}$(100 nm) are used as anode and cathode layers, respectively. The dotted (full) lines give the energy sets $A$ and $B$, respectively. In this work, 3D KMC simulations are shown to yield a fair description of the current voltage curves and emission profiles reported in Ref. [34] when using set $B$ and including dipole moments on TPBi, or when using set $A$, neglecting the dipole moments on TPBi and assuming a strongly reduced electron hopping attempt rate (see Sec. 5).

Figure 3

TPBi-layer-thickness dependence of the TPBi ionization energy and the work function, obtained from UPS experiments of evaporation-deposited films of TPBi on a $\mathrm{Au}$ substrate.

Figure 4

Comparison of the 3D KMC simulations results for the devices in Fig. 2 with the experimental results of Ref. [34] [thick dashed curves in (a) and (b), and all data in (c)]. The simulations marked $A$ and $B$ use frontier energy-level sets $A$ or $B$ (see Fig. 2) with for all materials ${\nu }_{1,e}=0.01\times {\nu }_{1,h}$ and ${\nu }_{1,e}=0.3\times {\nu }_{1,h}$, respectively (see Secs. 5a and 5b). (a) $J(V)$ curves from simulations without and including TPBi dipole moments. (b) Current-density dependence of the external quantum efficiency [${\eta }_{\mathrm{EQE}}$, full curves, see Eq. (8)] and of ${\eta }_{\mathrm{EQE,EML}}$ [dashed curves, see Eq. (9)]. (c) Emission profiles as a function of the distance to the $\mathrm{HTL}\mid \mathrm{EML}$ interface, obtained from sense-layer experiments at the indicated voltages and expressed with respect to the intensity that is obtained using a sense layer at the $\mathrm{EML}\mid \mathrm{ETL}$ interface. (d),(e) Normalized emission profiles for various voltages, obtained from 3D KMC simulations neglecting and including the TPBi dipole moments. The 7-, 9-, and 11-V data are for clarity shifted by 0.05, 0.10, and 0.15.

Figure 5

Results of a 3D KMC simulation study of the sensitivity of the performance of the devices in Fig. 2 (with energy-level set $B$) to a variation of the TPBi dipole moment $p$. (a) Dependence of the current density at various values of the voltage on $p$. (b) Roll-off curves ${\eta }_{\mathrm{EQE}}(J)$ for various values of $p$, obtained from simulations at 7, 9, and 11 V, and (for $p=0$ and 7 D) also at 5 and 6 V. The labels of each curve are located at the 7-V point. The dashed curve gives the experimental data [34]. (c) Normalized emission profiles in the EML at 9 V, for various values of $p$. Panels (a) and (b) show that the effect on the $J(V)$ characteristics and the EQE roll-off of “switching on” the static dipole moments of the TPBi sites in the ETL, while keeping all other simulation parameters fixed, becomes already significant beyond a value of the molecular dipole moments of approximately 3 D. Panel (c) shows that the resulting reduced effective electron mobility in the ETL strongly affects the shape of the emission profile.

Figure 6

Charge-carrier concentration profiles [(a)–(e)] and normalized emission profiles [(f)–(j)] across the thickness of the device, obtained from 3D KMC simulations at $V=11\mathrm{V}$ for varying values of the dipole-orientation parameter $\delta$ and for a fixed value of the asphericity parameter $\alpha =1.5$. For TPBi, $\delta =+0.068$ (see Sec. 3a). In (a)–(e) the red (blue) curves give the hole (electron) concentration. The figure shows that for large positive values of $\delta$ the hole blocking at the $\mathrm{EML}\mid \mathrm{TPBi}$ interface becomes nonideal, leading to singlet formation in the TPBi layer that is expected to contribute to an EQE loss due to quenching processes.

Figure 7

Dependence of the IQE and the radiative decay efficiency in the EML on the dipole orientation parameter $\delta$, obtained from 3D KMC simulations for the device in Fig. 2 at 7 and 11 V. For TPBi, $\delta =0.068$ (vertical dashed line, see Sec. 3a). The simulations were performed for $p=7\mathrm{D}$ and $\alpha =1.5$, using energy level set B. The closed symbols give ${\eta }_{\mathrm{IQE}}$ and the open symbols give ${\eta }_{r,\mathrm{EML}}$ [defined in Eq. (9)]. The curves are guides-to-the-eye. The figure shows that a variation of the net dipole orientation can significantly affect the IQE. For values of $\delta$ for which the difference between the full and dashed curves is large, the IQE is reduced strongly be a nonideal recombination efficiency. Such a loss could be prevented by improving the blocking of holes at the $\mathrm{EML}|\mathrm{ETL}$ interface.

Figure 8

Results of 3D KMC simulations of sense-layer studies of the emission profile of the device that is shown in Fig. 2, for four sets of frontier orbital energies ($A$–$D$, see Table 2) of the sense molecules. Dipole moments are not included; the simulations are carried out using the set of parameters that is discussed in Sec. 5a. (a),(b) Effect on the current density at 7 V (a) and 11 V (b) of adding a small concentration of sense molecules at various positions in the EML. The dashed line gives the result without the sense molecules, with an uncertainty that is given by the width of the gray zones. (c),(d) The (red) emission from the sense molecules at 7 V (c) and 11 V (e) as a function of their position in the EML. The dashed curves give the (green) ${\mathrm{Ir(ppy)}}_2$(acac) emission in the absence of the sense molecules, obtained from 3D KMC simulations. The emission intensities are normalized such that their average value is equal to unity.