Optical modeling of the emission zone profile and optimal emitter position based on the internal field profile of the air mode in organic light-emitting diodes.

We propose a theoretical formulation to calculate the internal profile of the air mode in the organic light-emitting diode (OLED) on the combination of the transfer matrix method and source-term method. The spatial distributions of the air mode are calculated in a top-emitting OLED with respect to the light polarization, extraction angle, dipole orientation, and dipole position. Air modes are also calculated on the basis of the previously used external source model, where the input optical wave is injected from the air into the OLED multilayer. Comparison of the calculated air modes between two models checks the validity of the external source model. In addition, we propose an improved formula to determine the optimal emitter positions that maximize the two-beam interference of the micro-cavity effect. In the improved formula, a non-ideal reflection phase shift at a reflective metal anode is treated as the skin depth of the air mode. Finally, the effect of the dipole orientation on the air mode is investigated. Compared with the air mode emitted by the horizontally oriented dipole, the air mode generated by the vertically oriented dipole has relatively small intensity and shows the opposite dependence of the emitter position variation. The calculation results of the internal profile of the air mode within the emission layer are matched with the profile of the emission zone obtained by output radiant flux on the basis of the currently used point dipole model.