Accurate optical simulation of nano-particle based internal scattering layers for light outcoupling from organic light emitting diodes

We present a numerical strategy for the accurate simulation of light extraction from organic light emitting diodes (OLEDs) comprising an internal nano-particle based scattering layer. On the one hand, the light emission and propagation through the OLED thin film system (including the scattering layer) is treated by means of rigorous wave optics calculations using the T-matrix formalism. On the other hand, the propagation through the substrate is modeled in a ray optics approach. The results from the wave optics calculations enter in terms of the initial substrate radiation pattern and the bidirectional reflectivity distribution of the OLED stack with scattering layer. In order to correct for the truncation error due to a finite number of particles in the simulations, we extrapolate the results to infinitely extended scattering layers. As an application example, we estimate the optimal particle filling fraction for an internal scattering layer in a realistic OLED geometry. The presented treatment is designed to emerge from electromagnetic theory with as few additional assumptions as possible. It could thus serve as a baseline to validate faster but approximate simulation approaches.