Modelling gratings on either side of the substrate for light extraction in light-emitting diodes

We present a three-dimensional model based on rigorous coupled wave analysis (RCWA) which allows us to study the influence of periodic structures on light extraction in light-emitting diodes. The gratings can be placed both at the interface between the emitting layers and the substrate, where they coherently interact with the dipole field, or at the interface between the substrate and air, where multiple incoherent reflections in the thick substrate contribute to the overall extraction. Even in the case of a grating at the interface between the substrate and air, these multiple incoherent reflections in the substrate still contribute to the overall extraction for large devices, an effect which has been mostly ignored in literature FDTD simulations.