Photonic crystals for optimal color conversion in light-emitting diodes: A semi-analytical approach

Based on effective-medium approximation, we analytically optimize the color conversion of GaN-based lightemitting p-n junctions, with respect to the size and spatial density of the used photonic crystals (PhCs), being filled with quantum dots (QDs). The model is two-dimensional and the incoherent excitation into the multiple quantum wells is mimicked by line sources of random electric and magnetic currents. Optimal operation is achieved by suppressing the radiation extraction for one visible color and simultaneously maximizing the emission for another color. For these cases, the field gets inevitably concentrated into the PhCs of QDs, where the conversion occurs, and the performance of the device is maximized. Several examples from these ultra-performing designs are provided, within which a secondary sweep can be applied by posing extra constraints related to cost or ease of fabrication.