Accounting for coherent effects in the ray-tracing of light-emitting diodes with interface gratings via mixed-level simulation

Abstract

Ray-tracing (RT) has long been the workhorse technique for analyzing light-emitting diode (LED) dies and packages and has led to significant improvements in extraction efficiency and beam shaping. However, to achieve further enhancements, nano-/microscale features such as patterned substrates and surface textures have been explored. The coherent effects arising from these near/subwavelength features are difficult to include in the RT of the packaged device. We show that under certain conditions these effects can have a significant impact on LED performance, especially if back-reflectors are present. Furthermore, we demonstrate that coherence must be accounted for even in structures that would otherwise be considered as having relatively large feature sizes, such as gratings with periods many times the wavelength. We present comparisons between the optical responses of prototypical periodically patterned substrates modeled with RT alone and with a mixed-level approach that combines RT and rigorous electromagnetic simulation, such as rigorous coupled wave analysis and finite-difference time-domain. Several examples with varying lateral periods are computed with both methods. It is shown that these results may differ, and that these differences can be significant if back reflection is present. We conclude that a mixed-level approach is an efficient and accurate method to model light extraction in modern LEDs.