Scale-Dependent Light Scattering Analysis of Textured Structures on LED Light Extraction Enhancement Using Hybrid Full-Wave Finite-Difference Time-Domain and Ray-Tracing Methods

A multiscale model that enables quantitative understanding and prediction of the size effect on scattering properties of micro- and nanostructures is crucial for the design of LED surface textures optimized for high light extraction efficiency (LEE). In this paper, a hybrid process for combining full-wave finite-difference time-domain simulation and a ray-tracing technique based on a bidirectional scattering distribution function model is proposed. We apply this method to study the influence of different pattern sizes of a patterned sapphire substrate on GaN-based LED light extraction from the microscale to the nanoscale. The results show that near-wavelength–scaled patterns with strong diffraction are not expected to enhance LEE. By contrast, microscaled patterns with optical diffusion behavior have the highest LEE at a specific aspect ratio, and subwavelength-scaled patterns that have antireflection properties show marked enhancement of LEE for a wide range of aspect ratios.