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A multiscale model that enables quantitative understanding and prediction of the size effect on the scattering properties of microand nanostructures is crucial for the design of light-emitting diode (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 micro-scale to the nano-scale. The results show that near-wavelength–scale patterns with strong diffraction are not expected to enhance the LEE. By contrast, micro-scale patterns with optical diffusion behavior have the highest LEE at a specific aspect ratio, and subwavelength-scale patterns that have antireflection properties show a marked enhancement of the LEE for a wide range of aspect ratios.

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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