Abstract
A multiscale model that enables quantitative understanding and prediction of the size effect on the scattering properties of micro- and 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.
Highlights
Over the past 10 years, numerous studies in the field of light-emitting diode (LED) solid-state lighting have focused on how to improve luminous efficacy
Of the LED, various textured structures have been proposed to avoid the occurrence of total internal reflection, including rough surfaces, patterned substrates, diffraction gratings, and photonic crystals
To unify the parameters of the of the geometry of textured structures with any scale, we use the aspect ratio, which is defined as the geometry of textured structures with any scale, we use the aspect ratio, which is defined as the ratio ratio of the structure height to the structure width
Summary
Over the past 10 years, numerous studies in the field of light-emitting diode (LED) solid-state lighting have focused on how to improve luminous efficacy. Light extraction efficiency (LEE) has played an important role in this research regarding the development of highly efficient LEDs [1,2]. The LEE of a typical LED is generally low, mainly because of the large refractive index difference between the LED material and the surrounding environment. Most of the photons are completely internally reflected and are trapped inside the LED. To substantially enhance the LEE of the LED, various textured structures have been proposed to avoid the occurrence of total internal reflection, including rough surfaces, patterned substrates, diffraction gratings, and photonic crystals
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