Computational upper-limit of directional light emission in nano-LED via inverse design

We demonstrate directional light emission in nano-LEDs using inverse design. Standard light-extraction strategies in LEDs have been limited to surface roughening or suppressing guided modes via LED structure modifications, which are insufficient for simultaneously achieving high-light extraction efficiency and directional emission. In this work, we use inverse design to discover high-efficiency directional emitting nano-LEDs. We first investigate the computational upper bounds of directional emission using free-form grayscale material, where material permittivity indicates an intermediate state between air and SiO₂. For a narrow emission angle (<±30°), the optimized grayscale design offers 4.99 times enhancement from the planar LED surface. Then, we apply fabrication constraints to our inverse design for discovering a single material (SiO₂) based design. The optimized SiO₂ surface design shows 4.71 times light extraction (<±30°) improvement compared with the planar configuration. This is a first theoretical demonstration of high light-extraction efficiency and directional emitting nano-LED designs.