Size-dependent top extraction and finite-NA capture in ultra-small blue GaN micro-LEDs via peripheral-emission-weighted FDTD analysis

Ultra-small blue GaN micro-LEDs (µLEDs) for near-eye displays require not only efficient top-side light extraction but also optical output that can be captured by finite-numerical-aperture (NA) projection optics. However, in this size regime, wave-optical interference, lateral pixel size, and edge-proximal emission non-uniformity can jointly affect both the extracted power and its angular distribution, making top-extraction-only or single-source analysis insufficient for evaluating usable forward output. Here, to address these limitations and directly evaluate finite-NA captured output under practical collection conditions in the ultra-small pixel regime, we conducted a peripheral-emission-weighted finite-difference time-domain (FDTD) analysis for size-dependent top extraction and finite-NA capture in ultra-small blue GaN µLEDs. The method incoherently combined representative dipole positions and polarizations and incorporated a radius-dependent peripheral weighting factor to effectively account for reduced peripheral radiative contribution associated with sidewall effects. For circular GaN µLEDs with pixel radii ranging from 2.0 to 2.8 μm, we investigated how p -GaN thickness and AlGaN electron-blocking-layer (EBL) insertion reshaped top light-extraction efficiency, angular emission, and NA-limited captured output. The simulations showed that p -side stack variations produced non-monotonic extraction behavior and shifted favorable thickness windows in a radius-dependent manner, while finite-NA metrics revealed changes in practically collectable output that were not captured by top extraction efficiency alone. This work provides a computationally efficient FDTD framework for evaluating how p -side-stack design and pixel size influence top-side extraction, finite-NA captured output, and their sensitivity to peripheral-emission reduction in ultra-small blue µLEDs.