Impact of Ga and N Vacancies at the GaN

Micro-light-emitting diodes ($\text{\ensuremath{\mu}}\mathrm{LEDs}$) based on $\mathrm{Ga}\mathrm{N}$ are a key component for next-generation displays, but serious surface $e$-$h$ recombination deteriorates the device efficiency. To gain microscopic insights into the surface recombination, we use hybrid functional first-principles calculations to investigate $\mathrm{Ga}$ (${V}_{\mathrm{Ga}}$) and $\mathrm{N}$ (${V}_{\mathrm{N}}$) vacancies on the $\mathrm{Ga}\mathrm{N}$ $m$ plane that can be created considerably during the production of one-dimensional $\mathrm{Ga}\mathrm{N}$ structures. We find that the surface ${V}_{\mathrm{Ga}}$ is not critical for nonradiative Shockley-Read-Hall (SRH) recombination in light of the large formation energy (>2 eV) and its shallow levels. In contrast, the surface ${V}_{\mathrm{N}}$ exhibits a low formation energy (2 eV) and develops a deep defect state near the midgap, indicating the possibility of becoming useful SRH recombination centers. By constructing configuration-coordinate diagrams, we demonstrate that the energy barriers for electron and hole capture on the surface ${V}_{\mathrm{N}}$ are small enough to cause significant capture coefficients due to strong electron-phonon coupling.