Previously, we showed within a sub-micron fin shape heterojunction, as current density increases, the non-radiative Auger recombination saturates mediated by the extension of the depletion region into the fin, resulting in a droop-free behavior. Here, we investigate the dependence of the fin aspect ratio (height to width ratio) on external quantum efficiency (EQE) of single n-AlGaN fin/p-GaN heterojunctions. Fins are arranged in an array format varying in width from 3000 to 200 nm. In this architecture, an n-metal contact is interfaced with the non-polar side facet of the fin. At a fixed current density, as the aspect ratio increases from 0.2 to 3 (the fin width reduces), we systematically observe an increase in the ultraviolet (UV) excitonic emission of the AlGaN fin and a 7× enhancement in the EQE. We explain this phenomenon by conserving the volume of the carrier depletion region within a fin. As the fin gets thinner, the base area of the depletion volume shrinks, whereas its height increases within the fin. This geometrical advantage allows a 200 nm wide fin to operate at 1/3rd the current density compared to a 3000 nm wide fin while generating a UV emission with a comparable power of 1 μW. These findings show additional parameters that can be used for developing brighter light sources, including the shape and aspect ratio of a heterojunction at the micro- or nano-scale.