We have fabricated tunnel-junction InGaN micro-LEDs using plasma-assisted molecular beam epitaxy technology, with top-down processing on GaN substrates. Devices have diameters between 5 µm and 100 µm. All of the devices emit light at 450 nm at a driving current density of about 10Acm-2. We demonstrate that within micro-LEDs ranging in size from 100 µm down to 5 µm, the properties of these devices, both electrical and optical, are fully scalable. That means we can reproduce all electro-optical characteristics using a single set of parameters. Most notably, we do not observe any enhancement of non-radiative recombination for the smallest devices. We assign this result to a modification of the fabrication process, i.e., replacement of deep dry etching by a tunnel junction for the current confinement. These devices show excellent thermal stability of their light emission characteristics, enabling operation at current densities up to 1kAcm-2.