We report the controllable growth of GaAs quantum complexes in droplet molecular-beam epitaxy, and the optical properties of self-assembled AlxGa1-xAs quantum rings embedded in a superlattice. We found that Ga droplets on a GaAs substrate can retain their geometry up to a maximum temperature of 490 degrees C during post-growth annealing, with an optimal temperature of 320 degrees C for creating uniform and symmetric droplets. Through controlling only the crystallisation temperature under As-4 in the range of 450 degrees C to 580 degrees C, we can reliably control diffusion, adsorption and etching rates to produce various GaAs quantum complexes such as quantum dots, dot pairs and nanoholes. AlxGa1-xAs quantum rings are also realised within these temperatures via the adjustment of As beam equivalent pressure. We found that crystallisation using As-2 molecules in the place of As-4 creates smaller diameter quantum rings at higher density. The photoluminescence of As-2 grown AlxGa1-xAs quantum rings embedded in a superlattice shows a dominant emission from the quantum rings at elevated temperatures. This observation reveals the properties of the quantum ring carrier confinement and their potential application as efficient photon emitters.