An optoelectronic device comprising a semiconductor structure includes a p-type active region, an n-type active region, and an i-type active region. The semiconductor structure is comprised solely of one or more superlattices, where each superlattice is comprised of a plurality of unit cells. Each unit cell can comprise a layer of GaN and a layer of AlN. In some cases, a combined thickness of the layers comprising the unit cells in the i-type active region is thicker than a combined thickness of the unit cells in the n-type active region, and is thicker than a combined thickness of the unit cells in the p-type active region. The layers in the unit cells in each of the three regions can all have thicknesses that are less than or equal to a critical layer thickness required to maintain elastic strain.