An assembly has a columnar structure arranged with one end on a substrate, wherein the structure is at least partly covered with a semiconductor layer structure having an active zone that generates electromagnetic radiation, the active zone has a band gap for a radiative recombination, and the band gap decreases along a longitudinal axis of the structure in a direction of a free end of the structure such that a diffusion of charge carriers in the direction of the free end of the structure and a radiative recombination of charge carrier pairs in the region of the free end of the structure are supported.