In at least one embodiment, the semiconductor layering sequence (1) is designed for generating light and comprises semiconductor columns (2). The semiconductor columns (2) have a respective core (21) made of a semiconductor material of a first conductivity type, and a core shell (23) surrounding the core (21) made of a semiconductor material of a second conductivity type. There is an active zone (22) between the core (21) and the core shell (23) for generating a primary radiation by means of electroluminescence. A respective conversion shell (4) is placed onto the semiconductor columns (2), which conversion shell at least partially interlockingly surrounds the corresponding core shell (23), and which at least partially absorbs the primary radiation and converts same into a secondary radiation of a longer wavelength by means of photoluminescence. The conversion shells (4) which are applied to adjacent semiconductor columns (2), only incompletely fill an intermediate space between the semiconductor columns (2).