In at least one embodiment, the method is designed for producing a light-emitting diode display (1). The method comprises the following steps: •A) providing a growth substrate (2); •B) applying a buffer layer (4) directly or indirectly onto a substrate surface (20); •C) producing a plurality of separate growth points (45) on or at the buffer layer (4); •D) producing individual radiation-active islands (5), originating from the growth points (45), wherein the islands (5) each comprise an inorganic semiconductor layer sequence (50) with at least one active zone (55) and have a mean diameter, when viewed from above onto the substrate surface (20), between 50 nm and 20 μm inclusive; and •E) connecting the islands (5) to transistors (6) for electrically controlling the islands (5).