In an embodiment a component includes a semiconductor body, a converter layer, a filling layer and an intermediate layer arranged in a vertical direction between the semiconductor body and the converter layer, wherein the semiconductor body has a surface which faces the converter layer, is structured and has vertical recesses, wherein the vertical recesses are filled with a material of the filling layer that has a higher thermal conductivity than silicone, wherein the intermediate layer or the semiconductor body has a higher mechanical hardness than the filling layer, and wherein the structured surface of the semiconductor body has local elevations and local recesses, the structured surface including exclusively the surface of an n-type or a p-type semiconductor layer.