Producing a light-emitting semiconductor component by connecting first and second semiconductor bodies

A light-emitting semiconductor component comprising:

• a first semiconductor body, which comprises an active zone, in which electromagnetic radiation is generated during the operation of the light-emitting semiconductor component, said electromagnetic radiation leaving the first semiconductor body at least partly through a radiation exit area;
• and
• a second semiconductor body, which is suitable for converting the electromagnetic radiation into converted electromagnetic radiation having a longer wavelength,
• wherein the second semiconductor body is electrically inactive,
• wherein the second semiconductor body is in direct contact with the radiation exit area and is fixed to the first semiconductor body there, in a manner free of connecting means,
• wherein the radiation exit area and the outer area of the second semiconductor body facing the radiation exit area in each case have a root-mean-square roughness value of at most 2 nm, and
• wherein the second semiconductor body is based on a III-V compound semiconductor material.