The invention claimed is:1. An optoelectronic component comprising:a semiconductor body comprising:a first region of a first conductivity type; wherein the first region comprises a recess therein;a second region of a second conductivity type; andan active region disposed between the first region and the second region;a contact region adjacent to the recess;wherein:the active region of the semiconductor body is designed to emit electromagnetic radiation;the semiconductor body has a first radiation exit surface at a main surface of the second region facing away from the active region;at least part of the electromagnetic radiation generated in operation exits the semiconductor body through the first radiation exit surface;the semiconductor body comprises a first electrical connection layer and a second electrical connection layer, wherein the second electrical connection layer is arranged at least partially in the recess; anda radiation transmissive carrier is arranged downstream from the first radiation exit surface, wherein the radiation transmissive carrier is materially bonded to the semiconductor body by a radiation transmissive bonding layer;wherein the extent of the contact region along the main extension plane of the semiconductor body corresponds to the extent of the recess along the main extension plane of the semiconductor body.2. The optoelectronic component according to claim 1, wherein the second region of the semiconductor body comprises a gallium phosphide compound semiconductor material.3. The optoelectronic component according to claim 1, wherein the recess does not completely penetrate the first region of the semiconductor body.4. The optoelectronic component according to claim 1, wherein the radiation transmissive bonding layer comprises a benzocyclobutene-based polymer, a silicon oxynitride, a titanium oxide, an aluminum oxide, or combinations thereof.5. The optoelectronic component according to claim 4, wherein the optical refractive index of the radiation transmissive bonding layer differs from the optical refractive index of the radiation transmissive carrier by a maximum of 10%.6. The optoelectronic component according to claim 1, wherein the main surface of the first region of the semiconductor body facing away from the active region further comprises a second radiation exit surface thereon, through which at least part of the generated electromagnetic radiation exits the semiconductor body.7. The optoelectronic component according to claim 6, wherein the first radiation exit surface and/or the second radiation exit surface are roughened.8. A method of manufacturing an optoelectronic component, wherein the method comprises:providing a growth substrate having a semiconductor body grown thereon,wherein the semiconductor body comprises:a first region of a first conductivity type,a second region of a second conductivity type, wherein the first region isdisposed between the growth substrate and the second region, andan active region disposed between the first region and the second region;forming a contact region in the second region of the semiconductor body;depositing a radiation transmissive bonding layer on a first radiation exit surface;arranging a radiation transmissive carrier on the side of the radiation transmissive bonding layer remote from the second region;detaching the growth substrate from the side of the first region remote from the active region;forming a recess in the first region, wherein the recess extends transversely to the main plane of extension of the first region and extends to the contact region; anddepositing a first electrical connection layer and a second electrical connection layer on the side of the first region facing away from the active region, wherein the second electrical connection layer is arranged at least partially in the recess,whereina doping material is introduced during the forming of the contact region; orthe forming of the contact region occurs after depositing the first electrical connection layer, and wherein the second electrical connection layer is electrically conductively connected to the second region by means of a high-temperature process during the forming of the contact region.9. The method for producing an optoelectronic component according to claim 8, wherein the surface of the second region facing away from the active region is roughened to produce a first radiation exit surface before or after the forming of the contact region in the second region.10. The method of manufacturing an optoelectronic component according to claim 8, wherein the surface of the first region facing away from the active region is roughened to produce a second radiation exit surface after detaching the growth substrate.11. The method of manufacturing an optoelectronic component according to claim 8, whereinthe entire contact region has a conductivity of the second conductivity type.12. The method of manufacturing an optoelectronic component according to claim 11, whereinthe contact region of a second conductivity type extends into the first region; andthe recess does not completely penetrate the first region transversely to the main extension plane of the first region.13. The method of manufacturing an optoelectronic component according to claim 8, whereinforming the contact region in the second region occurs after forming the recess in the first region;a doping material is introduced during the forming of the contact region; andthe entire contact region has a conductivity of the second conductivity type.14. An optoelectronic component comprising:a semiconductor body comprising:a first region of a first conductivity type,a second region of a second conductivity type, andan active region disposed between said first region and said second region;a recess in the first region of the semiconductor body;a contact region adjacent to the recess;wherein:a doping material of the second conductivity type is in the contact region;the active region of the semiconductor body is designed to emit electromagnetic radiation;the semiconductor body comprises a first radiation exit surface at a main surface of the second region facing away from the active region;at least a portion of the electromagnetic radiation generated in operation exits the semiconductor body through the first radiation exit surface;the semiconductor body comprises a first electrical connection layer and a second electrical connection layer; wherein the second electrical connection layer is arranged at least partially in the recess; anda radiation transmissive carrier arranged downstream from the first radiation exit surface, wherein the radiation transmissive carrier is materially bonded to the semiconductor body by means of a radiation transmissive bonding layer.