A process of producing a radiation-emitting organic-electronic device having a first and a second electrode layer and an emitter layer includes: A) providing a phosphorescent emitter with an anisotropic molecule structure and a matrix material, B) applying the first electrode layer to a substrate, C) applying the emitter layer under thermodynamic control, with vaporization of the phosphorescent emitter and of the matrix material under reduced pressure and deposition thereof on the first electrode layer such that molecules of the phosphorescent emitter are in anisotropic alignment, and D) applying the second electrode layer on the emitter layer.