A radiation-emitting semiconductor component has an improved radiation efficiency. The semiconductor component has a multilayer structure with an active layer for generating radiation within the multilayer structure and also a window having a first and a second main surface. The multi-layer structure adjoins the first main surface of the window. At least one recess, such as a trench or a pit, is formed in the window from the second main surface for the purpose of increasing the radiation efficiency. The recess preferably has a trapezoidal cross section tapering toward the first main surface and can be produced for example by sawing into the window.