A method can be used for fixing a matrix-free electrophoretically deposited layer on a semiconductor chip. A semiconductor wafer has a carrier substrate and at least one semiconductor chip. The at least one semiconductor chip has an active zone for generating electromagnetic radiation. At least one contact area is formed on a surface of the at least one semiconductor chip facing away from the carrier substrate. A material is electrophoretically deposited on the surface of the at least one semiconductor chip facing away from the carrier substrate in order to form the electrophoretically deposited layer. Deposition of the material on the at least one contact area is prevented. An inorganic matrix material is applied to at least one section of a surface of the semiconductor wafer facing away from the carrier substrate in order to fix the material on the at least one semiconductor chip.