Abstract: A process for preparing smoothened III-N, in particular smoothened III-N substrate or III-N template, wherein III denotes at least one element of group III of the Periodic System, selected from Al, Ga and In, utilizes a smoothening agent comprising cubic boron nitride abrasive particles. The process provides large-sized III-N substrates or III-N templates having diameters of at least 40 mm, at a homogeneity of very low surface roughness over the whole substrate or wafer surface. In a mapping of the wafer surface with a white light interferometer, the standard deviation of the rms-values is 5% or lower, with a very good crystal quality at the surface or in surface-near regions, measurable, e.g., by means of rocking curve mappings and/or micro-Raman mappings.