A ceramic layer is fabricated on a substrate by coating the substrate with a material containing chemical precursors of a ceramic. The precursors are transformed by a heat treatment into the ceramic to be fabricated. Different methods for heat insertion may be used for individual layers by absorbing particles, which are utilized in different concentrations or different chemical compositions. A targeted heat insertion even in lower layer regions, for example, by microwave animation, or ultraviolet or infrared light insertion is therefore possible. Beneficially, as a result, comparatively thick layers in particular can be fabricated by a single heat treatment layer.