A glass, ceramic or metal substrate with at least one self-cleaning surface comprising a layer with a micro-rough surface structure which is arranged on the substrate and made at least partly hydrophobic, wherein the layer contains a glass flux and structure-forming particles having a bimodal size distribution, wherein a first portion of structure-forming particles has a mean diameter from 0.2 to 3 μm and a second portion of structure-forming particles has a mean diameter from 3 to 15 μm, the glass flux and structure-forming particles are present in a volume ratio within the 0.1 to 5 range, and the micro-rough surface structure has a ratio of mean profile height to mean distance between adjacent profile tips within the 0.3 to 10 range.