A semiconductor module includes a substrate having a metallized first side and a metallized second side opposing the metallized first side. A semiconductor die is attached to the metallized first side of the substrate. A plurality of cooling structures are welded to the metallized second side of the substrate. Each of the cooling structures includes a plurality of distinct weld beads disposed in a stacked arrangement extending away from the substrate. The substrate can be electrically conductive or insulating. Corresponding methods of manufacturing such semiconductor modules and substrates with such welded cooling structures are also provided.