Semiconductor module having a base plate with a concave curvature

A structured metal layer in contact with an electronic component is applied on an upper side of a substrate of electrically insulating material. A metallic contact layer is applied to an underside of the substrate, with the underside configured as planar surface in a state of the substrate that is free of mechanical stress. The contact layer is connected to a metallic base plate via an intermediate layer. The contact layer is connected to the metallic base plate at an elevated temperature. The semiconductor module is then cooled. The side of the metallic base plate facing the substrate and the side of the metallic base plate facing away from the substrate are configured as planar surfaces in a state of the base plate that is free of mechanical stress. Upon cooling of the semiconductor module, the base plate forms a concave curvature on its side facing away from the substrate.