A semiconductor module and a stack arrangement of semiconductor modules is proposed. The semiconductor module comprises an insulated gate bipolar transistor, a wide band-gap switch, a base plate, and a press device. The insulated gate bipolar transistor and the wide band-gap switch are connected in parallel and are each mounted with a first planar terminal to a side of the base plate. Further, a second planar terminal of the insulated gate bipolar transistor and a second planar terminal of the wind band-gap switch are connected with an electrically conductive connection element, and the press device is arranged on the second planar terminal of the insulated gate bipolar transistor. Hence, when arranging the semiconductor modules in a stack arrangement, any press force is primarily applied to the insulated gate bipolar transistors of the semiconductor modules.