A semiconductor device includes a plastic package, at least one semiconductor chip and a rewiring level. The rewiring level includes an insulating layer and a rewiring layer. The rewiring layer includes either signal conductor paths and ground or supply conductor paths arranged parallel to one another and alternately, or only signal conductor paths arranged parallel to one another. In the latter case, an electrically conducting layer of metal which can be connected to ground or supply potential is additionally provided as a termination of the rewiring level or in the form of a covering layer.