A device wafer having a main surface including an edge region and a carrier having a further main surface including an annular surface region corresponding to the edge region of the device wafer are provided. An adhesive is applied in the edge region and/or in the annular surface region, but not on the remaining areas of the main surfaces. The device wafer is fastened to the carrier by the adhesive. The main surface and the further main surface are brought into contact with one another when the device wafer is fastened to the carrier, while the main surface and the further main surface are fastened to one another only in the edge region. The device wafer is removed from the carrier after further process steps, which may include the formation of through-wafer vias in the device wafer.