The present invention relates to a method for the manufacture of a semiconductor device by providing a first substrate; providing a doped layer in a surface region of the first substrate; providing a buried oxide layer on the doped layer; providing a semiconductor layer on the buried oxide layer to obtain a semiconductor-on-insulator (SeOI) wafer; removing the buried oxide layer and the semiconductor layer from a first region of the SeOI wafer while maintaining the buried oxide layer and the semiconductor layer in a second region of the SeOI water; providing an upper transistor in the second region by forming a back gate in or by the doped layer; and providing a lower transistor in the first region by forming source and drain regions in or by the doped layer.