Memory cells each having a cell capacitor and a cell transistor, which are arranged in a vertical cell structure, are provided in the cell array of a DRAM. By means of a deep implantation or a shallow implantation and subsequent epitaxial growth of silicon, a buried source/drain layer is formed, from which lower source/drain regions of the cell transistors emerge. The upper edge of the buried source/drain layer can be aligned with respect to a lower edge of a gate electrode of the cell transistor and this results in a reduction of a gate/drain capacitance and also a leakage current between the gate electrode and the lower source/drain region. A body connection plate for the connection of the channel regions is applied to the substrate surface and contact holes are introduced into the body connection plate. Upper source/drain regions of the cell transistors are formed by implantation through the contact holes.