Memory cells 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 with 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, which consequently 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 gate conductor layer structure is applied and there are formed, from the gate conductor layer structure, in a controlled transistor array, gate electrode structures of control transistors and, in the cell array, a body connection structure for the connection of body regions of the cell transistors.