The invention relates to a semiconductor memory, particularly a DRAM, in which the memory cells in each case have a trench capacitor arranged in a lower area of a trench hole and a vertical selection transistor which is formed adjoining an upper area of the trench hole and which connects an inner electrode of the trench capacitor to a bit line, a conductive channel being capable of being formed in dependence on the potential of a word line in the channel area, the channel area completely enclosing the trench hole in its upper area, and the associated word line at least partially enclosing the channel area.