A trench (2) is fabricated in a silicon body (1). The walls (4) of the trench are provided with a nitrogen implantation (6). An oxide layer between the source/drain regions (5) and a word line applied on the top side grows to a greater thickness than a lower oxide layer of an ONO storage layer fabricated as gate dielectric at the trench wall. Instead of the nitrogen implantation into the trench walls, it is possible to fabricate a metal silicide layer on the top sides of the source/drain regions in order to accelerate the oxide growth there.