Semiconductor memory having memory cells, each including first and second conductively-doped contact regions and a channel region arranged between the latter, formed in a web-like rib made of semiconductor material and arranged one behind the other in this sequence in the longitudinal direction of the rib. The rib has an essentially rectangular shape with an upper side of the rib and rib side faces lying opposite. A memory layer is configured for programming the memory cell, arranged on the upper side of the rib spaced apart by a first insulator layer, and projects in the normal direction of the one rib side face over one of the rib side faces so that the one rib side face and the upper side of the rib form an edge for injecting charge carriers from the channel region into the memory layer. A gate electrode is spaced apart from the one rib side face by a second insulator layer and from the memory layer by a third insulator layer, electrically insulated from the channel region, and configured to control its electrical conductivity.