The invention relates to a semiconductor memory having a multiplicity of memory cells and a method for forming the memory cells. The semiconductor memory generally includes a semiconductor layer arranged on a substrate surface that includes a normally positioned step between a deeper region and a higher region. The semiconductor memory further includes doped contact regions, channel regions, a trapping layer arranged on a gate oxide layer, and at least one gate electrode. The method for forming the memory cells includes patterning a semiconductor layer to form a deeper semiconductor region and a higher semiconductor region having a step positioned between the regions. The method further includes forming a first oxide layer and a trapping layer, and then removing portions of the trapping layer and the first oxide layer and applying a second oxide layer at least regions of a doped region, the trapping layer, and the step area, and applying a gate electrode to the second oxide layer and doping, at least in regions, of the deeper semiconductor region and the higher semiconductor region to form a deeper contact region and a higher contact region.