1. An integrated semiconductor memory comprising: a memory cell having a storage layer comprising a storage medium, wherein the memory cell can assume a first state of lower electrical conductivity and a second state of higher electrical conductivity, wherein the memory cell undergoes a phase transition between the first and second states, and wherein the respective state of the storage medium is set with the aid of an electric current flowing through the storage medium; wherein: the storage layer has a layer plane in which regions made from a different material than the storage medium are distributed and in which the storage medium is arranged between the regions made from the different material; the regions made from the different material have dimensions that are smaller than a feature size that can be dimensioned lithographically; and the different material adjoins patterned regions of an electrically insulating layer.