An integrated semiconductor memory includes a storage medium (6) arranged between two electrodes (10, 20), which storage medium may be a phase change medium, for example. The storage medium (6) can be put into a first state or a second state by means of an electric current, as a result of which an item of information can be stored. According to embodiments of the invention, a layer plane (L) is provided in which impurity particles made from a material (4) are embedded, as a result of which the current density in the storage medium is locally increased and the programming current required for reprogramming is reduced. As a result, the current consumption of memory elements containing a phase change medium is reduced, so that for the first time they can be embodied with minimal feature size, together with other components such as transistors, and integrated into a single semiconductor circuit and no longer have to be arranged in separate subcircuits.