A memory device, containing a first electrode, a second electrode and an oxide layer arranged between the first electrode and the second electrode, is produced. The oxide layer has a first zone and a second zone, with the first zone surrounding or being located on either side of the second zone, with the minimum distance d2 separating the two electrodes on the second zone of the oxide layer being less than the minimum distance d1 separating the two electrodes on the first zone of the oxide layer.