A memory device of the irreversibly electrically programmable type is provided with a memory cell having a dielectric zone disposed between a first electrode and second electrode. An access transistor is connected in series with the second electrode, and an auxiliary transistor is connected in series with the first electrode. The auxiliary transistor is biased to have a saturation current which is lower than a saturation current of the access transistor when both the auxiliary and access transistors are actuated. A number of the memory cells are arranged in a memory plane to form the memory device.