Memory using variable tunnel barrier widths

A re-programmable memory element, comprising:

• an electronically insulating tunneling barrier having a conductivity;
• a first material that has a higher conductivity than the tunneling barrier;
• and
• a second material that has a first conductivity higher than the tunneling barrier, the tunneling barrier is disposed in between the first material and the second material, and the first material, the tunneling barrier, and the second material are electrically in series with one another,
• wherein a first electric field across the tunneling barrier is operative to promote ion movement from the first material through the tunneling barrier to the second material, the ions operative to create a low conductivity region within the second material, the low conductivity region having a lower conductivity than the first conductivity,
• wherein a second electric field across the tunneling barrier is operative to promote ion movement from the second material through the tunneling barrier to the first material, the ions operative to remove the low conductivity region within the second material, and the second electric field having a direction opposite to the first electric field, and
• wherein the memory element exhibits a first resistance when the second material does not have the low conductivity region arid exhibits a second resistance when the second material includes the low conductivity region, the first resistance having a lower resistance than the second resistance.