A memory using a tunnel barrier that has a variable effective width is disclosed. A memory element includes a tunneling barrier and a conductive material. The conductive material typically has mobile ions that either move towards or away from the tunneling barrier in response to a voltage across the memory element. A low conductivity region is either formed or destroyed. It can be formed by either the depletion or excess ions around the tunneling barrier, or by the mobile ions combining with complementary ions. It may be destroyed by either reversing the forming process or by reducing the tunneling barrier and injecting ions into the conductive material. The low conductivity region increases the effective width of the tunnel barrier, making electrons tunnel a greater distance, which reduces the memory element's conductivity. By varying conductivity multiple states can be created in the memory cell.