A memory using a tunnel barrier is disclosed. A memory element includes a tunneling barrier and two conductive materials. 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 irreversibly formed for one time programmable memory. The tunneling barrier can be formed by mobile ions combining with complementary ions. 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.