A controllable resistive element and method of forming the same include a state device configured to provide a voltage-controlled resistance responsive to a voltage input. A dielectric layer is formed directly on the state device. A battery is formed directly on the dielectric layer, configured to apply a voltage to the state device based on a charge stored in the battery. A write device is configured to charge the battery responsive to a write signal. An erase device is configured to discharge the battery responsive to an erase signal.