Fractional Marcus-Hush-Chidsey-Yakopcic current-voltage model for redox-based resistive memory devices

We propose a circuit-level model combining the Marcus-Hush-Chidsey electron current equation and the Yakopcic equation for the state variable for describing resistive switching memory devices of the structure metal-ionic conductor-metal. We extend the dynamics of the state variable originally described by a first-order time derivative by introducing a fractional derivative with an arbitrary order between zero and one. We show that the extended model fits with great fidelity the current-voltage characteristic data obtained on a Si electrochemical metallization memory device with Ag-Cu alloy. We propose a circuit-level model supplemented with memory trace for describing electrical behavior of redox-based resistive memory devices.