Stability of Quantized Conductance Levels in Memristors with Copper Filaments: Toward Understanding the Mechanisms of Resistive Switching

Memristors are among the most promising elements for modern microelectronics, having unique properties such as quasicontinuous change of conductance and long-term storage of resistive states. However, identifying the physical mechanisms of resistive switching and of the evolution of conductive filaments in such structures still remains a major challenge. In this work, aiming at a better understanding of these phenomena, we experimentally investigate an unusual effect of enhanced conductive filament stability in memristors with copper filaments under the applied voltage and present a simplified theoretical model of the effect of a quantum current through a filament on its shape. Our semiquantitative, continuous model indeed predicts that, for a thin filament, the ``quantum pressure'' exerted on its walls by the recoil of charge carriers can well compete with the surface tension and crucially affect the evolution of the filament profile at voltages of around 1 V. At lower voltages, the quantum pressure is expected to provide extra stability to the filaments supporting quantized conductance, which we also reveal experimentally using a methodology focusing on retention statistics. Our results indicate that the recoil effects could be potentially important for resistive switching in memristive devices with metallic filaments and that taking them into account in the rational design of memristors could help achieve their better retention and plasticity characteristics.