Stability of quantized conductance levels in memristors with copper filaments: towards understanding the mechanisms of resistive switching

Memristors are amongst the most promising elements for modern microelectronics, having unique properties such as quasi-continuous change of conductance and long-term storage of resistive states. However, identifying the physical mechanisms of resistive switching and 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 semi-quantitative, continuous model predicts, indeed, 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 the voltages 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 novel methodology focused on retention statistics. Our results indicate that the recoil effects could potentially be important for resistive switching in memristive devices with metallic filaments and that taking them into account in rational design of memristors could help achieve their better retention and plasticity characteristics.