Assessing electric-field engineering of filamentary-type conduction in Cu/HfO2/Pt memristive devices using the quantum point-contact model

We explored the role of electric-field engineering in controlling filamentary-type conduction in Cu/HfO2/Pt memristive devices, utilizing the quantum point-contact (QPC) model for analysis. In a previous study, we reported that devices with a thicker oxide layer stack (20 and 15 nm) statistically exhibit higher resistance values in the high-resistance state (HRS) compared to devices with a thinner oxide layer stack (10 nm). In addition, thicker oxides exhibit higher and more broadly distributed set voltages compared to the more uniform distribution of set voltages occurring in thinner oxide layers. In this work, we thoroughly analyzed the electron transport characteristics of the electroformed devices (Cu conducting filament) using the QPC model, which allows us to infer the main features of the confinement potential barrier at the constriction's bottleneck. The obtained results indicate that the HRS current for the three thicknesses investigated follows a trend consistent with the predictions of the QPC model in terms of the aspect ratio energy barrier thickness/constriction radius (tB/R). Notably, the 10 nm samples exhibit a lower aspect ratio (tB/R < 1: wide nanogap) than the 15 and 20 nm samples (tB/R > 1: elongated nanogap). It was found that wide nanogaps are associated with lower variance of the HRS current and smaller set voltages. In view of these results, we suggest that optimizing the switching oxide layer thickness, therefore the shape of the filament, may be a suitable way to reduce variability of HRS current and set voltage to improve resistive switching performance.