Calculation and study for the growth process and electrical characteristics of the conductive filament in nanoscale...

After investigating the behavior of ions during the growth of conductive filaments, we suggested a model for the growth process and electrical characteristics of the conductive filament under current-driven mode. In this model, the ionic displacement equation is derived by Arrhenius law, and a differential equation for the conductive filament growth has been established. We have also proved that the dielectric layer with the leakage current under current-driven mode can be equivalent to a parallel plate capacitor, which has a the equivalent dielectric constant. Consequently, the forming/set time of the device is gotten. At the same time, the kinetics process of ion motion is analyzed in detail, so that many microscopic parameters of the ion motion, such as the height of the potential barrier, the jump step, mobility and diffusion coefficient, can be obtained. Due to divalent and monovalent copper ions all participate in conduction, an equivalent copper ion Cu^z+is used for replacing both Cu⁺and Cu²⁺, solving the computational complexity problem caused by multivalent metal ions. Finally, an equivalent circuit is proposed to calculate output voltage versus time characteristic. The calculation results of the model are consistent with experimental data.