Electric-field-induced migration of oxygen ions in epitaxial metallic oxide films: Non-Debye relaxation and $1/f$ noise

We have investigated the kinetics of current-induced change of resistance and conductivity noise in thin epitaxial metallic films of ${\mathrm{LaNiO}}_3.$ The resistance of the film changes at a very low current (threshold current density $J_{\mathrm{th}}\sim {10}^3{\mathrm{A}/\mathrm{c}\mathrm{m}}^2).\mathrm{}$ We find that the time dependence associated with the change of resistance shows a stretched-exponential-type dependence at lower temperature. Above a certain temperature scale $T^{*}\left(\approx 350\mathrm{K}\right),$ this crosses over to a creep-type behavior. At $T\sim T^{*},$ the time scale shows a drastic drop in the magnitude, and a long-range diffusion sets in, which leads to an increase in the conductivity noise. The phenomenon is like a “glass-transition” in the random lattice of oxygen ions. We observe that the stretched exponential relaxation function, as obtained from time dependence of resistivity change, can explain the spectral structure as well as the temperature dependence of the low-frequency conductivity noise. The frequency and temperature dependence of noise could clearly identify the various processes, which had been seen in the current-stressing experiments carried out in the time domain. This establishes a quantitative link between the dynamics of current-induced resistivity changes and the conductivity noise. Both the phenomena are direct consequences of the low-frequency dynamics associated with the migration of the oxygen ions. Though done in the specific context of oxide films (used in oxide electronics), this observation has a generic aspect, and the treatments developed here can be used for establishing a quantitative link between electromigration current stressing and the conductivity noise in other metallic interconnects as well.