Modeling of the Thermodiffusion-Induced Filament Formation in TiN/TaxO1−x/TiN Resistive-Switching Devices

Abstract

Nonvolatile memory devices have received a lot of interest in both industry and academia in the last decade. Transition metal oxide-based memories offer potential applications as universal memory and artificial synapses. Here we focus on the one-time conditioning of metal/oxide/metal structures leading to the formation of a conducting filament in $\mathrm{Ti}\mathrm{N}/{\mathrm{Ta}}_{x}{\mathrm{O}}_{1\ensuremath{-}x}/\mathrm{Ti}\mathrm{N}$ structures and develop a finite-element model of this process. The process considered here consists of two steps. First the thermal runaway increases the temperature of the device and sets up large temperature gradients. In the second step, the lateral temperature gradient drives the ion motion forming a $\mathrm{Ta}$-rich and $\mathrm{O}$-poor filament. The process comes to steady state when the ion flux due to concentration and stress gradients balances the thermophoretic fluxes. The model replicated the structure of the filament including the size of the $\mathrm{Ta}$-rich filament core (20 nm diameter), the surrounding $\mathrm{Ta}$-depleted ring (50 nm), and the compositions of both regions. In addition, the model reproduced characteristic dynamics of the electroformation with slow changes of conductance during the incubation period, rapid increase of conductance during compositional runaway, and saturation. The range of critical material parameters, namely transport heats for $\mathrm{Ta}$ and $\mathrm{O}$, is discussed.