# Multiscale Modeling for Application-Oriented Optimization of Resistive Random-Access Memory
## 3 Results
### Switching Reliability Optimization  
The fundamental mechanism enabling analog resistance switching in RRAM devices is the diffusion of oxygen ions in the oxide layer. This process is greatly affected by the interaction of ions with the surrounding lattice, thus by the material's properties, and in turns affects many of the device's electrical properties. For example, as previously discussed, precise control of oxygen ion diffusion is key to achieving well-separated resistance levels. Even more importantly, the properties of the ion diffusion process are of paramount importance for evaluating the variability and endurance of RRAM devices [83]. In fact, precise switching between different resistance levels requires the dielectric barrier to be consistently modulated for the full lifespan of the device, with little to no variations between the cycles. Conversely, the newly proposed stochastic learning algorithms for SNNs can take advantage of device variability and non-uniformity. In both cases, the oxygen ion diffusion process must be thoroughly investigated for specific optimization of the devices. The presented multiscale modeling platform, fully accounting for the oxygen ion kinetics, can be used to investigate its effects on the reliability and variability of RRAMs.  
The simulations of a TiN/5 nm HfO\({}_{\text{x}}\)/TiO\({}_{\text{y}}\)/TiN stack RRAM device, shown in Figure 10, reveal the high sensitivity of the device reset operation to the oxygen ion diffusion kinetics properties. Starting from a correctly formed device (Figure 10a), the reset operation was simulated considering slow and anisotropic (motion predominantly in the vertical direction) oxygen diffusion (Figure 10b), corresponding to well-performed reset operation. Then, starting from the same post-formed conditions, the simulation was performed for fast and anisotropic oxygen diffusion (Figure 10c), corresponding to an excessively high voltage reset process, and for slow and isotropic oxygen diffusion (Figure 10d). Interestingly, this last condition describes the diffusive motion of oxygen ions due to the sole temperature field.  
An efficient reset operation was only obtained in the first case, where the oxygen ions are carried towards the CF in a mostly anisotropic way (some radial motion is beneficial) and are provided with enough time for recombination with the CF oxygen vacancies. In the case of fast diffusion of the oxygen ions (i.e., for an excessively high-voltage reset process), the latter condition is hindered: a significant portion of the oxygen ions are swept through the oxide, recombining along the CF length and eventually forming a dielectric barrier near the bottom electrode, as suggested in [52]. Finally, the slow and isotropic diffusion of oxygen ions leads to an inefficient reset of the device, as the excessive scattering of ions in the device volume prevents the formation of a fully dielectric barrier. The simulation results are in accordance with the experimental results showing thermally-driven oxygen ions diffusion from the \"reservoir\" to the CF [84].  
The set operation is also affected by the diffusion of newly generated oxygen ions towards the TiO\({}_{\text{x}}\) \"reservoir\" at the top electrode. Significant radial motion of the oxygen ions during the set operation would spread the ions in the \"reservoir\", not creating ion storage in sole proximity to the CF, leading to an increasingly ineffective reset operation and possibly to failure of the device. The cycling endurance of a device is clearly negatively affected by excessive radial motion of the oxygen ions induced by the diffusion. Therefore, convenient process recipes to optimize material properties can be implemented based on the results of these simulations to optimize the endurance and switching uniformity of RRAM devices, depending on the specific application target and its requirements.