# Multiscale Modeling for Application-Oriented Optimization of Resistive Random-Access Memory
## 3 Results
### Effects of Forming Conditions  
The presented multiscale modeling platform allows the effects of the forming condition (i.e., temperature, current compliance, voltage stress mode) on the performance and properties exhibited by the device after the forming process to be investigated. The beneficial effects of a high-temperature forming process have been thoroughly reported in the literature, and have been associated with lower forming voltages and variability of the low resistance state, while improving the stability and reliability of the device [76; 77; 78]. The external temperature affects the forming process assisting the defect generation and promoting the oxygen ion diffusion in the device, leading to a lower density of oxygen ions near the conductive path after the forming process. The subsequent oxygen ion/vacancy recombination is strongly reduced, resulting in a higher stability and lower variability of the conductive path. This is evidenced in Figure 4a, which shows the low state resistance distribution exhibited by TiN/5 nm HfO\({}_{\text{v}}\)/TiO\({}_{\text{y}}\)/TiN RRAM stacks after the forming process at two different external temperatures (i.e., 25 and 125 \({}^{\circ}\)C), using a ramped voltage and a 1 mA compliance current. In accordance with the literature [76], the experimental data (marked by the symbols in Figure 4a) show that the higher forming temperature leads to a tighter resistance distribution. The effects of the forming temperature on the oxygen ions/vacancies generation and diffusion can be effectively investigated using the presented multiscale modeling platform. The simulations of the forming processes (shown by the lines in Figure 4), whilst not perfectly matching the measured samples, accurately reproduce the trend and order of magnitude of the experimental data, showing a tighter resistance distribution in the higher temperature forming case. The discrepancy between the experimental results and those of the simulation can be ascribed to several effects not considered in these simulations, mainly, the oxide thickness and area variations due to the fabrication process tolerances, and process-dependent interface effects between the oxide and the electrodes. The microscopic differences caused by the higher forming temperature can be better appreciated in Figure 4b,c, which shows the simulated oxygen ions/vacancies distribution in the device after the forming process. At a low temperature (25 \({}^{\circ}\)C), the conductive path (in this case, a CF) made of oxygen vacancies is tightly surrounded by oxygen ions affecting its resistance and stability. Conversely, at a high temperature (125 \({}^{\circ}\)C), the oxygen ions are scattered in the device volume, affecting the CF to a lesser extent and leading to a tighter resistance distribution. The platform can therefore be used to explore the best strategies to control the device-to-device variability of RRAMs for specific applications: for instance, high-temperature forming could reduce the variability for high-accuracy DNNs, while precisely controlling the temperature during the forming process could be used to obtain the desired variability level, optimizing the performance of stochastic learning networks. The forming compliance current has a very strong impact on the morphology of the conductive path as it allows the defect generation processes in the device to be controlled by limiting the maximum current flow and power dissipation in the device. For example, in filamentary RRAMs, it has been observed that the magnitude of the compliance current allows the diameter of the CF to be controlled [57]. Moreover, it also greatly affects the low resistance state magnitude and variability: a sufficiently high compliance current allows the formation of a dense population of defects, forming low-resistance CFs with a similar morphology, while a low compliance current leads to a sparse population of defects, forming weak CF characterized by a larger variability.