# Multiscale Modeling for Application-Oriented Optimization of Resistive Random-Access Memory
## Materials and Methods
### RRAM Devices  
In RRAMs, the analog resistance switching is controlled by a reversible, voltage-driven, and ion-based mechanism that allows the geometry of a conductive path within a dielectric layer to be modulated. Different switching mechanisms have been proposed for the implementation of RRAM [26; 42; 43], with each one requiring the comprehensive knowledge of different physical processes for being thoroughly understood. In CBRAMs [44; 45; 46], a conductive filament (CF) is created (and dissolved) in a solid electrolyte by means of redox reactions. By applying a positive voltage to the \"active\" electrode (the anode), it releases metallic cations into the electrolyte that migrate towards the \"inert\" electrode (the cathode) pushed by the electric field. Once they reach the cathode, the cations are reduced, contributing to the formation of the CF and eventually connecting the two electrodes. Through reversing the redox process by applying a negative voltage to the anode, the CF is progressively dissolved. Optimizing CBRAMs requires an understanding of the kinetics and interplay between the redox processes and the transport of metallic cations in solid electrolytes (i.e., drift and diffusion). Moreover, all the effects related to the material interactions and geometry must be considered. In OxRAMs [47; 48; 49; 50; 51], a conductive path constructed of oxygen vacancies is formed in a high-k oxide layer (e.g., TiO\({}_{2}\), HfO\({}_{2}\), TaO\({}_{5}\)), breaking the oxide atomic bonds (Figure 1a). When applying a voltage to the oxide layer (Figure 1b), its lattice bonds are stretched. With a sufficiently high voltage, the bonds eventually break, generating a negatively charged oxygen ion and a positively charged oxygen vacancy (Frenkel pair). If no recombination of the pair occurs, the oxygen ion and vacancies migrate in opposite directions under the action of the electric field. However, due to their relatively high diffusion energy barrier [52], the oxygen vacancies experience little to no motion, locally increasing the electrical conduction and power dissipation in the material. The resulting temperature increment supports the creation of new oxygen ions/vacancies, leading to the rapid formation of a highly conductive path of oxygen vacancies between the two electrodes (Figure 1c). The conductive path can be broken by recombining the oxygen vacancies with the oxygen ions, i.e.,bringing the oxygen ions near the oxygen vacancies by applying a negative voltage to the oxide layer (Figure 1d). The analog resistance switching in OxRAMs relies on the modulation of a conductive path created during a forming process, consisting of a current-controlled breakdown of the dielectric. After the formation, only a thin portion of the formed conductive path is affected by the oxygen ion/vacancies generation and recombination processes. The conductance switching thus requires precise control of the geometrical properties of a thin insulating barrier. Depending on the forming conditions (i.e., temperature, current compliance, voltage stress mode), the conductive path can assume either a uniform or filamentary shape. In the former [51], the dielectric conduction is uniformly modulated across its section and the resistance is thus controlled through the insulating barrier thickness only. In the latter [47; 48; 49; 50], a CF is formed within the dielectric, enabling control of the resistance by both the barrier thickness and the CF diameter. The design of OxRAMs requires an understanding of the complex processes of oxygen ions/vacancies generation, diffusion, and recombination under the action of an external electric field; their interplay with the charge transport in dielectrics; and the effects of the material properties and geometries on all those processes. In this work, we focus on the multiscale simulation of OxRAM devices, and investigate the interplay between the physical mechanisms involved and their impact on the device performance, reliability, and variability.