# Multiscale Modeling for Application-Oriented Optimization of Resistive Random-Access Memory
## Materials and Methods
### Multiscale Modeling of RRAMs  
The multiscale modeling platform sketched in Figure 2 allows the RRAM devices to be thoroughly investigated. Starting from the key material properties, calculated using ab-initio methods [53; 54; 55], and the other device-specific properties (e.g., geometry and materials), the platform models the electrical device response considering all the complex physical mechanisms involved in the different RRAM operations, while accounting for all the resulting changes in the 3D electric and temperature fields, and in the material structure. Figure 1: Structure and operation of a filamentary OxRAM device. **(a)** Device in pristine conditions. **(b)** Forming operation: a positive voltage is applied to the top electrode, generating oxygen ion/vacancy pairs. The ions (blue spheres) migrate under the effect of the electric field, leaving the oxygen vacancies (red spheres) behind. **(c)** Formed device with a conductive filament (CF) made of oxygen vacancies connecting the two electrodes. **(d)** Reset operation: a negative voltage is applied to the top electrode, bringing the oxygen ions near to the oxygen vacancies. The resulting recombination leads to partial dissolution of the CF and the formation of a dielectric barrier. The multiscale modeling platform comprises three main modules, addressing charge transport, charge trapping, and the generation/diffusion/recombination of atomic species (i.e., oxygen vacancies and interstitial ions), respectively. For a comprehensive simulation of charge transport, many mechanisms are considered, including trap-assisted tunneling (TAT), thermo-ionic emission (TE), the Poole-Frenkel effect (PF), and Drift-Diffusion (DD) through conduction and valence bands, and through sub-bands originating from metal-rich regions formed within the oxide. Interestingly, in most RRAM devices, the TAT and DD phenomena dominate the charge transport dynamics, the first at low defect densities (i.e., the conduction in the oxide is mainly defect-assisted, typical of binary and ternary oxides [56; 57; 58; 59; 60; 61; 62]), and the latter for sufficiently high defect densities (i.e., a conductive path is present within the oxide). The TE and the PF phenomena are typically negligible in materials with a medium/high bandgap, such as transition metal oxides [63]. The TAT conduction is described using a multiphonon TAT model, inherently considering the electron-phonon coupling oxides by accounting for the atomic lattice rearrangement in the vicinity of the defect due to the presence of a trapped charge [56; 57; 58; 64]. The TAT transport considered is fully described in [65]. This model requires knowledge of the relaxation energy, \(\mathrm{E_{REL}}\), associated with the atomic lattice relaxation process; the defect thermal ionization energy, \(\mathrm{E_{T}}\); and the defect density in the material, \(\mathrm{N_{T}}\). Both \(\mathrm{E_{REL}}\) and \(\mathrm{E_{T}}\) are calculated by means of ab initio methods (i.e., Density Functional Theory and Molecular Dynamics simulations). The DD conduction is best described by adopting the Landauer approach [66], which accounts for delocalized electron flow in the conductive path. The defect-assisted charge transport naturally results in localized power dissipation at the defect sites, affecting the temperature distribution in the device. The power dissipation is self-consistently computed across the entire device volume by including the charge carrier's energy released at both the defects (at every charge trapping event) and the lattice (due to inelastic scattering mechanisms, i.e., optical and acoustic phonons). The temperature distribution in the device volume is calculated from the power dissipation by solving the Fourier's Law for heat conduction. Figure 2: Multiscale modeling platform for RRAM devices. The device-level simulation engine includes three main modules: one for the simulation of charge transport; one for charge trapping; and one for the simulation of atomic species generation, diffusion, and recombination.