# Multiscale Modeling for Application-Oriented Optimization of Resistive Random-Access Memory
## 3 Results
### Conductance Switching Cycle  
The presented multiscale modeling platform allows the whole conductance switching cycle to be simulated. Starting from a pristine device with specified geometries and materials, it is possible to investigate the device formation and the following conductance switching operations (SET and RESET) under different conditions. The electric and temperature fields and the location of atomic species in the device can also be monitored during simulations to gain insights into the involved switching mechanisms and their interplay. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Symbol** & **Quantity** & \multicolumn{3}{c}{**Material**} \\ \hline  & & **HfO2** & **Ta2O5** & **TiO2** \\ \hline \multicolumn{5}{c}{**Material Parameters**} \\ \hline E\({}_{\text{G}}\) & Band-gap (eV) & 5.8 & 3.6 & 1.3 \\ \(\chi\) & Electron affinity (eV) & 2.4 & 3.4 & 4.3 \\ k & Relative dielectric permittivity & 21 & 25 & 95 \\ m\({}_{\text{e}}\)* & Electron tunneling effective mass & 0.25 m\({}_{0}\) & 0.3 m\({}_{0}\) & 0.2 m\({}_{0}\) \\ WF & TiN work function (eV) & 4.57 & 4.57 & 4.57 \\ \hline \multicolumn{5}{c}{**Defect Parameters**} \\ \hline E\({}_{\text{T}}\) & Defect thermal ionization energy (eV) & 1.7–2.7 & 0.8–1.2 & 0.1–0.5 \\ E\({}_{\text{REL}}\) & Defect relaxation energy (eV) & 1.19 & 0.88 & 0.7 \\ N\({}_{\text{T}}\) & Defect density (cm\({}^{-3}\)) & \(5\times 10^{19}\) & \(5\times 10^{19}\) & \(5\times 10^{19}\) \\ \hline \multicolumn{5}{c}{**Metal-Oxygen Bond Breakage Parameters**} \\ \hline p\({}_{0}\) & Polarizability (eÅ) & 5.2 & 1.8 & 4 \\ E\({}_{\text{A,G}}\) & Activation energy (eV) & 2.1 & 1.0 & 5.3 \\ G\({}_{0,\text{G}}\) & Effective bond vibration frequency (Hz) & \(4.5\times 10^{13}\) & \(4.5\times 10^{13}\) & \(4.5\times 10^{13}\) \\ \hline \multicolumn{5}{c}{**Oxygen Ion Diffusion Parameters**} \\ \hline \(\Gamma\) & Field acceleration factor (eÅ) & 0.3 & 0.2 & 0.4 \\ E\({}_{\text{A,D}}\) & Activation energy (eV)—in \(\chi\)/y/z direction & 0.8/0.8/0.7 & 1.2/1.2/1.0 & 1.0/1.0/0.75 \\ G\({}_{0,\text{D}}\) & Effective bond vibration frequency (Hz) & \(4.5\times 10^{13}\) & \(4.5\times 10^{13}\) & \(4.5\times 10^{13}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. As an example, Figure 3a shows the I-V characteristic curves of a simulated device made of a TiN/5 nm HfO\({}_{\mathrm{x}}\)/TiO\({}_{\mathrm{y}}\)/TiN stack RRAM device, including the forming (solid red), the reset (dotted green), and set (dashed blue) operations. The simulations are performed by applying ramped voltages and a compliance current of 10 \(\upmu\)A. In the pristine state (state A), the conduction is dominated by the TAT through the relatively few preexisting defects in the material (i.e., oxygen vacancies accumulated at grain boundaries), which determines the very high initial resistance of the device. At a low voltage (V \(<\) V\({}_{\mathrm{FORM}}\) = 1.7 V in Figure 3), both the electric field and the power dissipation are too small to result in strong localized defect generation, leading to a very modest and uniform generation of defects across the whole volume of the device. Once the applied voltage exceeds V\({}_{\mathrm{FORM}}\), the oxide bonds start to break under the effect of the increasing electric field, creating a significant number of atomic defects. Due to the different diffusion energy barriers, the oxygen ions generated drift towards the top electrode under the effect of the electric field, while the oxygen vacancies mostly remain in place. Noticeably, the oxygen ions accumulate at the TiO\({}_{\mathrm{x}}\) layer, creating the so-called \"oxygen reservoir\".