## 3 Results and Discussion
### Numerical Simulations  
In order to support our previous hypothesis, we performed 2D numerical simulations using SILVACO ATLAS TCAD software. In addition to the typical electronic behavior, we modeled the transport of two ionic mobile species with both positive (cations) and negative (anions) charges, both present in the active layer at an initial constant concentration. According to [PERSON] et al. (2018), the mobile vacancy density for various halide perovskite is as high as 10\({}^{17}\) cm\({}^{-3}\), i.e., higher than the 10\({}^{15}\) cm\({}^{-3}\) residual P-type doping assumed for the perovskite active layer. In our case, the simulated device structure consists of an MAPI perovskite active layer with variable thickness, capped with a standard hole transport layer (HTL) and the electron transport layer (ETL). Anions and cations can move just within the active layer. All of our numerical simulations with Silvaco ATLAS TCAD start computing the carrier concentrations in the complete 2D structure at an external applied bias of 0 V and without illumination. After that, external bias and/or illumination is applied in several small steps to assure convergence and numerical accuracy, up to their final values. Simulation results show that the constant initial mobile ion distribution rearranges depending on the absence or presence of external bias voltage and illumination, as was expected. In particular, when the device is illuminated under 1-sun AM1.5G and no external voltage is applied (short circuit conditions), the inner built-in electric field forces the positive (negative) mobile ions to travel to the cathode (anode), creating an inhomogeneous distribution displayed in Figure 9. It is shown that the resulting ion distribution along the perovskite film is mainly homogeneous in the central part of the active layer, except for the interfaces with the ETL and HTL layers, where mobile ions accumulate. This ion rearrangement creates charged interfacial layers whose thickness and peak charge strongly depend on the perovskite thickness, in accordance with the results from the IS analysis in the previous section. On the other hand, when a positive voltage close to \(V_{\rm OC}\) is applied (+1 V), the direction of the internal electric field inside the device changes sign, and mobile ions are forced to redistribute traveling to the opposite electrode. Figure 8: Evolution of capacitances with irradiation time for (**a**) 350 nm and (**b**) 650 nm. To obtain further insight into the impact of the mobile ion redistribution in the device performance, Figure 10 shows the simulated device conversion efficiency as a function of the ion concentration (equal for anions and cations) for three different carrier mobilities (electron and hole) in the active layer. It is demonstrated that for 650 nm films, efficiency always drops as long as the ion concentration exceeds \(10^{13}\) cm\({}^{-3}\), regardless of the carrier mobility. In all cases, when the ion concentration increases, the electric field inside the perovskite decreases. Thus, the photogenerated charge extraction is not drift-assisted. In addition, Figure 10 shows that for the 350 nm active layer, the efficiency reduces only when carrier mobility is low and ion concentration is higher than \(10^{15}\) cm\({}^{-3}\), in accordance with the results from [PERSON] et al. [50]. This is because perovskite films with higher electron and hole mobilities have enhanced diffusion currents, so carriers do not rely on the internal electric field to move along the layer. Moreover, thinner films inherently present higher electric fields due to steeper gradients in their energy band structure, as is shown in Figure 11.  
Figure 10: Cell efficiency as a function of the ion concentration for three carrier mobilities (electron and hole), and for 350 nm and 650 nm devices. Figure 9: Mobile ions (cations and anions) concentration profile along with the 350 nm and 650 nm active layers, under 1-sun illumination with the applied voltage set to 0 V (\(J_{\text{SC}}\) conditions).