## 3 Results and Discussion  
### Pristine Characterization  
Figure 2 shows the solar cell parameters, \(J_{\text{SC}}\), \(V_{\text{OC}}\), fill factor (FF) and PCE, for pristine devices for the three different active layer thicknesses. Champion cell efficiency was 17.05% for a 650 nm thick sample and no significant dependence of the efficiency on the active layer thickness was observed. The trade-off between higher carrier absorption (in thicker devices) and more efficient carrier extraction (in thinner devices) is responsible for the nearly constant efficiency with thickness measured in pristine devices. In order to obtain a deeper insight into the dynamical physical mechanisms taking place in the device, samples were characterized using IS technique. Frequency is varied in order to observe dynamical mechanisms occurring from 1 us, such as carrier transport, up to 1 s, such as ion diffusion. The different physical processes occurring in the device appear in the impedance spectra as distinctive features (arcs, loops, etc.) at different characteristic frequencies [29; 30; 31]. The impedance spectra of perovskite solar cells typically show two or three arcs [32; 33; 34]. The high frequency arc is usually related to charge recombination, but there is no consensus about the physical interpretation of the medium and low frequency features. They have been previously attributed to device degradation, a \"giant dielectric\" effect [35; 36], electron accumulation at the contacts [37; 38] and ionic diffusion [39]. [PERSON] et al. suggested that the medium and low frequency relaxation processes are due to a coupled electronic-ionic impedance, e.g., where the distribution of ions in the perovskite is able to modify the rate of carrier recombination [40]. Figure 3 shows the Nyquist plots of pristine devices for the three active layer thicknesses at \(V_{\text{OC}}\) under 1-sun. At first sight, the spectra seem to have two distinctive semicircles. However, if the low frequency region is zoomed in (inset of Figure 3), a third medium frequency arc can be observed (dotted line in the inset). As we will present later, this third feature enhances with degradation. Figure 2: Solar cell parameters, (**a**) \(J_{\text{SC}}\), (**b**) \(V_{\text{OC}}\), (**c**) FF and (**d**) PCE, for pristine devices with different active layer thickness: 350, 500 and 650 nm characterized under 1-sun AMI.5 illumination. The statistics were performed for 12 cells for each thickness. Equivalent circuit modeling is used to quantify the resistive and capacitive contributions to the impedance spectrum over the measured frequency range. In this case, electrical parameters were obtained from the fit using the circuit shown in Figure 3. This is the hybrid Voight-Matryoshka configuration [34]. The circuit is a combination of the external series resistance (\(R_{\text{S}}\)), three resistive elements (\(R_{\text{HF}}\), \(R_{\text{MF}}\) and \(R_{\text{LF}}\)), two ideal capacitors (\(C_{\text{HF}}\) and \(C_{\text{LF}}\)) and one non-ideal capacitive element named constant-phase element (\(\text{CPE}_{\text{MF}}\)). The impedance of a CPE is given by \(Z_{\text{CPE}}=1/[\text{Q}(j\omega)^{\alpha}]\)[41], where Q is a parameter with units F-(Hz)\({}^{(1-\alpha)}\). \(C_{\text{HF}}\) represents the geometrical capacitance, which dominates the capacitive response in the high frequency region of the diagram, and it is associated with the dielectric constant of the perovskite layer (\(\varepsilon\)). \(C_{\text{MF}}\) and \(C_{\text{LF}}\) are medium and low frequency capacitances, respectively, where \(C_{\text{MF}}\) is an effective capacitance defined as \(C_{\text{MF}}=\left(\text{Q}\cdot R_{\text{MF}}\right)^{1/\alpha}\cdot R_{ \text{MF}}{}^{-1}\). The low frequency capacitance, \(C_{\text{LF}}\), has been related to ion diffusion and, eventually, ionic accumulation at the interfaces of the perovskite and the selective contacts [38]. On the other hand, the origin of \(C_{\text{MF}}\) is still under debate.