## 2 Defect States in Perovskite Materials
(**d**) Potential energy landscapes related to species in (**a**), (**b**) and (**c**). Root mean square displacement of iodine atom with respect to the position of I\({}_{\text{i}}\)\({}^{+}\). Dots are calculated points, lines are interpolated. (**e**) Steady-state photoluminescence (PL) spectra with increasing excitation fluence, showing enhanced near infrared (NIR, \(\sim\)1000 nm) emission at low excitation powers. (**f**) Photoluminescence dynamics probed at 1.56 eV, together with photocurrent decay and transient absorption kinetics. Reproduced with permission from _Energy Environ. Sci._**2018**, _11_, 702-713. Reference [22] as well as Reproduced with permission from _Energy Environ. Sci._**2016**, \(9\), 3472-3481. Reference [8]. Using the description of the minimum energy structures corresponding to each charged state of interstitial iodine, the reaction pathways (trapping pathway) can be visualized according to a global configuration diagram. Figure 9d shows that the energy minima of the three states have significantly different structures. This means that when the defect traps (or un-traps) charge, this is accompanied by large structural changes (as expressed by the root mean square displacement). In Figure 9d we can see that the trapping of an electron in \(\text{I}_{\text{i}}{}^{+}\) (this process is marked with (1) in red) results in a structural relaxation to the \(\text{I}_{\text{i}}{}^{0}\) (a) global minimum, depicted in black, formed by process (2). The thermodynamic barrier is only 0.10 eV above the \(\text{I}_{\text{i}}{}^{0}\)(b) local minimum. Process (3) depicted in green marks the pathway to un-trap the electron to go back the \(\text{I}_{\text{i}}{}^{+}\) state. If a hole is trapped, depicted in yellow by the process (4) to form the \(\text{I}_{\text{i}}{}^{0}\) (a) state, there is no barrier and structural rearrangement is limited. From this, it can be concluded that hole trapping and un-trapping is a fast process. It is expected that the large lattice reorganization for electron trapping at positive interstitials, results in long timescales for trapping and recombination. To support the computational findings, steady-state photoluminescence on MAPb\(\text{I}_{3}\) poly-crystalline thin film was used. Since interstitial iodine traps are sub-band gap states, this means that radiative recombination (emission from trapped holes) should be observed at energies below the band gap. Figure 9e, in fact, reveals weak emission in the 1.35-1.15 eV range, below the radiative recombination from the band gap (1.58 eV). Also, at increased excitation energies, quenching of emission is observed. This is expected from radiative trap-assisted recombination since increasing excitation will saturate the traps, which have no time to recombine radiatively. Figure 9f shows the photoluminescence, which corresponds to the fast band-to-band radiative recombination. There is also a slow component which does not match any radiative feature, but follows the photo-current, and therefore is suggested to rise from non-radiative recombination of free holes with electrons trapped by \(\text{I}_{\text{i}}{}^{+}\) (arrow (3) in Figure 9d). If electrons are trapped, it takes a long time before they recombine and therefore they will remain inactive for a long time. Trap filling for a long time reduces the effective trap density, which has direct implications on the \(\text{V}_{\text{OC}}\). [PERSON] et al. determined the quasi-Fermi level splitting by estimating the steady-state carrier dynamics and with this calculated the \(\text{V}_{\text{OC}}\) for different trap situations (Table 1) [8]. In the ideal case of defect-free perovskite, when only bimolecular recombination occurs, the \(\text{V}_{\text{OC}}\) is 1.30 V. Short-lived carriers reduce the \(\text{V}_{\text{OC}}\) to 1.14 V; whereas increasing the lifetimes of the holes increases this value by 0.12 V, creating a \(\text{V}_{\text{OC}}\) close to the Shockley-Queisser limit. The presence of trap states in the form of lattice defects has been widely observed.