## 2 Defect States in Perovskite Materials
The slow charge carrier dynamics and stability-threatening phenomena, such as current-voltage hysteresis, are not readily explained by the presence of shallow traps and only the limited amount of deep level traps. Ion defect transport has been widely observed in perovskite material and is another possible origin that potentially lowers power conversion or even device stability. DFT simulations have shown that ionic disorder in perovskite leads to low formation energies for Schottky-type defects associated with anion and cation vacancies [19]. [PERSON] et al. carried out calculations in order to examine the pathways and relative activation energy for the vacancy-mediated migration of the cations and anions [4]. They proposed a hopping mechanism, as shown in Figure 8.  
Using transition-state calculations between adjacent sites, they mapped out energy profiles for these mechanisms. The lowest activation energy was found for iodide ions, which was 0.58 eV compared to 0.84 eV and 2.31 eV for MA\({}^{+}\) and Pb\({}^{2+}\), respectively. The authors suggested that iodine vacancy-assisted diffusion is favorable since this migration pathway is more ideal as it does not involve motion through the unit cell and they argued that the high activation energy for Pb\({}^{2+}\) rises from the immobile Pb sub-lattice. Other theoretical work supports the proposed general mechanism; the ion mobility is directly related by the transport activation energy and the hopping distance [20]. In these studies the iodine ion is also confirmed as the most mobile ion [20; 21]. Recently, iodine interstitial defects were identified as the main source for trapping electrons and holes in MAPbI\({}_{3}\)[22; 23]. These results showed significant differences with previous studies (Figure 7) [17; 24]. Where early studies proposed that defects with low formation energies that form shallow traps are predominant, more high-level calculations based on hybrid DFT showed that iodine interstitials, in fact, induce deep levels in the MAPbI\({}_{3}\) band gap [23]. [PERSON] and co-workers performed DFT calculations that included both dispersion correlation corrections and spin-orbit coupling. They calculated that interstitial iodine can lead to a deep trap for both electron and holes at the +/0 and 0/- ionization levels placed at 0.57 and 0.29 eV below and above the CB and VB edges, respectively [22]. Figure 7: Calculated transition energy levels of various types of point defects in MAPbI\({}_{3}\) (interstitials (i), ion substitutions and vacancies (V) are indicated). The formation energies of neutral defects are shown in parentheses. The acceptors (red, trapping electrons) and donors (blue, trapping holes) are ordered by the formation energies (from left to right). Reproduced with permission from _Adv. Mater._**2014**, _26_, 4653–4658. Reference [17]. In addition, [PERSON] et al. studied the photochemistry of the defect states. The various charge states of interstitial iodine (I\({}_{\text{i}}\)) result in different local geometrical structures: Figure 9a shows the positive I\({}_{\text{i}}\)\({}^{+}\) state, resulting in a trimer structure of a coordinated I\({}_{3}\)--molecule, this is an electron trap (+/0); the neutral I\({}_{\text{i}}\)\({}^{0}\) state (Figure 9b), here iodine formed a bridged dimer; and a negatively charged I\({}_{\text{i}}\)\({}^{-}\), which is a hole trap (0/\(-\)) with a similar structure to that of I\({}_{\text{i}}\)\({}^{0}\) (Figure 9c). Figure 8: Ion transport mechanisms in MAPbI\({}_{3}\). (**a**) \(\Gamma\) migration along an octahedron edge; Pb\({}^{2+}\) migration along diagonal direction (\(110\)). (**b**) MA\({}^{+}\) migration into a neighboring vacant A-site. Reproduced with permission from _Nat. Commun._**2015**, \(6\), 7497. Reference [4]. Figure 9: Interstitial iodine defects as hole and electron traps in MAPbI\({}_{3}\). Local geometrical structures of interstitial iodine (**a**) as a cation I\({}^{+}\), (**b**) as a neutral atom, I, and (**c**) as iodide, \(\Gamma\)\({}^{-}\).