## 2 Defect States in Perovskite Materials  
Several studies show that imperfections or defects in perovskites induce (high densities of) deep-level traps [8; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. These deep-level traps will trap either electrons or holes, that do not escape by thermal activation but will recombine non-radiative as described by Shockley-Read-Hall theory (see Section 1). Shallow traps are defined as traps that lie closer to the CBM or VBM than the thermal activation (\(K_{B}T=23.5\) meV at 0 \({}^{\circ}\)C, \(K_{B}T=29.6\) meV at 70 \({}^{\circ}\)C) and are thus less detrimental to device performance. In this section, the different types of defects are discussed in depth. We will first highlight some experimental approaches to gain insight into the chemical nature of defects in perovskites. Next, several computational studies that describe defects and their photophysical properties on a more atomistic level will be discussed. [PERSON] et al. used temperature-dependent space charge-limited current (SCLC) techniques [12]. With this technique, the density of trap states (\(DOS_{T}\)) can be extracted from the current-voltage characteristics. Figure 5 shows that for single-crystal MAPbI\({}_{3}\) the \(DOS_{T}\) appears to be localized only \(\sim\)0.2 eV from the conduction band and \(\sim\)0.1 eV form the valence band. From this, it can be concluded that MAPbI\({}_{3}\) contains both shallow hole traps and shallow electron traps. However, with a combination of transient and steady-state photoluminescence spectroscopy, [PERSON] et al. analyzed carrier dynamics and showed that deep traps for electrons are the predominant decay pathway [8]. Furthermore, using deep level transient spectroscopy the presence of charge traps placed in the middle of the band gap was observed [13]. The chemical nature of charge traps has also been studied with several spectroscopic techniques. X-ray techniques usually focus on the perovskite structural parameters; common structural phase transitions can be observed as a function of temperature, including orthorhombic-tetragonal-cubic transformations. Combining x-ray and neutron diffraction experiments to analyze changes in bond distances, [PERSON] et al. showed that for the tetragonal perovskite structural disorder can be associated with the formation of I\({}_{2}\)[14]. Figure 6 shows a proposed mechanism: through the migration of iodine to a vacancy (MA vacancy at the lattice A-site) the I\({}_{2}\) molecule is formed. Figure 5: Density of the trap states (with their energetic distribution) within the band gap, extracted from the temperature-dependent properties. The valence band has less traps, with a slightly smaller energy distribution. Reproduced with permission from _Adv. Mater._**2016**, _28_, 3406–3410. Reference [12]. Using X-ray photoemission spectroscopy (XPS), the formation of vacancies from the methylammonium site (V\({}_{\rm MA}\)) and iodine site (V\({}_{\rm I}\)) were shown. The loss of MA and I species did not lead to significant changes in photoluminescence properties of the material. This apparent defect tolerance was explained by the fact that the V\({}_{\rm MA}\) and V\({}_{\rm I}\) defect lie close to or within the conduction and valence band, respectively [15]. In contrast, an early study that also used XPS showed that metallic Pb\({}^{(0)}\) is present in the perovskite layer with high concentration in the bulk [16]. This defect, resulting from V\({}_{\rm Pb}\), was correlated to the density of states above the valence band. They also observed reduced PLQE when the Pb content was increased. The experimental work discussed above demonstrates that (polycrystalline) perovskite can accommodate several different defects. However, to understand defects and their chemical nature on an atomistic level, computational modeling has become an essential tool.