## 2 Doping of Perovskites with Mono- and Tri-Valent Metals  
Doping of perovskites with hetero-valent cations is an intriguing subject and there is little consensus on the exact mechanism behind improved properties of hetero-valent doped perovskites. [PERSON] et al. [20] reported the doping of MAPbI\({}_{3}\) with monovalent halide-based salts such as NaI, CuBr, CuI and AgI. The formed structures were studied with scanning electron microscopy (SEM) and the resulting structures are depicted in Figure 1.  
On the left, PbI\({}_{2}\) is depicted and on the right the pristine MAPbI\({}_{3}\) and after doping with CuBr, CuI, NaI and AgI, respectively. Undoped MAPbI\({}_{3}\) appears in large tetragonal shaped perovskite crystals on top of the TiO\({}_{2}\) but when the material is doped with CuBr, the TiO\({}_{2}\) is relatively better covered (Figure 1b). Moreover, the TiO\({}_{2}\) layer is considerably better covered with continuous and uniform perovskite when the material is doped with CuI and AgI (Figure 1c,e). The perovskite films including CuI and AgI additives are reported to be nearly pinhole free as compared to pristine and other samples. Additionally, it was concluded that such doping has had significant effects on the absorption and hole motilities when compared to pristine MAPbI\({}_{3}\). The exact roles of these proposed \"dopants\" are still not entirely clear. Reports with inconsistent conclusions are published on doping of perovskite structures with Bi\({}^{3+}\). [PERSON] et al. reported [21] on the introduction of Bi\({}^{3+}\) in MAPbBr\({}_{3}\). They referred to earlier reports [7] by [PERSON] and co-workers. [PERSON] et al. claimed that hetero-valent doping of MAPbBr\({}_{3}\) with Bi\({}^{3+}\) caused a four orders of magnitude conductivity enhancement and a significant bandgap narrowing within the resulting material. [PERSON], on the other hand, reported that no metal-halide octahedral lattice tilting was observed. The angle between X-B-X in two unit cells in a lattice is directly correlated with the bandgap of the overall material. The bandgap-change due to Bi\({}^{3+}\) doping was a result of misinterpretation from light transmission measurements that were caused by a color change that arose due to the introduction of crystal defects. [PERSON] additionally reported that Bi\({}^{3+}\) introduction is detrimental to device performance at all concentrations. Crystal defects are introduced upon doping and unfavorable non-radiative recombination is facilitated as a consequence. A report [22] from 2016 by [PERSON] et al. described the doping of perovskite with Al\({}^{3+}\). The ionic radius of Al\({}^{3+}\) is much lower than Pb\({}^{2+}\) (53 vs 119 pm) and it was therefore not expected that Al would replace Pb in the lattice. Extensive analysis with crystallography and mass spectroscopy revealed that Al\({}^{3+}\) was not significantly incorporated in the lattice but expelled to the surface and grain boundary edges during the crystallization process. All evidence considered, [PERSON] et al. conclude that a small amount of Al\({}^{3+}\) doping results in better crystallization with fewer crystal defects in the film. The exact mechanism behind this is difficult to determine; however, they postulate a mechanism as follows: impurity ions can slow down crystallization by absorbing to the surface of the crystal and sterically inhibiting growth. Another mechanism could be that these impurities alter the surface energy of the crystal growth front, accelerating crystallization. In low concentrations, they infer that Al\({}^{3+}\) facilitates enhanced crystallization and especially the growth of the (hh0)-plane, resulting in better orientated crystalline domains. In Figure 2, a schematic diagram of the perovskite grown under the influence of the Al\({}^{3+}\) doping is depicted. In the left column of Figure 2, it is illustrated how crystal defects, which potentially exist in the form of terraces, grow under normal conditions.