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Compared with silicon-based solar cells, organic-inorganic hybrid perovskite solar cells (PSCs) possess a distinct advantage, i.e., its application in the flexible field. However, the efficiency of the flexible device is still lower than that of the rigid one. First, it is found that the dense formamidinium (FA)-based perovskite film can be obtained with the help of N-methyl-2pyrrolidone (NMP) via low pressure-assisted method. In addition, CH 3 NH 3 Cl (MACl) as the additive can preferentially form MAPbCl 3−x I x perovskite seeds to induce perovskite phase transition and crystal growth. Finally, by using FAI·PbI 2 ·NMP+x%MACl as the precursor, i.e., ligand and additive synergetic process, a FA-based perovskite film with a large grain size, high crystallinity, and low trap density is obtained on a flexible substrate under ambient conditions due to the synergetic effect, e.g., MACl can enhance the crystallization of the intermediate phase of FAI·PbI 2 ·NMP. As a result, a record efficiency of 19.38% in flexible planar PSCs is achieved, and it can retain about 89% of its initial power conversion efficiency (PCE) after 230 days without encapsulation under ambient conditions. The PCE retains 92% of the initial value after 500 bending cycles with a bending radii of 10 mm. The results show a robust way to fabricate highly efficient flexible PSCs.

In this note an idea of quasi-homogeneous normal form theory using new grading functions is introduced, the definition of N th order normal form is given and some sufficient conditions for the uniqueness of normal forms are derived. A special case of the unsolved problem in a paper of Baider and Sanders for the unique normal form of Bogdanov Takens singularities is solved. AcademicPress, Inc.

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