Pair modes of organic cations in hybrid perovskites: Insight from first-principles calculations of supercell models

摘要

We have studied the properties of the prototype hybrid organic-inorganicperovskite CH$_3$NH$_3$PbI$_3$ using relativistic density functional theory(DFT). For our analysis we introduce the concept of CH$_3$NH$_3$$^+$ "pairmodes", that is, characteristic relative orientations of two neighboringCH$_3$NH$_3$$^+$ cations. In our previous work [Phys. Rev. B 94, 045201 (2016)]we identified two preferential orientations that a single CH$_3$NH$_3$$^+$cation adopts in a unit cell. The total number of relevant pairs can be reducedfrom the resulting 196 combinations to only 25 by applying symmetry operations.DFT results of several 2$\times$2$\times$2 supercell models reveal thedependence of the total energy, band gap and band structure on the distributionof CH$_3$NH$_3$$^+$ cations and the pair modes. We have then analyzed thepair-mode distribution of a series of 3$\times$3$\times$3 supercell models withdisordered CH$_3$NH$_3$$^+$ cations. Our results show that diagonally-orientedCH$_3$NH$_3$$^+$ cations are rare in optimized CH$_3$NH$_3$PbI$_3$ supercellstructures. The prevailing pair modes are advantageous for the formation oflinear domains. Our pair-mode concept provides combined atomistic-statisticalinsight to understand the disordered structures in bulk hybrid perovskitematerials.