Formation and Composition-Dependent Properties of Alloys of Cubic Halide Perovskites

Distinct shortcomings of individual halide perovskites for solar applications, such as restricted range of band gaps, propensity of ABX(3) to decompose into AX + BX2, or oxidation of 2ABX(3) into A(2)BX(6), have led to the need to consider alloys of individual perovskites such as [FA,Cs] [Pb,Sn] [Br,I](3). This proposition creates a nontrivial material selection problem associated with a six-component structure, spanning a continuum of three sets of compositions (one for each sublattice) and requiring control of phase separation or ordering in each alloyed subfield. Not surprisingly, material and structure choices were made thus far mostly via trial-and error explorations among a large number of arrangements. Here, we use ideas from solid-state theory of semiconductor alloys to analyze the behaviors of the canonical [FA,Cs][Pb,Sn]I-3 alloy system, where FA is formamidinium. Density functional calculations utilizing specially constructed supercells are used to calculate the composition dependence of band gaps, energy of decomposition, and alloy mixing enthalpies. A number of clear trends are observed for A-site alloys [Cs,FA]SnI3 and [Cs,FA]PbI3, as well as for B-site alloys Cs[Sn,Pb]I-3 and FA[Sn,Pb]I-3. To understand the physical reasons that control these trends, we decompose the alloy properties into distinct physical terms: (i) the energies associated with removing the octahedral deformations (tilting, rotations, B-site displacements) of the individual components, (ii) the energies for compressing the larger component and expanding the smaller one to the alloy volume V(x), (iii) the charge-transfer energies associated with placing the alloyed units onto a common lattice, and finally, (iv) structural relaxation of all bonds within the cells. This analysis clarifies the origin of the observed trends in band gaps, decomposition energies, and mixing enthalpies. Unlike a number of previous calculations, we find that the proper description of alloy physics requires that even the pure, nonalloyed, end-point compounds need to be allowed to develop local environment-dependent octahedral deformation that lowers significantly the total energy and raises their band gaps.