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

Abstract

Distinct shortcomings of individual halide perovskites for solar applications, such as restricted range of band gaps, propensity of ABX 3 to decompose into AX+BX 2 , 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 non-trivial material-selection problem associated with a 6-component structure, spanning a continuum of three sets of compositions (one for each sub lattice), 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 alloys system, where FA is formamidinium. Density functional calculations utilizing specially constructed supercells (SQS) 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]SnI 3 and [Cs,FA]PbI 3 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 of 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 bang gaps, decomposition energies and mixing enthalpies. Unlike a number of previous calculations we find that the a proper description of alloy physics requires that even the pure, non-alloyed 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.

Unified theory for light-induced halide segregation in mixed halide perovskites

“…the specific exchange-correlation functional used in the DFT calculations (see 'Methods') and the limited size of the used supercells. Also, thermally induced random orientations of the MA and FA molecules 44 can influence the phase diagrams. On the other hand, we expect that the observed trends in the phase diagrams are reliable, because the relative accuracies in the calculations of the free energies under I ↔ Br exchange for the investigated compounds are expected to be better than the absolute accuracies.…”

Composition and dimension dependent static and dynamic stabilities of inorganic mixed halide antimony perovskites

“…The significantly lower ∆H f for Cs 3 Sb 2 Cl 9 translates into a much steeper change in ∆H f with respect to the Cl content in Cs 3 Sb 2 Cl y I 9−y solid solutions. Since the function relating the physical properties of (halide perovskite) alloy to its composition could exhibit 'bowing effect' originated from subtle structural relaxations, and charge transfers between ions occupying the same type of lattice sites, 36,37 we fit ∆H f (y) to the following quadratic relationship: We note that experimentally, Cs 3 Sb 2 Cl y I 9−y was found to adopt 2D structures when y is between 3.8-4, 21,35 which is in the regime where 2D structures are found to be more stable according to our theoretical results. However, Peng et al 35 also found that for y > 4, the mixed halide sample no longer existed as solid solution.…”

Mapping temperature-dependent energy–structure–property relationships for solid solutions of inorganic halide perovskites

“…Such a behaviour is temperature independent. Qualitatively, E g (x) exhibits a 'bowing-effect' which has been widely documented for halide perovskites, 65 but the extent of bowing effects shows no strong variance across three halides. The standard deviations in E g (x, T ), which can be directly related to the strength of electron-phonon couplings, 66 did not reveal clear compositionaldependency in this case, which are indicated by the sizes of the markers in Fig.…”