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
ABX3 to decompose into AX + BX2, or oxidation
of 2ABX3 into A2BX6, 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]­I3 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]­I3 and FA­[Sn,Pb]­I3. 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.