Ba-induced phase segregation and band gap reduction in mixed-halide inorganic perovskite solar cells

All-inorganic metal halide perovskites are showing promising development towards efficient long-term stable materials and solar cells. Element doping, especially on the lead site, has been proved to be a useful strategy to obtain the desired film quality and material phase for high efficient and stable inorganic perovskite solar cells. Here we demonstrate a function by adding barium in CsPbI2Br. We find that barium is not incorporated into the perovskite lattice but induces phase segregation, resulting in a change in the iodide/bromide ratio compared with the precursor stoichiometry and consequently a reduction in the band gap energy of the perovskite phase. The device with 20 mol% barium shows a high power conversion efficiency of 14.0% and a great suppression of non-radiative recombination within the inorganic perovskite, yielding a high open-circuit voltage of 1.33 V and an external quantum efficiency of electroluminescence of 10−4.


Computational details 137 Ba EFG tensor calculations
We start from the assumption, that the 137 Ba cation is incorporated into the CsPbBr 3 lattice at either the A-or B-site replacing the Cs or Pb atom, respectively, without significantly changing the perovskite lattice formed by the [PbBr 6 ] 4octahedra.
We assemble the final clusters from CsPbBr 3 structure as Cs 54 BaPb 26 Br 108 (denoted as "Pb-Ba_large"), Cs 22 BaPb 6 Br 36 (denoted as "Pb-Ba_small") and Cs 18 BaPb 8 Br 3 (denoted as "Cs-Ba"), analogously to the ones used in the previous paper by Kubicki et al., 1 ensuring charge compensation, high symmetry and direct comparability of the results. The clusters are shown in Supplementary Figure 17 and all of the structures are given in the Amsterdam Density Functional (ADF) 2,3 suite input and output format in the zip-file 137Ba_efg.zip. We use the highly symmetric cubic (Pm-3m) structure of CsPbBr 3 to simplify the cluster assembly. We expect the results to carry over to the orthorhombic (Pnma) room temperature structure observed experimentally.
For the EFG tensor calculations we used the ADF 2,4 suite within the density functional theory (DFT) framework. For the calculations we employed the GGA BP86 3,5 functional including the Grimme 6 dispersion correction and relativistic effects up to spin-orbit couplings within the ZORA 7-9 approximation. We used all-electron triple-ζ basis sets with two polarization functions (TZ2P). 10 For all of the investigated systems the DFT calculated EFG tensor parameters are given in Supplementary Table 4. Note, that the calculated EFG tensors from Pb-Ba_large and Pb-Ba_small should be the same, as they represent the same system. However, from Supplementary Table 4 it is evident, that the asymmetry parameter and especially the NQCC value differ significantly. This shows the importance of using large enough clusters so as to minimize the effect of symmetry breaking and the influence of atoms outside of the included coordination shells. Here, we choose Pb-Ba_large as estimator for the experimental data, as the larger cluster more accurately describes the central 137 Ba atom and its coordination. We also note, that for even larger clusters with an increased symmetry we expect an even smaller asymmetry parameter and NQCC. However, computationally, a larger cluster is not feasible or would require the use of less accurate basis-sets. Thus, the values calculated here should only be considered as an upper limit, rather than a quantitative measure.

Cs chemical shift calculations
We start from the assumption, that the 137 Ba cation is incorporated into the CsPbBr 3 lattice at either the A-or B-site replacing the Cs or Pb atom respectively, without significantly changing the perovskite lattice formed by the [PbBr 6 ] 4octahedra.
As starting point we use both the highly symmetric cubic (Pm-3m) structure of CsPbBr 3 and the orthorhombic (Pnma) room temperature structure observed experimentally.
We assemble an unperturbed cluster from the CsPbBr 3 structure as Cs 20 Pb 8 Br 36 (denoted as "CsPbBr 3 "), analog to the ones used in the previous paper by Kubicki et al., 1 ensuring charge compensation, high symmetry and a direct comparability of the results. Subsequently, we generate perturbed structures by replacing one to three of the non-central Cs atoms (or one of the Pb atoms) with Ba atoms, while maintaining the charge neutrality of the system. All of the clusters are shown in Supplementary Figure 18 and 19 and all of the structures are given in the ADF 2,3 suite input and output format in the zip-file 133Cs_chemical_shift.zip. A short description of the different clusters in given in Supplementary Table 1. For the chemical shielding calculations we used the ADF 2 4 suite within the DFT framework.
For the calculations we employed the GGA BP86 3,5 functional including the Grimme 6 dispersion correction and relativistic effects up to spin-orbit couplings within the ZORA 7-9 approximation. We used all-electron triple-ζ basis sets with two polarization functions (TZ2P). 10 The calculated 133 Cs magnetic shieldings ( ) were referenced to chemical shifts ( ) using the relation = − . . The offset (a=2538) and slope (b=0.388) were calculated through a linear regression using the calculated and experimental chemical shifts of (hexagonal) -CsPbI 3 , (tetragonal) rt-CsPbCl 3 and (orthorhombic) rt-CsPbBr 3 . 11 -13 For all of the investigated systems the DFT 133 Cs calculated magnetic shieldings and shifts are given in Supplementary Table 1.

Structure optimization
We further investigate the symmetry preservation of the more chemically probable and energetically more stable structure featuring Ba incorporation, whereby Ba replaces Pb on the B-site. To that end, we generated a 2x2x2 periodic supercell with one Pb replaced by a Ba atom. Next, we optimized the positions of all the atoms using a periodic system within the DFT framework and the generalized gradient approximation (GGA) functional PBE 14 within the Quantum Espresso suite. 15 The DFT optimization includes the Grimme 6 dispersion correction and relativistic effects up to spin-orbit couplings. For every calculation we use a plane-wave maximum cutoff energy of 100 E Ryd and a 2x2x2 Monkhorst-Pack 16 grid of k-points. The energy convergence threshold was set to 10 -4 Ry and the force convergence threshold was set to 10 -3 F Ryd .
The optimization lead to no significant changes within the structure, with an all atom root-mean-square deviation below 0.03 Å. All the QE output and input files are given in the zip-file relaxation.zip.