Enhanced visible light absorption in layered Cs3Bi2Br9 through mixed-valence Sn(ii)/Sn(iv) doping

Lead-free halides with perovskite-related structures, such as the vacancy-ordered perovskite Cs3Bi2Br9, are of interest for photovoltaic and optoelectronic applications. We find that addition of SnBr2 to the solution-phase synthesis of Cs3Bi2Br9 leads to substitution of up to 7% of the Bi(iii) ions by equal quantities of Sn(ii) and Sn(iv). The nature of the substitutional defects was studied by X-ray diffraction, 133Cs and 119Sn solid state NMR, X-ray photoelectron spectroscopy and density functional theory calculations. The resulting mixed-valence compounds show intense visible and near infrared absorption due to intervalence charge transfer, as well as electronic transitions to and from localised Sn-based states within the band gap. Sn(ii) and Sn(iv) defects preferentially occupy neighbouring B-cation sites, forming a double-substitution complex. Unusually for a Sn(ii) compound, the material shows minimal changes in optical and structural properties after 12 months storage in air. Our calculations suggest the stabilisation of Sn(ii) within the double substitution complex contributes to this unusual stability. These results expand upon research on inorganic mixed-valent halides to a new, layered structure, and offer insights into the tuning, doping mechanisms, and structure–property relationships of lead-free vacancy-ordered perovskite structures.


Computational Details
The computational methods are described in the main manuscript. Below is additional information.
For defect calculations involving Sn B -V X (X = Cs, Bi, Br), a 56-atom supercell was used, whilst for (Sn Bi -Sn Bi ) and isolated Sn Bi defects, both a 56-atom and a 112-atom supercell were employed in order to investigate concentration effects, produced from 2 x 2 x 1 and 2 x 2 x 2 cubic expansions of the hexagonal Cs 3 Bi 2 Br 9 unit cell. The same plane-wave energy cutoff (350 eV) was employed as for bulk electronic structure calculations, with a 2 x 2 x 1 Γcentred Monkhorst-Pack k-point mesh (equivalent to a k-point density of 0.31 Å -1 ).
For the 112-atom 2x2x2 supercell, 'rattling' the non-defective structure by applying random atomic displacements following a normal distribution (σ = 0.25 Å), prior to geometry relaxation, resulted in octahedral tilting and a final energy 0.256 eV (2.3 meV/atom) lower than the unperturbed structure. As such, 'rattling' was applied to each defective 112-atom supercell and compared to the 'rattled' non-defective supercell when calculating these defect formation energies, to ensure the global minimum on the structural potential energy surface was obtained.
To account for spurious finite-size supercell effects, a modified version of the Kumagai-Oba anisotropic charge correction scheme (eFNV) was implemented, with a 2/3 scaling of the point-charge correction energy, which has been shown to produce accurate results for defect formation energies. [1][2][3] If necessary, Moss-Burstein type band filling corrections were also applied. For the calculation of optical transitions involving a change in defect supercell charge (i.e., electronic transitions from (Sn Bi • -Sn Bi / ) to (Sn Bi  -Sn Bi / ) + h VBM + or to (Sn Bi • -Sn Bi  ) + e CBM -), charge corrections were performed using the GKFO method for vertical defect transitions, 4 again with a 2/3 scaling of the point-charge correction energy. For calculations of the energy of inter-valence charge transfer (IVCT), corresponding to the optical transition (Sn Bi • -Sn Bi / ) to (Sn Bi  -Sn Bi  ), the excited-state electron band occupancies were fixed to (Sn Bi  -Sn Bi  ) and a static total energy calculation was performed.
To determine the chemical potential limits of the system, structural relaxation and calculation of total energies were performed for the relevant competing phases and elemental references, using the same level of theory (HSE06+SOC) and plane-wave energy cutoff (350 eV), with a well-converged k-point mesh in each case. To ensure the equilibrium structure was used in each case, all structures within 70 meV of the GGA DFT-predicted ground state (as provided by the Materials Project database; materialsproject.org) were considered for each material. In total, 40 competing and reference phases were calculated.
Bader charge density partitioning for the comparison of species' oxidation states was performed using the bader package as provided by the Henkelman group. 5 All calculation data and analyses are provided in an online repository at doi.org/10.5281/zenodo.4780949.     In the COHP plot in Figure S6, the peak just below the Fermi level corresponds to the occupied Sn(II)-Br state in the bandgap (Figure 3d), while the peak ~1.5 eV above this corresponds to the unoccupied Sn(IV)-Br state. We see that, while the lower-energy Sn(II)-Br state is indeed overall anti-bonding in nature, it is significantly less so than the Sn(IV)-Br state. This is facilitated by the additional hybridisation of Sn 5p and strong electron-phonon coupling (allowing substantial distortion of the local environment), simultaneously reducing the anti-bonding character of the Sn(II) 'lone-pair' state and firmly splitting the Sn-Br levels in the band gap.

Dielectric Constant
Due to the extremely-shallow, anharmonic barrier between the two structural polymorphs of   9 Ionic response (ε Ionic ) determined using the relation ε 0 = ε Optic + ε Ionic . The same is true for the +2 and -2 charge states. and the +2 charge state is doubly-Δ < Δ stabilised relative to the -2 charge state. Thus, the instability of the -1 charge state, relative to the neutral/-2 charge states, is slightly lower than that of the +1 charge state, relative to the neutral/+2 charge states.
This can be seen from the positions of the Sn Bi defect levels in the gap in the DOSs for the neutral (Figures S4 and S5) and doubly-charged cases (in all cases, greater separation between VBM and acceptor levels than CBM and donor levels).
Chemical potential analysis establishes the following stability map ( Figure S7) for Cs 3 Bi 2 Br 9 , with CsBr and BiBr 3 determined as the most relevant competing phases. Both 12.5% and 25% Sn-doped Cs 3 Bi 2 Br 9 were found to be thermodynamically stable under Sn-rich conditions. The stability plots for the doped materials are shown Figure S8. At the Sn-rich limit, the competing phases are CsSn 2 Br 5 and CsSnBr 3 . Figure S9. Variation in the intervalence absorption band maxima in previously reported A 2 BX 6 structures (left) and A 3 B 2 X 9 structures reported in this work (right). The difference in behaviour is attributed to the defect motif formed. Figure S10. XRD patterns and, inset, XPS spectra for a representative Sn-doped Cs 3 Bi 2 Br 9 sample immediately after synthesis (black traces) and after storage in air for 2 weeks (red traces).  Figure S11. Comparison of solid-state NMR spectra of two separately synthesised batches of the 23.5% Sn-doped Cs 3 Bi 2 Br 9 . A: quantitative 133 Cs NMR spectra. B: 119 Sn spectra. The 119 Sn spectra of batch 2 were recorded using a shorter recycle delay of 15 s, hence the small differences in lineshape). Figure S12 shows the high energy part of the low-temperature (10 K) photoluminescence spectra from Fig. 4 c. The undoped Cs 3 Bi 2 Br 9 exhibits a narrow free exciton peak at 2.67 eV, followed by a broader peak (~2.59 eV), resulting from recombination via defects located in the proximity of the surface. 10,11 In the 9.1% Sn-doped sample, the free exciton peak of Cs 3 Bi 2 Br 9

Low-temperature PL
persists over the broadened spectral emission, which is attributed to residual undoped  Figure S12. Low-temperature (10 K) steady-state photoluminescence spectra obtained for the undoped and Sn-doped Cs 3 Bi 2 Br 9 . Intensities have been normalised by the multiplication factors given.

Thin Film Deposition and Characterisation
The as-prepared powders of undoped, 10% Sn-doped and 23.5% Sn-doped Cs 3 Bi 2 Br 9 were individually dissolved in a 4:1 (vol/vol) DMF/DMSO solvent mixture and stirred at 80 o C for 2 hours. Upon filtration of the solutions with 0.2 µm PTFE syringe filters, thin films were prepared on glass substrates by spin coating at 3500 rpm for 50 s and then annealing at 200 o C for 10 min. All processing of the perovskite solutions and subsequent fabrication of the thin films was performed under inert atmosphere. Three batches of films were made to ascertain reproducibility of the results. As shown in Figure S13, undoped and 10% Sn-doped thin films appear pale yellow, whilst the 23.5% Sn-doped sample is noticeably darker. Optical absorption spectra measured in transmission mode are shown in Figure S14. Undoped 10% Sn 23.5% Sn Figure S14. Absorption spectra of Cs 3 Bi 2 Br 9 and Sn-doped Cs 3 Bi 2 Br 9 thin films.

Quantification of the 119 Sn spectrum of the 23.5% Sn material
The material nominally contains 23.5% Sn. The quantitative 119 Sn spectrum shows that 28% of that is incorporated into Cs 3 Bi 2 Br 9 : 0.235•0.28=0.0658. Since there are 2 Bi atoms per molecular unit, the formula of the doped materials is Cs 3 Bi 1.87 Sn 0.13 Br 9 .
We subsequently calculate the weight percent of each component. We first calculate the masses each of component (molecular weight • mol% from the quantitative spectrum): 1:1 ratio 1:10 ratio Figure S16. Diffuse reflectance spectra taken for undoped Cs 3 Bi 2 Br 9 (grey line) and Sn doped Cs 3 Bi 2 Br 9 using different sample : BaSO 4 weight ratios.