Bandgap Lowering in Mixed Alloys of Cs2Ag(SbxBi1-x)Br6 Double Perovskite Thin Films

Halide double perovskites have gained significant attention, owing to their composition of low-toxicity elements, stability in air and long charge-carrier lifetimes. However, most double perovskites, including Cs2AgBiBr6, have wide bandgaps, which limit photo conversion efficiencies. The bandgap can be reduced through hallowing with Sb3+, but Sb-rich alloys are difficult to synthesise due to the high formation energy of Cs2AgSbBr6, which itself has a wide bandgap. We develop a solution-based route to synthesis phase-pure Cs2Ag(SbxBi1-x)Br6 thin films, with the mixing parameter x continuous varying over the entire composition range. We reveal that the mixed alloys (x between 0.5 and 0.9) demonstrate smaller bandgaps (as low as 2.08 eV) than the pure Sb- (2.18 eV) and Bi-based (2.25 eV) compounds, with strong deviation from Vegard's law. Through in-depth computations, we propose that bandgap lowering arises from the Type II band alignment between Cs2AgBiBr6 and Cs2AgSbBr6. The energy mismatch between the Bi and Sb s and p atomic orbitals, coupled with their non-linear mixing, results in the alloys adopting a smaller bandgap than the pure compounds. Our work demonstrates an approach to achieve bandgap reduction and highlights that bandgap bowing may be found in other double perovskite alloys by pairing together materials forming a Type II band alignment.

5 bandgap of 1.9-2.1 eV. 9,13 Another factor was that only a maximum of 37.5% Sb could be introduced through powder melt synthesis, limiting the extent of bandgap reduction. 23 Intriguingly, mixed Cs 2 Ag(Sb x Bi 1-x )Br 6 alloys have exhibited a non-linear reduction in the bandgap, i.e., bandgap bowing, with increasing Sb content. 23,25 Bandgap bowing has also been found in Pb/Sn perovskite alloys, and, in this case, the bowing is pronounced, such that the mixed alloy exhibits a smaller bandgap than either of the pure Pb-or Sn-based compounds. [26][27][28] An important question would be whether a similar phenomenon occurs in Cs 2 Ag(Sb x Bi 1-x )Br 6 alloys.
So far, there is a lack of understanding of the extent of bandgap bowing in Sb-Bi double perovskite alloys and whether the mixed compositions could exhibit a smaller bandgap than the pure compounds. This requires the full composition range in Cs 2 Ag(Sb x Bi 1-x )Br 6 alloys to be synthesized. However, synthesizing phase-pure Cs 2 AgSbBr 6 is challenging, particularly in thin film form. This is due to the high formation energy of Cs 2 AgSbBr 6 and the small ionic radius of Sb 3+ relative to Bi 3+ . 29 Recently, Liu et al. synthesized thin films of Cs 2 Ag(Sb x Bi 1x )Br 6 alloys by dipping their substrates in a heated solution of the precursor salts dissolved in dimethyl sulfoxide (DMSO). 25 But they were only able to achieve up to 75% Sb alloying and were not able to synthesize the pure Sb-based compound. Colloidal nanocrystal synthesis routes have been found to be more successful in growing less thermodynamically-favored compounds (e.g., iodide-based double perovskites, which have a positive heat of formation).
Yang et al. recently developed a route to grow Cs 2 AgSbBr 6 nanocrystals. 29 But it is also desirable to achieve phase-pure Cs 2 AgSbBr 6 as bulk thin films, which do not have carriers confined within individual grains, as is the case for nanocrystals bound with long-chain ligands.
In this work, we achieved the synthesis of Sb-Bi double perovskite alloys over the entire composition range in thin film form. We found that the mixed alloys have a lower bandgap than the pure Bi-and Sb-based double perovskites, with similar pronounced nonlinear bandgap behavior to that found in lead-tin perovskite alloys. [26][27][28] Through X-ray diffraction (XRD) and Rutherford Backscattering Spectrometry (RBS), we found all films to be phase-pure, with the thin film composition in the bulk matching the ratio of elements in the precursor solution. We Cs 2 Ag(Sb x Bi 1-x )Br 6 thin films were synthesized by solution processing. The CsBr, AgBr, SbBr 3 and BiBr 3 precursors were mixed according to their stoichiometric ratio in DMSO with a concentration of 0.5 mol·L -1 . In contrast to the dipping method used by Liu et al., 25 we used a lower annealing temperature and shorter annealing time (detailed in the Experimental section in the SI), which may have contributed to the successful synthesis of phase-pure Cs 2 AgSbBr 6 .
Photographs of the films (approx. 200 nm thickness in all cases) are shown in Fig. 1a, and it was observed that the mixed compositions have a deeper color. To determine the bulk composition of the films, we performed RBS measurements ( Fig. 1b and Table 1). It was found that the Sb/Bi ratio from the RBS measurements matched the stoichiometry in the precursor solution, indicating no change in the composition during crystallization. This is indicative of no phase impurities precipitating out during film synthesis.  The phase-purity of the films was determined through XRD measurements (Fig. 2a).
Cs 2 AgSbBr 6 and Cs 2 AgBiBr 6 have the same cubic structure and space group (Fm3 " m). The lattice constants were found to be 11.184 Å for Cs 2 AgSbBr 6 and 11.255 Å for Cs 2 AgBiBr 6 , with a continuous variation between these extremes through the alloying range, as could be seen from the continuous shift in peak positions ( Fig. 2b and Fig. 3d). Common phase impurities for the Sb-Bi double perovskites are Cs 3 Bi 2 Br 9 and Cs 3 Sb 2 Br 9 . Both impurities have almost the same diffraction patterns with their double perovskite counterparts, but one of the main differences is a peak from Cs 3 Bi 2 Br 9 at 8.95°, or from Cs 3 Sb 2 Br 9 at 9.10°. 30 Neither impurity peaks were found to be present here. However, these XRD measurements were taken using a 1D linescan, and it is possible that the impurity peaks were not detected due to preferred orientation. We therefore performed 2D XRD measurements (Fig. S2, SI). We synthesized the whole alloying range of double perovskite thin films and intentionally induced a Cs 3 (Bi,Sb) 2 Br 9 phase impurity to the films with 50% Sb. From the 2D XRD patterns, we found that the diffraction peak should be detectable by the 1D linescan if it is present. Therefore, the absence of any phase-impurities in the 1D XRD patterns in Fig. 2a shows the films to be phase-pure.
The diffraction patterns also showed no peak splitting, but the full width at half maximum  Standard optical transmittance and reflectance measurements (using a UV-visible spectrophotometer with an integrating sphere) were used to determine the absorption coefficient of the double perovskite thin films (Fig. 3a). All films showed a slow increase in the absorption coefficient for photon energies >2 eV, before rising sharply to >10 5 cm -1 at >2.6 eV. An absorption coefficient exceeding 10 5 cm -1 at >2.6 eV is characteristic of a direct bandto-band transition. Both Cs 2 AgBiBr 6 and Cs 2 AgSbBr 6 have indirect bandgaps due to the effects of the Ag d orbitals at the band-edges, and the alloys are also expected to have indirect bandgaps. 6 Therefore, to determine the indirect bandgap, we investigated the absorption onset in the lower photon energy range (i.e., between 2-2.6 eV), leaving the discussion of the absorption in the higher photon energy range to later in the paper. We observed that the alloys with 70-90% Sb showed a lower-energy absorption onset than the pure Sb-and Bi-based films.
However, the indirect bandgaps resulted in the absorption coefficients being small close to the band-edge, making it difficult to accurately determine the bandgap from standard transmittance and reflectance measurements. Therefore, we performed PDS measurements, which are sensitive to the absorbance 3-4 orders below the band-edge (operating details in the Experimental section, SI).
A consequence of the high sensitivity to low absorbance is that the measurements in PDS saturate for high absorbance at >2.6 eV (Fig. 3b), and the peaks in the absorption coefficient seen in Fig. 3a are not observed in the PDS measurements plotted on a semi-logarithmic scale (see later in the paper for a discussion of these peaks). The normalized absorbance from PDS measurements at the band edge (in the range of 2-2.3 eV) is approximately 3 orders of magnitude lower than the absorbance at 2.6 eV, where the absorption coefficient is >10 5 cm -1 (Fig. 3a). Thus, the absorption coefficient at the band edge should be on the order of 10 2 cm -1 .
We note that silicon, which is a typical indirect bandgap material, has an absorption coefficient of 10 2 cm -1 at the band edge. 31,32 The absorption plots shown in Fig  was acquired by fitting the XRD measurements (Fig. 2a). The bandgap was obtained from the Tauc plot constructed from the PDS data in part c To extract numerical values of the bandgap and quantify their variation with composition, we fitted the PDS absorbance data using a Tauc plot, which is a plot of (ahn) 1/n against hn. The rationale can be seen from Eq. 1 where α is the absorption coefficient, h is Planck's constant, ν is the photon frequency, A is a proportionality constant, E g is the bandgap, and n = 2 for an indirect bandgap. 31,32 Therefore, by plotting (αhν) 0.5 against (hv), the bandgap can be extracted from the intercept between the tangents fit to the absorption onset and background (Fig. 3c). From these Tauc plots, we found the system to exhibit significant bandgap bowing (Fig. 3d). The compound with x = 0.9 demonstrated the lowest bandgap of 2.08 eV, which is smaller than the bandgap of Cs 2 AgSbBr 6 (2.18 eV) and Cs 2 AgBiBr 6 (2.25 eV). It is possible that the lower bandgap extracted for the compound with x = 0.9 than for materials with x = 0.5 and x = 0.7 (both 2.10 eV) were due to errors in the fitting process, which may have arisen in part from the lower slope in the absorption onset of the material with x = 0.9. Nevertheless, we emphasize that from the Tauc plots, the compounds with x = 0.5-0.9 all have smaller bandgaps than the pure Bi-and Sbbased compounds, which is consistent with our analysis of the PDS absorbance measurements in Fig. 3b. This is also consistent with the trend in bandgaps we extracted from the Tauc plot ( Fig. S4, SI) based on the absorption coefficient measurements (Fig. 3a). In addition, the bandgap lowering was smooth, with no switch in the bandgap from indirect to direct. This bandgap lowering behavior is similar to the Pb-Sn perovskite system and has not been previously observed in Sb-Bi double perovskites. To delve closer to the origin of bandgap lowering, the 'natural' band offset of the two double perovskite materials was calculated following the alignment procedure of Butler et al. 36  Typically, the energies of valence electrons become less negative as one moves down a group in the periodic table, corresponding to a decrease in ionization energies. However, for Bi 3+ and 14 Sb 3+ , this is not the case, with the Bi 3+ 6s 2 lone pair being lower in energy than the Sb 3+ 5s 2 lone pair. 37 This is a result of the relativistic contraction of the Bi 6s orbital, due to its large atomic number, resulting in a more localized, lower-energy valence s orbital, compared to Sb 5s. 38 Consequently, the more-diffuse, higher-energy Sb 5s 2 lone-pair has a stronger interaction with the Ag 4d and Br 4p orbitals, due to a reduced energy separation of the bonding orbitals (Fig.   S5, SI). This produces both greater dispersion in the valence band and a higher VBM, as shown in Fig. 4e. In a similar manner, the elevated position of the CBM in Cs 2 AgSbBr 6 can be understood by considering the ionization energies and ionic orbital energies. While the first ionization energy of Sb is indeed larger than that of Bi, the third ionization energy (corresponding to the removal of a p electron from Sb 2+ /Bi 2+ ) is in fact 0.3 eV lower for Sb than for Bi, 37 indicating higher energy cationic p states. When the pnictogen elements are in the +3 oxidation state, as is the case in these materials, the third ionization energy provides an improved estimate for the energy of the unoccupied p orbitals. Hence, we argue that, in the +3 formal charge state, the Sb valence p orbitals are in fact higher in energy than those of Bi, suggesting a higher energy CBM for Cs 2 AgSbBr 6 , as witnessed in our investigations. The origins of bandgap bowing in semiconductor alloys are typically due to chemical effects (e.g., differences in electronegativity), local size-mismatch effects or changes in the lattice parameter. [39][40][41] For the Pb-Sn perovskite alloy system, Im et al. attributed bandgap bowing to the combined effect of spin-orbit coupling and composition-induced phase change. 28 Snaith and coworkers proposed that the short range ordering of preferred atomic scale clusters allow the bandgap of the mixed alloy to be below that of both pure compoounds. 27 In contrast, Stevanović and coworkers found that the strong nonlinearity in bandgap was primarily due to the mismatch in energy between s and p atomic orbitals of Pb and Sn. 26 The Pb-Sn alloys have a higher VBM dominated by Sn-5s and I-5p orbitals and lower CBM dominated by Pb-6p and I-5p orbitals. They found that spin-orbit coupling, structure changes and short-range ordering did not have a significant effect on bandgap bowing, and proposed that a homogeneous structure would have improved stability over a structure with short range ordering.
In the case of Cs 2 Ag(Sb x Bi 1-x )Br 6 , we propose that the Type II staggered gap alignment between the pure compounds allows for the non-linear mixing of electronic states such that bandgaps lower than that of either pure material are obtained (Fig. 4e). Upon addition of Bi to the pure Sb double perovskite, the conduction band will be lowered because the CBM wavefunction amplitude is preferentially allocated to the Bi sites, producing a 'Bi-like', lowerenergy conduction band state. The presence of Bi will also enhance spin-orbit coupling, further reducing the energy of the CBM. On the other hand, the highest energy valence band state will remain 'Sb-like', with greater wavefunction amplitude at the Sb sites yielding a VBM only slightly below that of the pure Sb material. This mixing of electronic states in the alloys to produce a low-energy CBM, dominated by Bi-Br interactions, and a high-energy VBM, dominated by Sb-Ag-Br interactions, produces bandgaps in the double perovskite alloys which are lower than that of either pure material.
As the alloy mixing parameter x approaches extreme values (x → 0 or x → 1), the ability of the band extrema states to simultaneously adopt Bi and Sb character is diminished, hence the bandgap increases toward the pure double perovskite values. Therefore, we propose that this orbital-mixing behavior, facilitated by the Type II bandgap alignment, is the origin of the nonlinear, non-monotonic variation in bandgap with composition in the Sb-Bi double perovskite system.
Another possible contribution to bandgap bowing is volume deformation, whereby variation in the lattice constant upon alloying results in non-linear transformation of the electronic structure. 26 This mechanism, however, more commonly dominates in alloys involving more chemically-distinct materials than is the case here. Moreover, due to the small positive bandgap deformation potentials calculated for the Sb and Bi compounds (ΔE g ~ 0.02 eV), we rule out this mechanism. Relative to the experimentally-observed bowing (~ 0.1 eV, Fig. 3d), volume distortion alone is not the origin of bandgap bowing in this alloy system.
Finally, we return to discuss the sharp peak in the absorption coefficient of the films at >2.6 eV (Fig. 3a). This is especially evident for Cs 2 AgBiBr 6 . Previous work attributed the sharp absorption peak in Cs 2 AgBiBr 6 to an exciton associated with the direct transition. 24,[42][43][44][45] However, there is also the possibility that these features in the pure compounds and mixed alloys are due to a narrow density of states at the band-edges. To explore this possibility, we computed the absorption spectra for Cs 2 AgSbBr 6 and Cs 2 AgBiBr 6 without excitonic effects (Fig. 4f). These spectra were broadened by convoluting with a Gaussian peak with a FWHM of 0.15 eV. For both materials, the calculated absorption spectra exhibit peaks at 2.8 eV, in agreement with the experimental measurements. These peaks arise from the relatively-weak dispersion of the electron bands at the CBM and VBM of the materials (Fig. 4a, b), yielding peaks in both the density of states (Fig. 4c, d) and thus the optical absorption (Fig. 4f). This strongly suggests that the peaks observed in the experimental UV-visible measurements are the result of direct transitions between the relatively-flat electron bands. That said, the exciton binding energy of Cs 2 AgBiBr 6 was calculated to be 167 meV within effective mass theory, which is sufficiently large that stable exciton formation is possible in these systems.
Curiously, the computed absorption spectrum for Cs 2 AgSbBr 6 shows a distinct absorption peak (Fig. 4f), whereas the measured peak from UV-visible spectrophotometry became less distinct with increasing Sb content, until there was barely an observable peak for the pure Sbbased compound (Fig. 3a). This may have been due a 'smearing out' of the absorption peak due to structural disorder. [46][47][48] We calculated the absorption spectra for the pure Sb-based compound convoluted with Gaussian peaks with wider FWHM (0.2 eV, 0.3 eV, 0.4 eV; Fig.   S6, SI). These show that the peak becomes indistinguishable when broadening is large, as witnessed experimentally and consistent with the PDS measurements. Thus, peak broadening as a result of disorder leads to the observed 'smeared-out' absorption spectrum in Fig. 3a.
In conclusion, we successfully synthesized phase-pure Cs 2 AgSbBr 6 thin films, as well as Cs 2 Ag(Sb x Bi 1-x )Br 6 with x varying over the full compositional range. In doing so, we found that the mixed double perovskites with x between 0.5 and 0.9 to have the smallest bandgaps, lower than those of the pure compounds. From the electronic band alignment, we found that the origin of bandgap bowing in this double perovskite alloy is due to chemical rather than structural effects. The Type II band alignment between Cs 2 AgBiBr 6 and Cs 2 AgSbBr 6 , in combination with non-linear mixing of the electronic states, results in the alloy having smaller bandgaps than either pure material. Our work demonstrates a novel route to reduce the bandgap of Cs 2 AgBiBr 6 and Cs 2 AgSbBr 6 , which could be generalized to other halide double perovskites.
That is, we propose that alloys formed from compounds with a Type II band alignment could exhibit similar bandgap lowering. This may prove crucial for improving the suitability of double perovskites for photovoltaic and photocatalytic applications.

Supporting information
The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXX.
Supporting information includes the following parts: film deposition methods, computation methods, characterization methods, fitting of the RBS measurements, 2D XRD patterns, SEM of Cs 2 Ag(Sb x Bi 1-x )Br 6 thin films, Tauc plot fitting of the UV-visible spectroscopy data, schematic molecular orbital diagram of Cs 2 AgSbBr 6 and Cs 2 AgBiBr 6 , and calculated optical absorption spectra.

AUTHOR INFORMATIONS
Author contribution † Z.L. and S.K. contributed equally to this work. Corresponding author *Email: r.hoye@imperial.ac.uk

Notes
The authors declare no competing financial interest.