German Edition: DOI: 10.1002/ange.201807421Perovskites Hot PaperInternational Edition: DOI: 10.1002/anie.201807421

Small-Band-Gap Halide Double PerovskitesAdam H. Slavney+, Linn Leppert+, Abraham Saldivar Valdes, Davide Bartesaghi,Tom J. Savenije, Jeffrey B. Neaton,* and Hemamala I. Karunadasa*

Abstract: Despite their compositional versatility, most halidedouble perovskites feature large band gaps. Herein, wedescribe a strategy for achieving small band gaps in thisfamily of materials. The new double perovskites Cs2AgTlX6

(X = Cl (1) and Br (2)) have direct band gaps of 2.0 and0.95 eV, respectively, which are approximately 1 eV lower thanthose of analogous perovskites. To our knowledge, compound2 displays the lowest band gap for any known halideperovskite. Unlike in AIBIIX3 perovskites, the band-gaptransition in AI

2BB’X6 double perovskites can show substantialmetal-to-metal charge-transfer character. This band-edge orbi-tal composition is used to achieve small band gaps through theselection of energetically aligned B- and B’-site metal frontierorbitals. Calculations reveal a shallow, symmetry-forbiddenregion at the band edges for 1, which results in long (ms)microwave conductivity lifetimes. We further describe a facileself-doping reaction in 2 through Br2 loss at ambient con-ditions.

The exceptional optoelectronic properties of lead-halideperovskite solar-cell absorbers[1] have instigated a renewedinterest in this well-known family of materials. Althoughoptimization of these absorbers have afforded record solar-cell efficiencies,[2] there is now growing appreciation for theneed for new perovskite compositions.[3] Studying analoguesis a time-tested method for understanding the origins of

a champion materialQs remarkable properties and establishingdesign rules for realizing these properties in alternativecompositions. To access greater compositional variationwithin the perovskite lattice, we[4] and others[5] recentlyexplored the photophysical properties of the AI

2BB’X6 (X =

halide) double perovskite platform. Unlike AIBIIX3 perov-skites, which are restricted to 2 + B-site cations, doubleperovskites can support oxidation states from 1 + to 4 + forthe B-site metals. This compositional flexibility should afforddiverse electronic structures, as observed in oxide perovskites,which range from insulators to metals.[6] However, to date, thevast majority of halide double perovskites[4, 5, 7] are eitherchlorides or bromides with band gaps over approximately2 eV. Indeed, halide substitution has been the most exploredmethod for reducing the band gap in halide perovskites, withiodides affording the lowest band gaps.[8] Herein, we demon-strate that double perovskites enable a different method forcreating small band gaps—through the energetic alignment ofthe frontier orbitals of the B and B’-site metals. This strategyallows us to form chloride and bromide double perovskiteswith band gaps that are about 1 eV smaller than those ofanalogous perovskites with the same halide. To our knowl-edge, the bromide perovskite features the smallest band gapreported for a halide perovskite since their discovery in1883.[9]

Crystalline powders of Cs2AgTlCl6 (1) and Cs2AgTlBr6

(2) were precipitated from solutions containing Tl2O3, CsX,and AgX (X = Cl@ , Br@) in 6m HCl and 9m HBr, respectively.Importantly, the stoichiometric precursors produce mixturesof Cs3Tl2X9

[10] and AgX, and the double-perovskite phaseforms only upon addition of several equivalents of CsCl (for1) or AgBr (for 2 ; see Supporting Information). Slowlycooling the solutions from 100 88C to room temperatureproduces crystals suitable for single-crystal X-ray diffraction(XRD) (Table S1 in the Supporting Information), whichreveals a cubic double perovskite structure (Figure 1, Fig-ure S1) with Fm3̄m symmetry, consisting of a 3D network ofcorner-sharing halide octahedra with alternating Ag+ and Tl3+

centers. For both 1 and 2, the Ag@X bond distances areunchanged from the related Cs2AgBiX6 structures,[4,5] whilethe Tl@X bonds are ca. 0.1 c shorter than the Bi@X bonds(Table S2). Recently, we demonstrated that dilute alloying ofTl3+ (< 1 atom %) into Cs2AgBiBr6 afforded a large band gapreduction, from 1.95 to approximately 1.5 eV in Cs2Ag-(Bi1@xTlx)Br6 (x = 0.075).[11] This alloyed material is effectivelya Tl3+/Bi3+ solid solution where now both x = 0 and x = 1endpoints are known (Figure 1).

The optical absorption properties of 1 and 2 (Figure 2A)were determined by diffuse reflectance measurements onpolycrystalline powders. Reflectance spectra are particularlysensitive to particle size,[12] so we performed our optical

[*] A. H. Slavney,[+] Dr. A. Saldivar Valdes, Prof. H. I. KarunadasaDepartment of ChemistryStanford UniversityStanford, CA 94305 (USA)E-mail: hemamala@stanford.edu

Dr. L. Leppert[+]

Institute of Physics, University of Bayreuth95440 Bayreuth (Germany)

Dr. D. Bartesaghi, Prof. T. J. SavenijeDepartment of Chemical EngineeringDelft University of Technology, Delft (Netherlands)

Dr. D. BartesaghiMaterials Innovation Institute2628CD Delft (Netherlands)

Prof. J. B. NeatonDepartment of Physics, University of California (USA),andMolecular Foundry, Lawrence Berkeley National Laboratory (USA),andKavli Energy NanoScience, Institute at BerkeleyBerkeley CA 94720 (USA)E-mail: jbneaton@lbl.gov

[++] These authors contributed equally to this work.

Supporting information and the identification number(s) for theauthor(s) of this article can be found under:https://doi.org/10.1002/anie.201807421.

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analyses on dispersions of small (, 1 mm) particles toeliminate effects of weakly absorbing defects (see Figure S2and the Supporting Information).[13] Submicron-sized parti-cles were formed through rapid precipitation of a hotprecursor solution in liquid N2 (see Supporting Information).The reflectance spectra were converted to pseudo-absorptionspectra using the Kubelka–Munk transformation.[14] Taucplots of the transformed data, assuming a direct, forbiddentransition (discussed below), place the band gap of 1 at1.96 eV and of 2 at 0.95 eV (Figure S3). Bandgap estimatesvary based on measurement and data fitting methods and wereport the highest measured values (see discussion in theSupporting Information). These values are strongly red-shifted from typical values for chloride (2.5–3.3 eV)[7c,15] andbromide (1.8–2.3 eV)[16] perovskites. Notably, the band gap ofthe bromide perovskite 2 is significantly smaller than thosetypically observed for iodide perovskites (1.2–1.6 eV).[8,17] Asdescribed below, a symmetry-forbidden band-edge transitionin 1 and 2 could cause overestimation of the band gap byapproximately 0.2 eV. Thus, to our knowledge, 2 possesses thesmallest reported band gap for a halide perovskite.

We observe no photoluminescence (PL) in 1 and 2 (evenat 20 K) despite their calculated direct band gaps (see below),which typically lead to rapid radiative carrier recombination.A similar lack of band-edge PL in the direct band gap,isoelectronic double perovskite Cs2AgInCl6 has been attrib-uted to a symmetry-forbidden band gap transition.[18] Wecalculated the transition dipole matrix elements along thehigh-symmetry lines L ! G and G ! X of 1 using(generalized) Kohn–Sham eigenstates from density functionaltheory (DFT) in the independent particle approximation with

the experimental crystal structure (Figure 2B; seeSupporting Information for details). Indeed, ourDFT calculations show that at G and along G ! Xthe dipole matrix elements are identically zero,representing a series of symmetry-forbidden Eg !A1g type transitions. However, the dipole matrixelements increase rapidly away from G along the G

! L line and along other directions in reciprocalspace, representing increasingly allowed transi-tions at energies above the band gap. The fre-quency-dependent linear absorption spectrum,calculated using the ab initio GW-Bethe-Salpeter

approach (see Supporting Information), exceeds 104 cm@1

only 0.17 eV above the band edge (Figure 2C), indicatingthat the region in k-space associated with symmetry-forbid-den transitions in these materials is small (smaller than the0.27 eV region in Cs2AgInCl6 ; See Supporting Informationand Figure S13). Thus, although symmetry-forbidden transi-tions are present in 1 and 2, they appear to have a relativelyminor effect on the absorption properties. After excitation,carriers thermalize into the forbidden region and largelyremain there as the energy width of the forbidden region(170 meV) is several times that of thermal energy at roomtemperature (26 meV). Carriers confined to the forbiddenregion cannot recombine radiatively, explaining the materialsQlack of PL. Notably, this results in ms-long carrier recombi-nation lifetimes in 1, observed through time-resolved micro-wave conductivity measurements (Figure 2D, Figures S8,S9),which are more typically seen in indirect-gap semiconductors.A similar case has been observed, and intensely studied, forthe high-performing perovskite solar-cell absorber(CH3NH3)PbI3.

[19]

To understand the origin of the small band gaps in 1 and 2,we performed calculations with ab initio many-body pertur-bation theory in a “one-shot” G0W0 approach, including spin-orbit corrections (SOCs).[20] G0W0 calculations reliant onDFT starting points with (semi)local exchange-correlationfunctionals greatly underestimate experimental band gaps ofTl- and Pb- containing perovskites.[21] We therefore used thescreened hybrid functional of Heyd, Scuseria, and Ernzerhof(HSE06) as a starting point for our G0W0 calculations, asimplemented in VASP. That is, we use DFT-HSE to constructthe zeroth-order GreenQs function G0 and screened Coulomb

Figure 1. Single-crystal structures of A) Cs2AgBiBr6 and C) Cs2AgTlBr6 (2).[31] Thestructure in (B) of Cs2Ag(Bi1@xTlx)Br6 is for illustration only.[8] Tl Black, Bi orange,Ag white, Br brown and Cs turquoise. Photographs of Cs2AgBiBr6 (left) and 2 (right)crystals. Photograph and structure of Cs2AgBiBr6 reproduced from Ref. [4].

Figure 2. A) Absorption spectra of 1 and 2 (solid lines) and those of Cs2AgBiCl6 and Cs2AgBiBr6 (dashed lines). B) Transition dipole matrixelements (jP j 2) along high-symmetry lines in reciprocal space calculated within the independent particle approximation. C) Absorption spectrumof 1 calculated using the ab initio GW-Bethe-Salpeter approach. The red box highlights the symmetry-forbidden region. D) Time-resolvedmicrowave conductivity traces of crystals of 1 showing ms-long conductivity. Samples were excited at 2.06 eV.

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interaction W0 (see Supporting Information). Our calculatedG0W0@HSE06 band gap for 1 is 1.9 eV, in very goodagreement with the experimental band gap of 1.96 eV. For 2the G0W0@HSE06 band gap underestimates the experimentalgap of 0.95 eV by more than 0.3 eV. Self-consistency in theeigenvalues (GW0) can afford better agreement with experi-ment:[21] the GW0@HSE06 band gap for 2 is 0.8 eV (Table S3).The DFT-HSE-SOC band structure of 1 (Figure 3B) isexpected to be similar to the G0W0@HSE06 band structurebut can be generated at greatly reduced computationalexpense.

We attribute the small observed band gaps in 1 and 2 toa combination of two factors. First, the presence of diffuse,spherical Tl3+ 6s (and some Ag+ 5s) orbitals at the conductionband minimum (CBM) leads to large overlap with the halideorbitals and consequently a highly dispersive conductionband. This is evidenced by the small electron effective masscalculated for 1 (m*

e ¼0.23, Table S4). Highly dispersivebands are correlated with small band gaps as increasingbandwidth brings band extrema closer together. Second, a lowband gap is consistent with a small intrinsic energy differencebetween filled Ag 4d and vacant Tl 6s orbitals, inherited fromthe atomic limit (Figure 3 C). In 1 and 2 the CBM containsmostly Tl-centered orbitals (with minor contributions fromempty Ag 5s orbitals) while the valence band maximum(VBM) is dominated by Ag-centered orbitals. Consequently,the band-gap transition may be considered predominantlya metal-to-metal charge transfer (MMCT). Many doubleperovskites have similar MMCT character in their bandedges[22] and thus their band gaps depend strongly on theenergy spacing between the two metalsQ frontier orbitals. Forexample, Cs2AgIBiIIICl6

[5] and Cs2TlITlIIICl6[15] are isostruc-

tural with 1 and represent a single substitution at the B site,replacing either Tl3+ with Bi3+ or Ag+ with Tl+, respectively.However, with band gaps of 2.77 eV and approximately2.5 eV for Cs2AgBiCl6 and Cs2TlITlIIICl6, respectively, thesematerials are more typical chloride perovskites. The greaterthan 0.5 eV difference between the band gaps of thesecompounds and that of 1 demonstrates that it is only incombination that Ag+ and Tl3+ yield reduced band gaps. To

further validate this claim, we used the WANNIER90 code toconstruct a tight-binding Hamiltonian of 1 and Cs2AgBiCl6 ina basis of maximally localized Wannier functions[23] centeredat each atomic site (Figure S12). We find that the energydifference between the on-site energies (Table S5) of filledAg 4d and vacant Tl 6s orbitals (in the VBM and CBM of 1,respectively) is only 2.3 eV whereas that between filled Ag 4dand vacant Bi 6p orbitals (in the VBM and CBM ofCs2AgBiCl6, respectively) is 4.8 eV. This analysis confirmsthat the frontier molecular orbitals derived from Ag+ (4d10)and Tl3+ (6s0) atomic orbitals (and halide orbitals) lierelatively close in energy, and bands with these orbitalcharacters also lie closer together compared to doubleperovskites with a greater energetic mismatch between thefrontier orbitals of the two B-site metals (Figure 3C).

Substitution of Tl3+ for Bi3+ in Cs2AgBiBr6 also results ina shift of the CBM from L to G and of the VBM from X to G

yielding a direct band gap in 2. As we previously reported,[11]

substitution of Tl3+ for Bi3+ in the solid solution Cs2Ag-(Bi1@xTlx)Br6 (x& 0.06) generates a new impurity bandderived mostly from Tl 6s orbitals, which lies below the hostlatticeQs CBM. Consistent with those results, the conductionband in 2 has predominantly Tl 6s character (Figure S10). In2, the CBM occurs at the G point due to the pure s character ofthat band; in contrast, Cs2AgBiBr6 has mixed s and pcharacter in its conduction band. The Cs2AgBiCl6 valenceband (Figure 3A) features both Bi 6s and Ag 4d orbitalcharacter at X (the VBM), whereas the lower-lying G pointpossesses only Ag 4d character. The Cs2AgBiBr6 valenceband is similar. When Bi3+ is replaced with Tl3+, the loss ofBi 6s character decreases the energy of the band at the Xpoint. In contrast, the energy of the G point is unaffected, andit becomes the new VBM in 2, yielding a direct gap.

We obtained alternating-current conductivity measure-ments on single crystals of 2 with graphite contacts using theVan der Pauw method (Figure 4 inset, Figures S4,S5). Thegraphitic contacts act as ion-blocking electrodes and isolatethe materialQs electronic response. Most metals react withhalide perovskites and are unsuitable as electrodes. Theelectronic conductivity of 2 increases rapidly with time upon

Figure 3. Band structures of A) Cs2AgBiCl6 and B) Cs2AgTlCl6 (1), calculated with DFT-HSE06+ SOC in their primitive unit cells using measuredlattice parameters. Band structures are shown in duplicate with only metal orbital contributions shown; chloride orbitals are present but omittedfor clarity. The conduction bands are rigidly shifted to match the experimental band gaps, and all bands are shifted to align the Cs 5s bands.C) Top: Schematic representation of the relative energies of the atomic orbitals (lines) and bands (rectangles) for closely related doubleperovskites demonstrating the dominant metal-to-metal charge-transfer character of the band gaps and the origin of the anomalously low bandgaps in 1 and 2. Bottom: Photographs of Cs2TlITlIIICl6 (left), 1 (center), and Cs2AgBiCl6 (right).

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removing the crystal from the supernatant (Figure S6).Crystals grown from HBr solutions containing 200 mmdissolved Br2 have around one order of magnitude lowerinitial conductivity than those grown without Br2. Addition-ally, the headspace gas above crystals of 2 contains molecularBr2, which brominates alkenes and can be observed by massspectrometry (Scheme S1, Figure S7). Most strikingly, whencrystals that have been separated from the mother liquor forseveral days are soaked in a gaseous Br2 atmosphere(0.22 atm), using the apparatus shown in Figure 4, thecrystalsQ conductivity decreases from 10@2 Scm to 10@5 S cmand increases again upon removal from the Br2 atmosphere

(Figure 5). This process can be repeated several times with noapparent decomposition of the bulk crystal. Long exposuretimes of 2 to Br2 (> 100 h) create a thin, yellow surface layer,which was removed by polishing prior to measurement toobserve only the bulk response. After days of degassing, 2approaches an asymptotic limit of conductivity, whichdepends on sample history, but is around 10@3 S cm fora sample at room temperature and approximately 10@2 S cmfor a sample at 60 88C. No changes in the powder XRDpatterns of 1 and 2 occur upon exposure to light (0.75 sun atca. 60 88C) or moist air (55% RH) over 40 days (Figure S14),although polished crystals of 2 exposed to moist air forma transparent insulating surface layer after around 24 h.

Together these results point to a spontaneous defectreaction where loss of neutral Br (as Br2 from the surface) iscoupled to the simultaneous formation of cationic halidevacancies (V1Br) and n-type doping of the material (throughthe addition of electrons, e

0; Equation (1)):

2 Br>Br $ Br2 gð Þ þ 2 V1Br þ 2 e0 ð1Þ

(Br>Br represents a Br atom at a Br site in the lattice). Changesin self-doping appear to be diffusion-limited, and thus thisreaction is likely facile and reversible. Therefore, the crystalspontaneously loses Br2 and self-dopes as it equilibrates withthe atmosphere devoid of Br2. This process is analogous to thewell-studied oxygen-exchange reaction observed in manyoxides, including oxide perovskites.[24] Equilibration of defectconcentrations with I2 pressure at 120 88C has been observed in(CH3NH3)PbI3 pellets.[25] Highly oxidized perovskites, such asCs2SnIVI6

[17c,26] and Cs2PdIVBr6,[27] also display a propensity for

n-type doping, with calculations suggesting halide vacanciesas compensating defects. Due to limited crystal size we couldnot obtain similar measurements on 1. However, we expecthalogen loss to occur at higher temperatures in 1 as a result ofthe more positive reduction potential of chlorine and theincreased strength of metal–chloride bonds.

Even under high Br2 pressures (0.22 atm), 2 appears toremain n-type. The conductivity increases monotonically withBr2 loss rather than displaying a minimum (corresponding toa transition from p-type to intrinsic to n-type). This suggeststhat achieving p-type doping in 2 will be difficult except underhighly oxidizing conditions. This spontaneous self-doping willlead to a substantial vacancy and electron concentration in 2over time unless properly encapsulated. This defect popula-tion could also contribute to the lack of PL in these materials.

In conclusion, the new double perovskites Cs2AgITlIIICl6

(1) and Cs2AgITlIIIBr6 (2) display direct band gaps that areapproximately 1 eV smaller than those of analogous perov-skites. To our knowledge, 2 has the lowest band gap of anyhalide perovskite at 0.95 eV. We also describe a halogendegassing and self-doping reaction in 2 that is likely general tohalide perovskites and analogous to the well-known role ofoxygen partial pressure in oxide electrical transport proper-ties. Thus far, mostly iodide perovskites have displayedsuitable band gaps (Eg& 1.4 eV)[28] for absorbers in single-junction solar cells. Smaller band gap perovskites (Eg

& 1.0 eV)[29] are sought for perovskite-on-perovskite tandemsolar cells. Importantly, 1 and 2 demonstrate that bromides

Figure 4. Apparatus used to expose crystals of 2 to a known pressureof Br2. The system is maintained under static vacuum and a partialpressure of 0.22 atm Br2 is obtained with a 19 88C water bath. Inset:Photograph of a single crystal of 2 with carbon contacts in a 4-pointprobe configuration.

Figure 5. Changes in the conductivity of a single crystal of 2 over timedue to the loss and reabsorption of Br2. Time zero corresponds toremoval of the crystal from the Br2 atmosphere.

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and chlorides do not limit us to large band gaps. The toxicityof Tl should be considered with respect to any applications of1 and 2. However, the fundamental design rules stated hereare applicable to a very large family of materials and 1 and 2are ideal model systems for demonstrating the electroniceffects of B-site substitution. The Group 14 ABX3 perovskiteshave ns2 and np0 orbitals of the same metal in their VBM andCBM, respectively. In contrast, the band gap transition indouble perovskites features a charge transfer between twodifferent metals, allowing wide control of the band gapthrough appropriate choice of B-site-metal pairs. Most halideperovskites have large band gaps, although material com-pression has led to band gap closure.[30] The strategy describedhere for accessing small band gaps should be important forfurther expanding the electronic portfolio of this importantfamily of materials, whose full technological utility is stillbeing revealed.

Acknowledgements

We thank S. Weber at the University of California, Berkeleyfor valuable discussions and K. Walker at Stanford Universityfor experimental assistance. This work was funded by theDepartment of Energy, Laboratory Directed Research andDevelopment program at SLAC National Accelerator Labo-ratory (DE-AC02-76SF00515). A.H.S. is supported by theVeatch award from Stanford Chemistry. Work by J.B.N. andL.L. was supported by the National Science Foundation(NSF; DMR-1708892). L.L. acknowledges partial support bythe Feodor-Lynen program of the Alexander von HumboldtFoundation. Work by D.B. and T.J.S. was performed under thePartnership Program of the Materials Innovation InstituteM2i and the Foundation of Fundamental Research on Matter(F71.4.15562a), Netherlands Organisation for ScientificResearch. This work used the Stanford Nano Shared Facili-ties, supported by the NSF (ECCS-1542152).

Conflict of interest

The authors declare no conflict of interest.

Keywords: absorber · band gap · band structure · doping ·halide double perovskite

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[31] CCDC 1863107 and 1863105 (for Cs2AgTlCl6 and Cs2AgTlBr6,respectively) contain the supplementary crystallographic datafor this paper. These data can be obtained free of charge fromThe Cambridge Crystallographic Data Centre.

Manuscript received: June 27, 2018Accepted manuscript online: August 7, 2018Version of record online: August 31, 2018

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12770 www.angewandte.org T 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2018, 57, 12765 –12770