Fine Structure of Excitons in Vacancy Ordered Halide Double Perovskites Bruno CuccoClaudine KatanJacky EvenMikael KepenekianGeorge V olonakis

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Fine Structure of Excitons in Vacancy Ordered Halide

Double Perovskites

Bruno Cucco,†Claudine Katan,†Jacky Even,‡Mikael Kepenekian,†George Volonakis†,∗

†Univ Rennes, ENSCR, INSA Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes),

UMR 6226, France

‡Univ Rennes, INSA Rennes, CNRS, Institut FOTON - UMR 6082, Rennes, France

∗Corresponding author: yorgos.volonakis@univ-rennes1.fr

Vacancy ordered halide double perovskites (VODP) have been widely explored throughout

the past few years as promising lead-free alternatives for optoelectronic applications. Yet, the

atomic-scale mechanisms that underlie their optical properties remain elusive. In this work, a

throughout investigation of the excitonic properties of key members within the VODP family

is presented. We employ state-of-art ab-initio calculations and unveil critical details regard-

ing the role of electron-hole interactions in the electronic and optical properties of VODP.

The materials family is sampled by picking prototypes based on the electronic conﬁguration

of the tetravalent metal at the center of the octahedron. Hence, groups with a valence com-

prised of s, p and d closed-shells are represented by the known materials Cs2SnX6, Cs2TeX6

and Cs2ZrX6(with X=Br, I), respectively. The electronic structure is investigated within

the G0W0many-body green’s function method, while the Bethe-Salpeter equation is solved

to account for electron-hole interactions that play a crucial role in the optical properties

of the family. A detailed symmetry analysis unravels the ﬁne structure of excitons for all

compounds. The exciton binding energy, excitonic wavefunctions and the dark-bright split-

ting are also reported for each material. It is shown that these quantities can be tuned over

a wide range, form Wannier to Frenkel-type excitons, through for example substitutional

engineering. In particular, Te-based materials, which share the electronic valency of corner-

sharing Pb halide perovskites, are predicted to have exciton binding energies of above 1 eV

and a dark-bright splitting of the excitons reaching over 100 meV. Our ﬁndings provide a

fundamental understanding of the optical properties of the entire family of VODP materi-

als and highlight how these are not in fact suitable Pb-free alternatives to traditional halide

perovskites.

arXiv:2210.14081v2 [cond-mat.mtrl-sci] 18 Nov 2022

Perovskites are some of the most common naturally occurring compounds in nature. These AMX3

materials are made of three-dimensional networks of corner-sharing octahedra, and have been

employed in a broad range of applications, like solar cells 1, highly-efﬁcient light-emitters 2, mem-

ories 3, photo-catalysts 4, transistors 5and superconductors 6. A2MX6vacancy ordered double per-

ovskites (VODP), are a particular sub-family of halide perovskites, which have recently emerged

as promising materials for a broad range of applications 7,8. In fact, the oxidation of Sn+2in its

tetravalent state Sn+4leads to a structural transformation from the CsSnI3perovskite to the more

stable VODP Cs2SnI69. To-date, the successful synthesis of many VODP materials have been

reported, with tetravalent M-site atoms like Te 10, Ti 11, Zr 12, Hf 13, Pd 14, Pt 15, Se 16, Sb 17,

Sn 18 and Ge 19. Most of these materials are stable and exhibit tunable electronic and optical

properties making them targets of choice for optoelectronic applications, such as solar cells 11,18

and light-emitting devices 12, 20–22. Among these properties, there is growing interest for the po-

tential presence of strong excitonic effects in VODP 23,24, as the materials are made of isolated

metal-halide octahedra, which are intrinsically structurally conﬁned 25. Such excitonic properties

are critical for the potential application of these photo-active materials, as for example they can

limit charge carrier separation, or enhance photo-emission, hence open pathways for new opto-

electronic devices that take advantage of such exciton physics. A deep understanding of the exci-

tonic processes is necessary for probing the origins of the tunable and broad photoluminescence

that is observed in VODP 13,26, which is commonly associated to excitons trapping. In fact, the

formation of self-trapped excitons due to strong lattice distortions is one of the most discussed

and debated underlying mechanisms 13,20,27,28. To-date, a detailed description of even the most

fundamental excitonic features of the VODP is still missing.

In this letter, we analyze the role of the electronic structure including electron-hole (e-h) inter-

actions in the VODP materials by employing state-of-art ab-initio G0W0and Bethe-Salpeter cal-

culations. We unveil key details of their electronic band structure and show the impact of e-h

interactions on their optical properties. Prototypical VODP materials, Cs2SnX6, Cs2TeX6and

Cs2ZrX6(with X=Br, I), are categorised based on the electronic conﬁguration of the tetravalent

atom at the M-site with a valency comprised of an s, p and d closed-shell, respectively. 10,12,18.

The halogen atoms are identiﬁed as a tuning parameter to control the empty space in between the

isolated metal-halide octahedra. We further show the effects of both M- and X-site substitutions

on the electronic and optical properties by performing a symmetry analysis of the electronic struc-

tures. We ﬁnd the most critical quantities of the photo-active VODP materials, such as the charge

carrier effective masses, exciton binding energies and dark-bright exciton splitting and establish

trends which allows the enhancement of these parameters via substitutional engineering. Te-based

materials exhibit promising hole transport properties, while Sn-based VODP are most favoring

electron transport. In addition, we show that Te-based materials on one hand exhibit promising

electronic structure with an active lone pair, similar to Pb halide perovskites, on the other exhibit

drastically different excitonic features, which can be explained due to strong electron-hole interac-

tions. Thus, we demonstrate that VODP even when sharing the same electron conﬁguration with

Pb halide perovskites, cannot be considered as their Pb-free alternatives. Finally, the absorption

onset of all materials are shown to be dominated by electron-hole interactions leading to excitons

ranging from Wannier-type to Frenkel-type. In all cases, the investigation of the exciton ﬁne struc-

ture reveals that a non-optically active dark state lies below the ﬁrst bright state. The electron-hole

exchange interaction at the origin of the splitting between dark and bright exciton states is partic-

ularly strong in the case of Te-based materials. Interestingly, by choosing a metal and a halide,

one can browse a range of exciton binding energies greater than 1 eV and of dark-bright splitting

greater than 150 meV.

VODP typically crystallize in the Fm¯

3m face-centered cubic lattice (space group number 225).

The lattice corresponds to a rock salt arrangement of corner-sharing MX6and ∆X6octahedra

with ∆being the vacancy site, or simply a double perovskite for which one of the two M-sites

is vacant, as show on Figure 1a. We sample the VODP family by selecting prototypes based

Figure 1: Vacancy ordered halide double perovskite family. Representation of the VODP family

of materials and chosen M4+metal sites. The boxes mark the s0, p0and d0columns for a +4

oxidation state and electronic conﬁguration of selected atoms. The atomic species in green have

been synthesized as VODP with the marked atoms at the M4+-site.

on the nominal valency (i.e. electronic conﬁguration) of the tetravalent cation at the M-site. In

Figure 1b we highlight the columns of the periodic table that correspond to atoms with s-p-d ﬁlled

closed-shells at a +4 oxidation state. The atomic species that are highlighted in each closed-shell

column were successfully employed to form stable VODP. Here we select period 5 of the periodic

table, thus Sn, Te and Zr as the atomic species at the M-site of each closed-shell VODP type,

generating 6 different materials Cs2TeX6, Cs2SnX6, and Cs2ZrX6(with X=Br, I). Interestingly,

Te4+is isoelectronic with the Pb+2ion, which is the building block of the most efﬁcient perovskite

materials for optoelectronic applications. As a starting point, the atomic coordinates and lattice

parameters for these materials are fully optimized using ab-initio calculations based on Density

Functional Theory (DFT) as detailed in the supplementary information ﬁle (SI). Table S1 of the

SI summarizes the obtained lattice parameters, metal-halogen bond lengths and volumetric size of

the vacancy. The optimized structures for all compounds are in the Fm¯

3m space group, except

Cs2SnI6, which exhibits very slightly rotated Sn-I octahedra with small octahedra distortions, in

agreement with the work of Jong et al. 29. As previously shown in the context of d0VODP,

halogen-halogen p-orbital interactions dictate the empty space formed by the vacancies in these

materials 25. Here the same is observed for all VODP regardless of the atom at the M-site, and

the volume of the empty space in between the MX6octahedra depends solely on the halogen size.

Hence, Br to I substitution can be used as a tuning parameter to control the size of the vacancy

from 33 to 40 Å3, as deﬁned in Table S1. As a ﬁnal assessment of the mechanical stability of

the optimized structures, we calculate the phonon dispersion for each material. These are shown

in Figure S1, where the absence of phonon imaginary modes in all studied compounds indicates

mechanical stability. The redshift of the frequency that is observed when going from bromides

to iodides is consistent with the increase of halogen’s atomic mass and thus damping of the M-X

oscillation modes.

Two critical parameters for the accurate calculation of excitonic properties are the band-gaps and

charge-carrier effective masses, as both can have strong impacts on the exciton binding energies

and the relative position of excitonic peaks. To this aim, we employ G0W0calculations that take

into account quasi-particle effects due to screened electron-electron interactions. Figure 2a shows

the electronic band structures for the bromides, while the electronic bands of the iodides can be

found in Figure S2a of the SI. Sn-based compounds exhibit direct band-gaps at the Γpoint. The

optical transition from the valence band maximum (VBM) to conduction band minimum (CBM) is

given by a transition from the irreducible representation F3/2,gto E1/2,gwhich is parity forbidden.

The ﬁrst direct dipole allowed transition for the Sn-based compounds is from VBM-1 (F3/2,u) to

CBM (E1/2,g), i.e. 300 meV and 350 meV larger than the fundamental band-gap of Cs2SnBr6

and Cs2SnI6, respectively. Due to the different orbitals involved at the band edges, Te-based com-

pounds have indirect band-gaps between the L-W high symmetry points. Interestingly, the shapes

of the Cs2TeX6valence band and the Cs2SnX6conduction band are the same, which is consis-

tent with the electronic conﬁgurations [Kr]5s2and [Kr]5s0for Te4+and Sn4+, respectively. We

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FineStructureofExcitonsinVacancyOrderedHalideDoublePerovskitesBrunoCucco,ClaudineKatan,JackyEven,MikaelKepenekian,GeorgeVolonakis;UnivRennes,ENSCR,INSARennes,CNRS,ISCR(InstitutdesSciencesChimiquesdeRennes),UMR6226,FranceUnivRennes,INSARennes,CNRS,InstitutFOTON-UMR6082,Rennes,FranceCorrespon...

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Fine Structure of Excitons in Vacancy Ordered Halide Double Perovskites Bruno CuccoClaudine KatanJacky EvenMikael KepenekianGeorge V olonakis

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