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Exploring Polaronic, Excitonic Structures and Luminescence in CsPbBr/CsPbBr 4

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byungkyun kang, and Koushik Biswas J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03333 • Publication Date (Web): 01 Feb 2018 Downloaded from http://pubs.acs.org on February 3, 2018

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The Journal of Physical Chemistry Letters

Exploring Polaronic, Excitonic Structures and Luminescence in Cs4PbBr6/CsPbBr3 Byungkyun Kang and Koushik Biswas* Department of Chemistry and Physics, Arkansas State University, State University, AR 72467, United States

ABSTRACT Among the important family of halide perovskites one particular case of allinorganic, 0-dimensional (0-D) Cs4PbBr6 and 3-dimensional (3-D) CsPbBr3 based nanostructures and thin films is witnessing intense activity due to ultrafast luminescence with high quantum yield. In order to understand their emissive behavior, we use hybrid density functional calculations to first compare the ground state electronic structure of the two prospective compounds. The dispersive band edges of CsPbBr3 do not support self-trapped carriers, which agrees with reports of weak exciton binding energy and high photocurrent. The larger gap 0-D material Cs4PbBr6, however reveals polaronic and excitonic features. We show that those latticecoupled carriers are likely responsible for observed ultraviolet emission around ~375 nm, reported in bulk Cs4PbBr6 and Cs4PbBr6/CsPbBr3 composites. Ionization potential calculations and estimates of type-I band alignment supports the notion of quantum confinement leading to fast, green emission from CsPbBr3 nanostructures embedded in Cs4PbBr6. TOC GRAPHIC

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Recent advances in hybrid organic-inorganic lead pervoskites and their interesting electronic properties have generated world-wide research attention in this class of ionic halide semiconductors. Their all-inorganic analogs are also under considerable scrutiny for potential optoelectronic applications. Among them, Cs-Pb-Br system of perovskite-like compounds are prominent, partly due to diversity in their chemical composition and geometric structure. These translate to favorable electronic and photophysical properties along with other attributes such as temperature stability and nonhygroscopicity.1-3 Possibility of mixed halogen ions in the anion sublattice allow further degree of freedom towards tunable band gap. Ease of synthesis via solution process or melt-grown is appealing for cost-effective applications. We note that the CsPb-Br system consist of several compounds such as CsPbBr3, CsPb2Br5, and Cs4PbBr6 each of which may have their own polymorphs.4 CsPbBr3 and Cs4PbBr6 are of particular interest as wide gap, defect-tolerant, green-emitting semiconductors with potential for high light yield. They are probably stable within narrow chemical potential ranges and therefore secondary phases may appear alongside the intended crystal. The likelihood of compositional coexistence has given rise to diverging hypotheses among researchers regarding the origin of green emission (~520 nm) observed in Cs4PbBr6/CsPbBr3 samples. Some insist on band edge recombination at CsPbBr3 whose electronic gap is about 2.3 eV.5,6 Several recent studies also talked about chemical transformation of Cs4PbBr6 nanocrystals (NC) to highly luminescent CsPbBr3 NCs.7-12 Others ascribe it to excitonic luminescence or recombination mediated by mid-gap defect states within bulk Cs4PbBr6, which has a larger band gap of about 3.9 eV.2,13-17 It is also opined that phase coexistence may be indeed beneficial or necessary for green emission due to quantum confinement effects that favor radiative recombination of excited carriers across the band edge of the smaller gap CsPbBr3, despite its very low exciton binding energy. This idea is supported by


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the reported ultrafast (sub-nanosecond) fluorescence decay time and high quantum yield in composite crystals containing CsPbBr3 nano-inclusions embedded in a Cs4PbBr6 matrix.18-20 These varying observations constitute a reason for further investigation of the two compounds. Several ab initio studies already described the ground state electronic structure of CsPbBr3 and Cs4PbBr6.8,14,21,22 Different crystalline geometry of the two compounds is prominently reflected in their distinctive electronic properties. Using accurate hybrid density functional calculations we briefly describe some of their salient features and show the emergence of polaronic and excitonic structures in Cs4PbBr6, which are absent in CsPbBr3. A self-trapped exciton (STE) found in this work is likely the first theoretical indication of the observed luminescence of Cs4PbBr6 in the ultraviolet (UV) range around ~375 nm, which can be ascribed to Pb2+ related emission. We shall discuss these properties and delve further into the possible nature of band-edge alignment between Cs4PbBr6 and CsPbBr3 as a way to explore mechanisms of radiative decay and observed green emission in Cs4PbBr6/CsPbBr3 composites. Semilocal exchange-correlation functionals often fail to properly describe band edge positions (predicting too high valence and too low conduction bands), and problems are particularly exacerbated in finding localized state solutions of polarons or excitons. We therefore use hybrid density functionals, PBE0 (25% exact Hartree Fock exchange)23 or HSE (25% exact Hartree Fock exchange and screening parameter µ = 0.3 Å-1)24,25 in most of our calculations, as implemented within Vienna ab initio simulation package (VASP).26-29 All hybrid calculations use uniform cutoff energy of 300 eV and force convergence of 0.05 eV/Å. Due to the large nuclear charge of Pb, spin-orbit coupling (SO) is included in all presented results. Band structure and Born effective charge calculations are performed using semilocal PBE functional.30 We find PBE with SO provide reasonably accurate band characteristics, except for the value of the band gap, 3 ACS Paragon Plus Environment


which is underestimated. Band structure plots, band gaps and valence band widths obtained using different semilocal and hybrid functionals are shown in the Supporting Information (SI, Figure S1 and Table S1). Experimental lattice constants of orthorhombic CsPbBr3 (a = 8.207 Å, b = 8.255 Å, c = 11.759 Å)31 and hexagonal Cs4PbBr6 (a = b = 13.7219 Å, c = 17.3153 Å, α = β = 90, γ = 120)1 are used for the majority of calculations. We note that optimized lattice constants are slightly overestimated, within 1-3% of the experimental values. Calculations of the static dielectric tensor and Born effective charge using linear response requires accurate force convergence, for which we used optimized lattice constants and relaxation criteria of 0.001 eV/Å. There are at least three reported structural phases in the Cs-Pb-Br system.4 Among them CsPbBr3 adopts an orthorhombic structure at room temperature, consisting of corner sharing [PbBr6] octahedra.3,31 Cs4PbBr6 adopts a low-symmetry structure (space group R-3c), which appears to be composed of almost disjointed [PbBr6] octahedra held together by Cs-Br bridges.1,32 For this reason it is often referred to as a 0-dimensional (0-D) structure, while CsPbBr3 is considered as 3-D distorted perovskite. A third phase, CsPb2Br5, adopts a tetragonal structure, and also likely a wide gap semiconductor. It is not addressed in our current work. The notable structural differences between CsPbBr3 and Cs4PbBr6, viz., tilted corner shared octahedral network in the former versus almost decoupled octahedra in the latter, translates to distinctive features in the electronic structure of the respective compounds. Figure 1a,b shows the electronic density of states (DOS) of the two compounds. The corresponding band structures obtained using PBE(SO) functional are given in SI, Figure S1. The decoupled octahedra in Cs4PbBr6 creates narrow, nondispersive valence and conduction bands, whereas the interconnected octahedral network of CsPbBr3 promotes hybridization between Pb and Br pstates creating dispersive band edges. The calculated band gap of Cs4PbBr6 is 3.93 eV obtained


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using HSE, and that of CsPbBr3 is 2.29 eV obtained by PBE0 functional, both including SO. These values are consistent with experimental reports.3,5,6 Although the two mentioned hybrid functionals differ in the way the exchange interaction is treated, saving the band gap values, they do not introduce any qualitative difference in band ordering and dispersion in either compound (see Figure S2). We should note that excluding SO in semilocal PBE functional leads to fortuitous agreement with the experimental band gaps of both materials, however, band edge positions and large splitting in the Pb 6p states that create the conduction band minimum (CBM) are not appropriately described. Under spin-orbit coupling the degenerate Pb 6p orbitals split in to 6P3/2 and 6P1/2 combinations, reducing the band gap by 0.5-1.0 eV. Hybrid functional calculations including SO provide better estimate of band widths and splitting in addition to the gap values.

Figure 1. Total and projected density of state (DOS) of (a) Cs4PbBr6 and (b) CsPbBr3. Hybrid functionals including SO are used. The zero of energy is set at the top of valence bands. Pb 6s, 6p and Br 4p are shown in the projected DOS (lower panel). Respective structures are shown as inset.



Despite the differences in band gap and band dispersion, the signature of the [PbBr6] octahedra is evident near the band edge of both compounds. The CBM is made by 6p orbitals of the less electropositive cation Pb, while the valence band maximum (VBM) is derived primarily from Br 4p in both materials. The large Pb-Pb separation (~8.4 Å) in Cs4PbBr6 ensures that conduction band edge remain narrow and dispersion-less. The Br 4p valence states hybridize with Pb 6s* antibonding levels near the VBM in CsPbBr3 and Cs4PbBr6 (see Figure 1a,b). The gap originates from bonding-antibonding interaction between Pb 6p and Br 4p. There is also noticeable cross-gap hybridization between nominally empty Pb 6p and filled Br 4p as evident from the atom and orbital projected DOS in Figure 1. Cross-gap hybridization between occupied and unoccupied states often lead to anomalously large Born effective charge and enhanced static dielectric constant. Born charge is the dynamical contribution to effective charge caused by changes in macroscopic polarization due to ionic displacement. The instability of Pb lone pair in CsPbBr3 and its impact on polarization becomes evident from a comparison of diagonal elements of the calculated Born effective charge tensor and static dielectric constant given in Table 1. The Pb-Brap bonds aligned to c-direction in corner shared 3-D octahedral network of CsPbBr3 results in Born charge that is twice the nominal ionic charge of Pb, while it is almost quadrupled in the case of Br. Similarly large values of the xx and yy components are obtained for Pb-Breq bonds in the ab-crystallographic plane of CsPbBr3. The disjointed octahedral network in 0-D Cs4PbBr6 inhibits the development of large lattice polarization, which is reflected in its relatively low Born effective charge compared to CsPbBr3, and also smaller values of static dielectric constant. Large static dielectric constant effectively screen carriers from charged defects, and in part responsible for the defect tolerant behavior of CsPbBr3 and analogous compounds such as the hybrid perovskite, CH3NH3PbI3.33


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Table 1. Calculated static dielectric constants and Born effective charge of Cs4PbBr6 and CsPbBr3. The Wyckoff positions are shown in parentheses beside the atoms to distinguish crystallographic sites. In case of CsPbBr3, Breq and Brap refer to Br ions at equatorial and apical location in the [PbBr6] octahedra. Cs4PbBr6

Static dielectric constants ( = 5.79, = 5.79, = 5.80) Atom type CsI (6a) CsII (18e) Pb (6b) Br (36f)

Born effective charge tensor (xx, yy, zz) ( 1.23, 1.22, 1.21 ) ( 1.37, 1.37, 1.19 ) ( 2.91, 2.91, 2.91 ) ( -1.08, -1.92, -1.04 ) CsPbBr3

Static dielectric constants ( = 20.67, = 22.84, = 20.45) Atom type Cs (4c) Pb (4b) Breq (8d) Brap (4c)

Born effective charge tensor (xx, yy, zz) ( 1.28, 1.28, 1.31 ) ( 3.81, 4.02, 4.03 ) ( -2.17, -2.33, -0.78 ) ( -0.81, -0.72, -3.83 )

Small Polarons. Dispersive VBM and CBM of CsPbBr3 do not allow charge carriers to localize, meaning that the carriers generated by external perturbation will remain free, and their transport will be primarily governed by intrinsic or impurity defect traps and scattering from lattice phonons. Cs4PbBr6, however, will be prone to carrier self-trapping which may lead to the formation of small polarons and excitons. Here, we use the term self-trapping to indicate that the Cs4PbBr6 crystal may spontaneously deform in the presence of a conduction electron or valence hole. PBE of course fails to predict polarons and excitons. In Cs4PbBr6 these are calculated using HSE including SO in 66- and 132-atom supercells. Brillouin zone integrations are performed using single Γ-shifted k-point (¼, ¼, ¼). Results from single Γ-point test calculations are also consistent. We investigate the possibility of such polaronic states by adding an extra electron in the conduction bands or creating a single missing electron (hole) in the valence bands. An



electron at CBM or hole at VBM will generally remain delocalized in a perfect crystal. In the presence of short-range electron-phonon coupling those charge carries may localize, which we can simulate by breaking the crystal symmetry and inducing local distortions (see SI for more details). The signature of a localized polaronic level becomes evident from a singly occupied state appearing inside the gap, below CBM, with the electron captured at Pb 6p. Figure 2a shows the atomic structure and charge density plot of an electron polaron localized around a Pb in 132atom supercell. In order to accommodate the localized electron, the lattice responds by significantly extending the six Pb-Br bonds from its optimized value of 3.04 Å to 3.29 Å. This electronic state, including the locally strained lattice, has lower total energy than a delocalized electron at the CBM of an otherwise perfect crystal. We estimate polaron binding energy (EB,epol)

from the total energy difference between relaxed configurations of localized electron state

and that of a delocalized electron placed at CBM. Tests performed with 66-, 132-, and 264-atom supercells provide fairly consistent binding energy values of 0.25, 0.22, 0.28 eV, respectively, which verifies the stability of the polaronic state over a delocalized electron state.

Figure 2. Calculated atomic structure and charge density isosurface of (a) electron and (b) hole polaron localized at a single octahedron of 132-atom supercell. Outward and inward relaxation of the Pb–Br bonds is indicated by arrows.


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Similar to the electron polarons, a valence hole is also subject to self-trapping in Cs4PbBr6 when it “floats up” to a localized state above the VBM. Creating a hole (missing electron) in the simulation cell accompanied by local symmetry-breaking distortion, results in a self-trapped hole state that is more stable than a delocalized hole. The local lattice relaxation that supports the selftrapped hole is qualitatively different from the well-known Vk centers that are commonly found in alkali and alkaline earth halides.34-38 The Vk centers are formed of covalently bonded dimers between two neighboring halogens (e.g., Br ) and the unoccupied hole state has distinct antibonding halogen (σ*) p-character. Interestingly, the localized hole state above the VBM of Cs4PbBr6 shown in Figure 2b is composed of antibonding Pb 6s* and Br 4p (σ*). All six Pb-Br bonds in the [PbBr6] octahedron decrease in length from 3.04 Å in the relaxed perfect host to about 2.88 Å. The absence of a Vk-like center is not surprising if we recall that the VBM of Cs4PbBr6 is derived from bonding-antibonding combination of Br 4p and Pb 6s* (see Figure 1a), and hence the self-trapped hole retains the same wavefunction character. The estimated hole binding energy (EB,h-pol) is about 0.09 eV, obtained from total energy difference between 132atom calculations of localized hole and delocalized hole at the VBM. We should note that in addition to the electron and hole polarons discussed above, other defects such as cation/anion vacancies and impurities may also induce localized states. Whether they play a prominent role will depend upon concentration and the nature of those defect levels. It is however expected that the polaronic states will inevitably form upon excitation, due to selftrapping in Cs4PbBr6 and generally play an important role in this halide. Self-trapped Excitons. The electron and hole polarons may create bound excitonic structures. In order to find the structure of such trapped excitations within a constrained density functional calculation scheme, we start with appropriate bond distortions applied to a single [PbBr6] 9 ACS Paragon Plus Environment


octahedron in the Cs4PbBr6 supercell. As with the polarons, we have tested for convergence with respect to size, using 66- and 132-atom supercells and single k-point (¼, ¼, ¼) shifted off Γ. We find a stable trapped excitation, namely STE, which is accompanied by tetragonal distortion in the [PbBr6] octahedron (see Figure 3a). Figure 3b shows that the Pb 6s hole (admixed with Br 4p) appears as an unoccupied state above VBM. Four Pb-Br bonds on the equatorial plane of the octahedron decrease to ~2.99 Å from an original length of ~3.04 Å. A conduction electron subject to the hole-state attractive potential, localizes at Pb 6p and a singly occupied level appears below the CBM as shown in Figure 3b. The two remaining Pb-Br bonds in the octahedron are elongated along the axial direction to ~3.39 Å. The energy of this trapped excitation is found to be 23 meV below that of an excited structure in the undistorted crystal geometry. Stability estimate is obtained from 132-atom calculations and this value should increase for larger supercells. More symmetry lowering distortions where the central Pb ion moves off-center may be able to further stabilize this excited structure, although our attempts have not proven successful thus far. We find its luminescence from total energy difference between this optimized STE and the same structure in its electronic ground state configuration. The luminescence energy is surprisingly consistent between 66- and 132-atom calculations, both estimate it to be about 3.2 eV (~387 nm). The value agrees with several photoluminescence emissions reported around 375 nm in Cs4PbBr6 crystals and provides evidence in favor of Pb2+ related 1S ↔ 3P transitions in the UV range.6,9,19,21 We may contrast the STE results with dispersive band edge states in CsPbBr3, where the delocalized electrons and holes are subject to strong screening owing to large dielectric constant, likely resulting in weakly bound WannierMott excitons.


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Figure 3. (a) Calculated structure of a self-trapped exciton (STE). Inward relaxation of four Br ions on equatorial plane and outward relaxation of two remaining Br ions in the axial direction are shown by arrows. (b) Calculated electronic DOS of STE structure shows unoccupied hole state (Br p + Pb s) and singly occupied electron state (Pb p + Br p) appearing inside the band gap.

Ionization Potential. Information regarding relative band edge positions is essential especially in Cs4PbBr6/CsPbBr3 heterostructures and composite crystals, which can be predicted from calculated ionization potential (IP) and electron affinity (EA). These are estimated from separate bulk and slab structure calculations of the respective compounds. An appropriately thick slab with adequate vacuum is used to estimate the difference between average electrostatic potential of the slab’s bulk-like center and the vacuum level. This potential step enables us to align the bulk VBM (obtained from separate host calculation) with the vacuum level, and obtain IP. The IP values can then be used for band edge alignment between Cs4PbBr6 and CsPbBr3. Details of IP-related calculations is given in SI (see Figure S3). Of course, the calculated IPs are sensitive to orientation and termination of the slab surfaces which may introduce some ambiguity in the results. Still, comparing the values of IP and estimates of EA (obtained using reported experimental band gaps), provide important insight regarding band alignment. According to



Figure 4 it is of type-I character, i.e., the VBM and CBM of CsPbBr3 are contained within the gap of Cs4PbBr6. One will notice a sizeable valence band offset of ~0.85 eV which would seem to defy the common anion rule, according to which it should be small in cases such as these two compounds. We have also seen from the density of states that the orbital character of the band edge states (Br 4p, Pb 6s, Pb 6p) is similar in both compounds. Despite the similarity, the separated [PbBr6] octahedra in Cs4PbBr6 produce atomic-like, nondispersive states resulting in deeper Br 4p as its VBM and higher lying Pb 6p creating the CBM. Whereas, the interconnected octahedra of CsPbBr3 with close proximity between cations and anions create dispersive and broad band edge states. The elevated VBM of CsPbBr3 is likely caused by stronger Pb 6s - Br 4p interaction that push its antibonding valence edge (Pb 6s*) to higher energy relative to Cs4PbBr6.

Figure 4. Calculated ionization potential (IP) and electron affinity (EA) relative to the vacuum level (dashed line). Experiment band gaps3,5,6 are used to align CBMs of Cs4PbBr6 and CsPbBr3.

Summary. A number of reports observed green luminescence in Cs4PbBr6/CsPbBr3 bulk phases and NCs, and several hypotheses exist regarding this emission. Early works by Nikl et al. and Kondo et al. described the presence of CsPbBr3 in phase-impure Cs4PbBr6 bulk crystal as the 12 ACS Paragon Plus Environment

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source of this emission.5,6 Other studies however seem to infer that the observed emission is not due to secondary CsPbBr3 phase, rather it is a consequence of excitonic or defect mediated recombination in phase-pure Cs4PbBr6.2,13-17,39 Recent surge in activity in this materials system due to remarkably high photoluminescence quantum yield (PLQY) obtained from solution processed composite crystals and thin films of Cs4PbBr6 containing CsPbBr3 inclusions point to a third possibility.18-20 Since low exciton binding energy and high photocurrent raises some doubt about efficient and fast emission in bulk CsPbBr3,13 it is contended that the green luminescence observed in samples containing those nano-islands embedded within Cs4PbBr6 matrix19,20 is a consequence of quantum confinement effect. Since we do not observe any polaronic or excitonic structure that may recombine in the visible range in pristine Cs4PbBr6 and no such carrier-lattice coupling is expected in CsPbBr3, let us then qualitatively explore this third possibility within the context of our computational results.

Figure 5. Configuration coordinate diagram showing emission around 3.3 eV due to conduction electron recombining with a hole polaron.

We first revisit emission process(es) in bulk Cs4PbBr6 that happen in the UV range. Electronhole pairs created by direct (vertical) transitions are likely to self-trap (typically within 13 ACS Paragon Plus Environment


picosecond timescale) creating polarons and excitons. The STE structure described earlier has an estimated emission energy of ~387 nm that agrees well with observed luminescence data around ~375 nm.6,9,19,21 As already noted, the calculated binding energy of this STE of ~23 meV is too low. Regardless of STE stability, an electron at CBM may radiatively recombine with a hole polaron which we find as another credible source for ~375 nm emission. This mechanism is illustrated in the configuration coordinate (Q) diagram of Figure 5. After exciting an electronhole pair across the band gap Eg, the hole self-traps creating new potential energy surface marked (e+h-pol), which is shifted from Q = 0 by ∆Q = 5.24 amu1/2Å due to local lattice distortion around hole polaron (see SI for definition of ∆Q). The vertical separation between the two is the hole binding energy, EB,h-pol. The next event is the optical transition (Eem) where an electron recombines with a hole polaron and all that remains is the locally distorted lattice given by the strain energy, ESt. The lattice finally relaxes to its ground state (Q = 0), losing ESt via phonon emission. From our calculated values of Eg (3.93 eV), EB, h-pol (0.09 eV), and ESt (0.53 eV) we estimate the emission peak, Eem to be around ~3.3 eV according to 132-atom calculations (estimated Eem from 66-atom calculation is also about 3.3 eV). Transitions at this energy can be expected to be radiative. Both STE emission and electron recombining with a hole polaron are signatures of 1S ↔ 3P transitions involving Pb2+ which is reminiscent of absorption A, B, C bands related to electronic excitation of lone pairs in ns2-ion doped alkali halides. Large Stokes shift in the observed UV emission of Cs4PbBr6 also bear resemblance with AX, AT bands in ns2doped halides.40-42 Here, we note that a recent study by Yin et al.21 found two broad emission bands around 3.56 eV and 3.07 eV at room temperature. The former was ascribed to 3P1 → 1S0, Pb2+ transition while the latter as charge transfer D bands. The described D band emission in this case necessitates the formation of native wrong-site defect, PbCs in Cs4PbBr6. It is possible that


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such a defect may form, which should be further verified by way of estimated defect concentration (or defect formation energy) and its optical and thermodynamic transition levels. As already shown, STE and hole polaron mediated transitions may well lead to these emission peaks in the UV range. The UV emission can radiatively excite the CsPbBr3 nano-inclusions. Alternatively, or in addition to radiative transfer, generated excitons or self-trapped electrons and holes may be able to transfer energy nonradiatively via hopping due to the type-I band offset shown in Figure 4. Preliminary nudged elastic band calculations about the diffusion of an electron polaron between two equivalent sites yield a relatively low barrier height of ~0.2 eV (66-atom, Γ-point only; see Figure S4), in spite of the disconnected octahedra in Cs4PbBr6. Ease of polaron diffusion aided by low barriers seems to be an interesting characteristic of luminescent materials such as in NaI (~0.2 eV) 43,44 and SrI2 (~0.12 eV).45 Semiconducting halides such as Tl6SeI4 and InI, who are not emissive, have much higher defect diffusion barrier (>0.5 eV).46,47 When localized charge carriers diffusing through Cs4PbBr6 encounter large and fairly even offset at the conduction and valence band edges (Figure 4), they will likely dissociate and it may serve to concentrate carriers in CsPbBr3. This would explain better efficiency and yield in nanostructures, composite crystals or thin films of mixed composition.5-8,18 Type-I behavior also ensures that carriers directly excited within CsPbBr3 will stay confined with increased chance of radiative recombination despite its weak exciton binding energy. There is one final point to be made about the role of spin-orbit interaction, causing the mixing between singlet-triplet states, and its impact on reduced STE lifetime and fast luminescence observed in these materials. Although the above discussions on bright green emitting Cs4PbBr6/CsPbBr3 composites seem plausible, a more deliberate optimization of different localized charge geometries with stringent convergence criteria will



help resolve additional details regarding absorption-emission behavior in this fascinating set of inorganic perovskites.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (K. B.). Notes The authors declare no competing financial interests. ACKNOWLEDGMENT The authors acknowledge support from the U.S. Department of Homeland Security under Grant Award Number, 2014-DN-077-ARI075. The support does not constitute an expressed or implied endorsement on the part of the Government. This research used resources of the National Energy Research Scientiﬁc Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Computational resource at Arkansas State was partially funded by NSF Grant No. ECCS-1348341. K. B. acknowledges helpful discussions with R. T. Williams (Wake Forest University).

Supporting Information Available: Calculated band structures, fundamental gap and valance band width, calculated DOS with different hybrid functionals, details of modeling polaronic structures, details of IP calculations and migration barrier of electron polarons. 16 ACS Paragon Plus Environment

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Exploring Polaronic, Excitonic Structures and ... - ACS Publications

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