Carrier Self-trapping and Luminescence in Intrinsically Activated

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Carrier Self-Trapping and Luminescence in Intrinsically Activated Scintillator: Cesium Hafnium Chloride (CsHfCl) 2

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Byungkyun Kang, and Koushik Biswas J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b02496 • Publication Date (Web): 10 May 2016 Downloaded from http://pubs.acs.org on May 14, 2016

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Carrier Self-trapping and Luminescence in Intrinsically Activated Scintillator: Cesium Hafnium Chloride (Cs2HfCl6)

By. Kang and Koushik Biswas* Department of Chemistry and Physics, Arkansas State University, State University, Arkansas 72467, Unites States

*E-mail: [email protected] Phone: (870) 972-2427

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ABSTRACT: There has been renewed interest in the scintillation properties of Cs2HfCl6 (CHC) primarily due to its favorable characteristics such as non-hygroscopicity, cubic structure and fairly high light yield without any intentional doping. In this work we report on its electronic and optical properties using first-principles calculations. As a large gap insulator (band gap ~6 eV), CHC favors the formation of localized charge carriers, viz., centers and electron polarons. The [HfCl6]-octahedra play a central role in trapping both types of localized carriers that leads to several low energy excitonic structures or self-trapped excitons (STE). The observed emission spectrum of CHC is compared with our modeled STE structures and their emission energies. We find that Zr present as an unintentional impurity has high solubility in CHC and may be responsible for a secondary emission peak observed around 480 nm. Finally, we mention the electronic structure of the bromide and iodide analogues of CHC as well as the mixed halide Cs2HfCl3Br3, and speculate on the possibility of higher light yield and faster scintillation.

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INTRODUCTION It is quite common that a material finds breakthrough technological application decades after it is first synthesized and characterized. Cs2HfCl6 (CHC) may turn out to be one such material. It has been studied along with its sister compound Cs2ZrCl6 as efficient phosphors without additional doping.1 Optical spectra of crystals doped with 4d and 5d transition metals was studied in the 1960s and early 1970s.2-5 Thus far, no further information about the electronic structure, band gap and optical coefficients are available on CHC. A recent study revisited and reported on the excellent scintillating properties of this self-activated and nonhygroscopic material.6 Here, self-activation implies that the luminescence can occur via intrinsic centers, without intentional “activator” doping. It also means this compound has efficient schemes for carrier self-trapping and their subsequent radiative recombination, which preclude the need for external activators and difficulties associated with their solubility and uniformity. Its cubic crystal structure and non-hygroscopicity are desirable for growing large single crystals, not quite common among other up and coming, high-performance halide scintillators such as LaBr3:Ce3+, SrI2:Eu2+ or CsBa2I5:Eu2+.7-11 Recent assessment of CHC is promising, where the light yield reached up to 54000 photons/MeV centered at 400 nm, a principal decay time of 4.37 µs and energy resolution of 3.3% at 662 keV.6 It compares favorably with another commercially available cubic halide belonging to the elpasolite family, Cs2LiYCl6 doped with Ce3+ which has a lower light yield of 20000 photons/MeV and scintillation decay time in the order of several µs.12-18 As we study and characterize further, CHC or other members of a larger family of A2BX6 compounds (A=Li, Na, K, Rb, Cs; B=Ti, Zr, Hf, Sn; X = Cl, Br, I) may emerge as useful scintillators for gamma spectroscopy. Apart from several important requirements such as high effective atomic number, high 3



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density, ruggedness, radiation resistance and cost, a scintillator’s response during the crucial time window between the energy deposition/absorption and emission (luminescence) process is possibly the main deciding factor that influences its performance. During this time there are excited charge carriers that are interacting with the lattice and may self-trap, which is a hallmark of halide chemistry. As the excited carriers migrate through the host they may also undergo non-radiative recombination at lattice defects and therefore do not contribute to the luminescence or add a slow component to the decay time. Others form excitons and radiatively recombine at luminescent centers. As with any solid, the knowledge of the electronic band structure of CHC is an important step towards an understanding of the processes that take place during this time window. Here we report on the calculated electronic and optical properties, as well as carrier trapping and emission mechanisms in CHC. The calculations are based on semilocal and nonlocal (hybrid) density functional methods. We find that after excitation, the holes and electrons self-trap forming centers and electron polarons.19 The [HfCl6]− octahedra play a central role in carrier trapping where the Hf d and Cl p states form narrow conduction and valence band edges, respectively. Our modeled triplet exciton geometries show the spatially localized wave functions around Hf and its neighboring Cl ions. Besides the host, the presence of Zr as an unintentional impurity introduces a narrow defect band which may create an additional luminescence center at the [ZrCl6]− octahedron. Finally, we provide a cursory look at the bromide and iodide analogues (Cs2HfBr6 and Cs2HfI6) and a mixed halide Cs2HfCl3Br3. Since the light yield of a scintillator has an inverse relationship with band gap ( LY ∝ 1 / E g ),20,21 these compounds may draw interest because of the reduced gap induced by heavier Br or I . There is also the prospect of additional favorable changes as a result of mixing in the anion sublattice.

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METHOD All calculations are performed using the projector augmented wave method as implemented within the plane-wave code, VASP.22-24 Optimized crystal structure and electronic properties are obtained using Perdew-Burke-Ernzerhof hybrid functionals (PBE0),25 which has a 25% nonlocal Fock exchange. For comparison, we also adopted the standard PBE,26 and HeydScuseria-Ernzerhof (HSE, 25% Fock exchange and 0.2 Å-1 screening parameter).27,28 All calculations have a uniform energy cutoff of 300 eV and forces are converged within 0.05 eV/Å. We have used a 4 × 4 × 4 Γ-centered k-point grid for calculating the formation enthalpies and properties of CHC host and other stoichiometric competing phases. We tested convergence with respect to higher k-mesh. Spin-orbit coupling (SOC) is included within the PBE0 method. We modeled the Zr defect using a 72 atom supercell and 2 × 2 × 2 k-grid. For the calculations of optical spectra we used a 4 × 4 × 4 k-point grid within the PBE0 and PBE0-SOC methods, while increasing the number of empty bands to 60. Using a higher 6 × 6 × 6 k-point grid did not produce noticeable changes in the calculated dielectric spectra. We further tested with 10 × 10 × 10 and 20 × 20 × 20 k-point grid using PBE functional and did not observe appreciable changes in the optical spectra. The polarons and STEs are modeled within a 36 atom cubic supercell using PBE0 functional and 2 × 2 × 2 k-grid. In order to check for supercell size effects, we repeated the hole and electron polaron calculations with a larger 72 atom supercell. The resulting binding energies differed by about 0.05 eV compared to the 36 atom cell. The small energy difference indicates that the polarons are reasonably modeled using 36 atom cells. We therefore report our results of the self-trapped excitons (STEs) using 36 atom supercells.29,30

RESULTS AND DISCUSSION 5



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Figure 1. The structure of Cs2HfCl6. Hf atoms are located at the center of the octahedra and Cl atoms are at the corners. Cs atoms are located in the holes between the octahedra. Electronic Structure. Cs2HfCl6 crystallizes in a K2PtCl6-type cubic structure (space group Fm-3m No. 225), having a reported experimental lattice constant of 10.42 Å.31 The structure is shown in Figure 1, where the Cs-ions occupy the 8c (¼, ¼, ¼) site. The [HfCl6] octahedra are centered on Hf at 4a (0, 0, 0) site and its Cl neighbors at 24e site (0.2382, 0, 0). The perfect arrangement of the octahedra seen here contrasts with the symmetry lowering distortions or rotations commonly found among many perovskite materials. We have used the experimental lattice constant of 10.42 Å which are typically more accurate that those obtained from density functional calculations. Therefore, the relaxed internal coordinates obtained after total energy minimization provide a good estimate of nearest neighbor distances and the resulting electronic structure. The calculated Hf-Cl bond length is 2.45 Å. Cs ions are coordinated with 12 Cl neighbors with a bond length of 3.69 Å.

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Figure 2. Calculated band structure of Cs2HfCl6 using the PBE0 functional. The energy of valence band maximum is set to zero. Figure 2 shows calculated band structure of Cs2HfCl6 using the PBE0 functional. The calculated direct gap at Γ is 6.34 eV. However, the fundamental gap is indirect and differs from the direct gap by only ~0.02 eV revealing the flat character of the band edges across the Brillouin zone. For comparison, the calculated direct gaps at Γ using PBE and HSE functionals are 4.26 and 5.59 eV, respectively. The electronic density of states (DOS) obtained from PBE0 and PBE0-SOC calculations are shown in Figure 3. Note that SOC introduces minor splitting of the Hf d levels at the conduction band minimum (CBM) resulting in a slight broadening of the corresponding DOS and lowering of the band gap by about 0.2 eV. Spin-orbit splitting of the conduction bands is not as large as observed in some other recent compounds whose heavy cation p states show a dramatic splitting and a corresponding decrease in the calculated band gap.32,33 CHC is a band insulator with the forbidden gap arising between the filled Cl− p states and the empty d states of Hf4+. This may be contrasted with Mott-type insulators where strong electron correlation effects produce an insulating gap between partially filled d or f states.34-36

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Figure 3. Calculated atom projected density of states (PDOS) of Cs2HfCl6 using (a) PBE0 and (b) PBE0-SOC. The character of the Hf d states near the bottom of the conduction band is shown in (c) and (d). Hf is more electronegative than Cs and its d levels create the lowest conduction bands (Figure 3). The large Hf-Hf distance (7.37 Å) reduces the hybridization among the atomic orbitals causing narrow bands, susceptible to carrier (electron) localization. The higher conduction bands are derived from the more electropositive Cs. The splitting of the conduction band is not atypical and indeed found in other multi-cation compounds,29,30 which may be strategically used to influence the fluorescent behavior. Similar effects may be also expected in the valence band by mixing dissimilar anions. The octahedral field of the ligands in the [HfCl6]2− complex splits the nominally empty d levels of Hf into threefold degenerate t2g and twofold degenerate eg states. The predominant t2g character of the lowest conduction bands is evident from Figure 3. Figure 4a shows these states where the lobes point between the ligands. The Hf eg states are located inside the upper conduction bands and hybridized with Cs d states (see Figures 3 and 4b). The valence band maxima (VBM) are derived from Cl p states. Similar to the CBM, the VBM also remains 8


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almost unaffected by spin-orbit interaction. However, we should expect noticeable change in case of the bromide or iodide compounds.11,37 The VBM and CBM are both conspicuous in their narrow widths, characteristics that are fundamental to carrier self-trapping via interaction with the crystal lattice. Some bonding interaction between the Hf and Cl can be seen in the lower part of the VBM in Figure 3a,b, between −2 to −4 eV. Those states arise due to hybridization between Cl p and the Hf d that are primarily of eg character. The lower valence bands (not shown) comprise of Cs 5p (~−7 eV), Cl s (~−14 eV), Cs s (~−20 eV) and Hf 5p (~−30 eV). Unlike the band edges, the Cs p and Hf p states lying deep inside the valence bands show significant spin-orbit splitting.

Figure 4. Charge density associated with the Hf d states in the lower conduction bands. (a) Atomic t2g orbitals in the lowest and (b) eg orbitals associated with upper conduction bands. Hf is at the center and Cl atoms are at the corners. The real and imaginary parts of the (isotropic) dielectric tensor calculated within the independent particle approximation are shown in Figure 5. The calculated values of absorption coefficients and refractive indices are also given as a function of photon energy. Although this treatment neglects local field effects and Coulomb interaction between electrons and holes (excitonic effects), it should still provide us with a fair picture about the onset of direct band to band absorption which occurs at values just above 6 eV. Strong absorption begins at the direct band gap with the first two peaks in the spectrum of ε2(ω) 9



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appearing just below and above 7 eV (Figure 5b). An early experimental report suggested absorption starting below 2400 Å for similar materials including Cs2HfCl6 and Cs2ZrCl6.2 Spin-orbit splitting at the VBM and CBM is important for optical transitions. In CHC the splitting is not large and the calculated imaginary part of the dielectric function, ε2(ω) without SOC were found to be slightly larger compared to those calculated with SOC. Similar results were obtained in different ZnX compounds (X = O, S, Se, Te) where intensities of the peaks obtained using SOC were lower and in fact, the results without SOC agreed better with experimental reports.38 At photon energies around 3 eV, which is close to the main emission peak of CHC the estimated refractive index remain constant at about 1.4. The optical properties are isotropic which raises their potential in transparent ceramics applications. Due to its large band gap, visible emission cannot be expected without lattice distortions and formation of polaronic or excitonic levels within the host gap which is the primary cause of luminescence.

Figure 5. Calculated optical properties of CHC: (a) real part of dielectric function, (b) imaginary part of dielectric function, (c) refractive index and (d) absorption coefficient using PBE0 and PBE0-SOC. Only xx-component is shown due to isotropic spectra.

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Cs2HfCl6:Zr. Due to their chemical similarity and difficulty of extraction, it is possible to have unintentional Zr4+ impurity in CHC. Indeed, Zr4+ was detected as a major impurity in CHC samples grown by Bridgman technique.6 Limiting Zr defects become difficult because its thermochemical properties are similar to Hf and even the compounds they commonly form are also quite identical. Zr inclusion causes minimal changes in the local lattice. This can be attributed to the chemical resemblance between tetravalent Hf and Zr and similar ionic radii 0.58 Å, 0.59 Å of Hf4+ and Zr4+, respectively.39 We can estimate the solubility of isovalent Zr in CHC by calculating the formation energy of a neutral substitutional defect given by: el el ∆H (ZrHf ) = (ED − Eh ) + (µHf + ∆µHf ) − (µZr + ∆µZr )

(1)

ED and Eh are the total energies of the defect-containing and the host supercells. Formation

of a ZrHf defect involves exchange of the atoms with their respective chemical reservoirs. The second and third terms on the right side of Eq. (1) represent the change in energy due to such exchange of atoms, where ∆µ is the chemical potential of an atom referenced to its bulk, µel. We mention that the ∆µ are free energies and can be varied with temperature and pressure, in other words dependent on growth conditions. For accurate calculation of ∆H (ZrHf ) we must then find the ranges, ∆µ of each constituent that permit the formation of CHC without the possibility of forming any other phases like CsCl, HfCl4. The requirements can be formulated as: 2∆µCs + ∆µHf + 6∆µCl = ∆H(Cs2HfCl6) = −19.67 eV, ∆µCs ≤ 0,

∆µHf ≤

∆µCs + ∆µCl ≤ ∆µHf + 4∆µCl ≤

0,

∆µCl ≤

0,

∆H(CsCl) = −4.15 eV, ∆H(HfCl4) = −9.81 eV. 11


(2)


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The calculated formation enthalpies are in good agreement with available experimental values (Table 1).40 After obeying the above rules, allowed ranges of chemical potentials ∆µHf and ∆µCs are shown in Figure 6, where CHC is thermodynamically stable. These values span the metal-rich (least negative ∆µ) to metal-poor (most negative ∆µ) condition of crystal growth without precipitating CsCl or HfCl4. After defining the ranges of ∆µHf and ∆µCs, we may now treat Zr as an impurity which forms ZrHf substitutional defects. It also requires that the stoichiometric compounds ZrCl2 or ZrCl4 does not form and we impose the conditions: ∆µZr +2∆µCl ≤ −5.46 eV and ∆µZr +4∆µCl ≤ −9.75 eV. These new restrictions have to be met while simultaneously satisfying those on ∆µHf and ∆µCs. It becomes obvious that the values of ∆µHf, ∆µCs, ∆µCl, ∆µZr will change depending on our location inside the polygon DEFG in Figure 6 and so does ∆H (ZrHf ) according to Eq. (1). If the impurity is unwanted then we have to tune chemical potentials and hence growth conditions that maximize the value of the defect formation energy. A choice of Hf-rich condition should resist formation of ZrHf defects. We find such conditions at points D or E in the chemical potential space shown in Figure 6 yielding a value of ∆H (ZrHf ) ≈ 0.15 eV. This low value can result in large defect concentrations of ≈1018-1019 cm−3. The other boundary points F and G on Figure 6 produce even lower or negative formation energies. It means ZrHf defects can freely form in the presence of Zr. Essentially, we start growing Cs2ZrCl6 as we go from Zr-poor to Zr-rich regime. It therefore becomes clear that purity of the starting materials will be important if we want to exclude Zr related defects in CHC.

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Figure 6. Calculated ranges of atomic chemical potentials shown by the shaded region where Cs2HfCl6 is stable under thermodynamic equilibrium. Table 1. Calculated Formation Enthalpies, ∆H (eV) of Different Competing Phases Compared with Experimental Values at 298 K and 1 Bar40 Formation enthalpy, ∆H (eV) Calculated Experiment CsCl -4.15 -4.59 HfCl4 -9.81 -10.27 -5.46 -5.20 ZrCl2 ZrCl4 -9.75 -10.16

Although the presence of Zr as a substitutional defect inside a CHC crystal will alter its electronic properties, the effect of such changes does not have to be substantial given its similarity to Hf. Figure 7 shows the calculated density of states using a 72-atom defect supercell. The Zr d states appear just below host CBM which is derived from Hf d. Under dilute conditions we can treat it as a shallow neutral defect which can ionize by capturing a thermalized electron from the CBM. The appearance of this discrete defect level close to the narrow conduction band edge will play a part in the spatial localization of electrons and holes. Carriers may now self-trap around Zr exclusive of other polaronic effects present in the pure crystal. This aspect of trapped carriers around a Zr or Hf is discussed in the next section.

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Figure 7. Calculated density of states of Cs16Hf7Cl48:Zr. Zr d state appearing below Hf in the conduction band is shown. The energy of the valence band maximum is set to zero.

Table 2. Calculated Binding Energy of and Electron Polarons in 36 and 72 Atom Host Supercells, and in a 36 Atom Defect Cell (Cs8Hf3Cl24:Zr) In the latter case the electron is trapped at the Zr substitutional defect and the is formed adjacent to Zr. Binding energy (eV) Cs8Hf4Cl24 Cs16Hf8Cl48 Cs8Hf3Cl24:Zr

0.71 0.66 0.73

Ee-pol 0.48 0.43 0.69

Self-trapped Carriers. A distinguishing feature of this large gap insulator from common compound semiconductors lies in its electronic structure. The narrow VBM and CBM of CHC and the deformable lattice in its excited state can support carrier localization via formation of small polarons and excitons.19,41-44 These lattice-coupled charge carriers become the most important intermediary between initial energy absorption and final light emission

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via luminescence. The excited hole is quickly captured via formation of Cl -2 molecular ion or the center.41-44 Here the two Cl atoms share a captured hole in a covalently bonded environment, reducing their Cl-Cl distance from 3.46 Å in the ordinary lattice to 2.62 Å. The

centers are common in alkali halides and have been extensively researched in the past decades.45 Aside from the , CHC also favors the formation of electron polarons which are not common among the alkali halides. The well-known scintillators NaI or CsI in their pure or undoped state have dispersive CBM, a characteristic also shared by some new scintillators like SrI2.46-49 It prevents the thermalized electrons to localize. CHC has a narrow Hf d band making up its CBM which can capture an electron and stabilize by inducing a local lattice polarization. In CHC it is achieved by uniformly elongating all six Hf-Cl bonds by about 0.07 Å compared to the perfect crystal. The behavior is similar to another well-known elpasolite scintillator Cs2LiYCl6.29,50 The locally deformed lattice serves to screen the localized carrier. The trapping of the hole or the electron accompanied with a lattice polarization involves a net gain in energy which can be quantified as their binding energy. We estimate the binding energies by calculating the charge transition levels, [E(+/0) – EV] for the and [EC − E(0/−)] for the electron polaron, which is a measure of stability relative to the delocalized hole at the VBM or a delocalized electron at CBM. Here EV and EC refer to the host VBM and CBM, respectively. The thermodynamic transition level of any defect, E (q / q′) , corresponding to a change in its charge state from q to q′ is given by:

E (q / q′) = [ E (q) − E (q′)] /(q′ − q) .

(3)

E (q ) and E (q′) refer to the calculated total energies of the relaxed structures of a defect at charge q and q′ . These transition levels are referenced with respect to the VBM or the CBM, and can be experimentally observed, for example in deep level transient spectroscopy 15



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(DLTS) measurements. Following this procedure, we calculated significant binding energies of the self-trapped carriers as shown in Table 2. The values obtained from a cubic 36-atom cell are not very different from those obtained using a larger 72-atom cell, which means inconsistencies resulting from supercell size effects are limited. The binding energy of polarons in Zr doped CHC are also shown in Table 2. The electron polaron localized at Zr has 0.21 eV higher binding energy than at a Hf-site. It probably reflects that Zr is more conducive to a lower oxidation state than Hf. Indeed, Zr is known to form ZrCl2 and ZrCl4 involving an oxidation state of +II and +IV. Table 3. Properties of STEs Optimized STE structures, corresponding charge densities of the localized electron and hole, calculated STE binding energies ( ∆B STE ) and emission energies are shown. The arrows in the structure figures indicate notable displacement of Cl ions from their equilibrium position. The charge densities of the isosurfaces are −0.005 and 0.005 e/bohr3 for the localized electron and hole state, respectively.

STE1

Self-trapped excitons STE2

STE3

Structure

Cs8Hf4Cl24

Localized electron state

Localized hole state

Binding energy, ∆BSTE (eV)

0.45

0.37

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0.01

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Emission energy (eV)

Cs8Hf3Cl24:Zr

Binding energy, ∆BSTE (eV) Emission energy (eV)

2.96

3.06

0.40

0.36

2.37

2.44

4.97

Unstable

Coulomb interaction between the electron and hole polarons causes them to further bind forming self-trapped excitons. We found several low energy STE geometries in CHC where one Hf ion captures the excited electron in its polaronic state and its two Cl neighbors share a

-like hole. Three triplet structures are shown in Table 3 along with their corresponding binding energies. Note that the STE binding energy is calculated relative to an isolated and electron polaron and given by: ∆BSTE = ESTE + E0 − EV k − Ee − pol , where ESTE , E 0 , EVk and Ee − pol are the respective energies of STE, host, , and electron polaron containing supercells. Among the three STEs shown in Table 3, the two most stable structures show an off-center location of the Hf and a corresponding distortion of the octahedron. STE1 is the most stable having the largest binding energy followed closely by STE2. Despite their close binding energies, there are some structural dis-similarities. Particularly, the two Cl ions located opposite to the relax further outward in STE2 (by about 0.44 Å) than in STE1. The is similar in both STEs, where the two Cl ions capturing the hole show a symmetric displacement from their ideal lattice positions. This observation is different from alkali halides where the STEs are formed between a Cl -2 molecular ion and a F-center. In those halides it was found that the Cl -2 polarizes in such a way that the hole is mainly localized on one Cl that is located closest to the F-center carrying the trapped electron.42 The distortion of the perfect octahedron in CHC breaks the degeneracy of t2g states facilitating a singly 17



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occupied triplet level inside the band gap while the empty (spin-polarized) states remain within the conduction bands. The occupied gap levels (state appearing just below 5 eV in the “up” spin channel) and corresponding charge density isosurface for the two STEs are shown in Figure 8. Note the occupied single particle level in STE1 is slightly lower in energy caused by a stronger interaction with the hole state and hence a stronger binding than STE2. The distance between the Hf and the two Cl forming the is also shorter in STE1 by about 0.03 Å. The STE3 structure has a small binding energy of about 0.01 eV which makes it unstable at room temperatures. It is interesting that in STE3 the hole is shared between four Cl ions that lie in a plane, while STE1 and STE2 retain the -like character of the hole (Table 3). Since Zr can be present as an unintentional impurity in CHC, we calculated the Zr-trapped excitons. Indeed, it can stabilize a triplet exciton in aforementioned STE1 or STE2 structures having similar binding energies as the Hf-centered STEs (Table 3). Therefore, both Hf and Zr play a role in the excitation and emission of STEs. We estimated the emission energies of the different STEs by considering the total energy difference between triplet (S = 1) and electronic ground state (S = 0), both constrained at the same triplet geometry. The values are shown in Table 3. Emission energies almost overlap for the STE1 and STE2 structures, both occurring close to 3 eV in case of Hf and 2.4 eV in Zr. These are in good agreement with the experimentally observed 400 nm main emission peak and a secondary peak around 480 nm.6

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Figure 8. Calculated local density of states of the nondegenerate Hf t2g levels in STE1 and STE2. Note that the level appearing below 5 eV is the singly occupied gap state in each structure. The empty states are resonant in the conduction band above 6 eV. The partial charge density of three (spin-polarized) t2g states are plotted using −0.005 e/bohr3. Cs2HfX6 (X=Br, I) and Cs2HfCl3Br3. Within the context of the current discussion around cesium-hafnium chloride, it may be worthwhile to take a glimpse at the bromide and iodide counterparts. We therefore briefly discuss the electronic structure of Cs2HfBr6 (CHB) and Cs2HfI6 (CHI). Table 4 lists their predicted lattice constants obtained after geometry optimization. For comparison we have also listed the experimental lattice constants of CHC and CHI.31,51 The lattice constants show an upward trend as we progress from the chlorides to the iodides. The general features of the electronic structure remain similar as seen from the calculated density of states in Figure 9. The contrast appears in the VBM where the Br or I p levels lie higher than Cl p, subsequently reducing the band gap. Smaller band gap in CHB and CHI may be beneficial due to potential for increased light yield in a scintillator.20,21 However, it deserves separate attention because the mechanisms of polaron and STE formation and emission may be affected due to the different halogen sublattice.

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Figure 9. Atom projected density of states of (a) Cs2HfBr6 , (b) Cs2HfI6 and (c) Cs2HfCl3Br3 calculated using PBE0 functional. The energy of the valence band maximum is set to zero. Table 4. Optimized Lattice Constant and Energy Gaps at Γ-point of Cs2HfBr6, Cs2HfI6, and Cs2HfCl3Br3 using PBE, PBE0 and PBE0-SOC Values of Cs2HfCl6 obtained using optimized and experimental lattice constants are shown for comparison.

Cs2HfCl6 Cs2HfCl6 Cs2HfBr6 Cs2HfI6

Lattice parameter (Å) 10.42 (Exp.)31 10.48 11.23 11.79 (11.61)a

Energy gap (eV) at Γ Structure

PBE

PBE0

PBE0-SOC

Cubic

4.12

6.34

6.22

Cubic Cubic

4.22 3.33

6.36 5.28

6.24 5.09

Cubic

2.18

3.85

3.57

3.37

5.36

5.23

3.51

5.43

5.18

Cs2HfCl3Br3 10.85 Cubic (config. 1) Cs2HfCl3Br3 10.85 Cubic (config. 2) a Experimental lattice constant of Cs2HfI6, Ref. 51.

In addition to the pure compounds a mixed halogen sublattice may also be a possibility, especially if we consider recent developments in the area of mixed halide hybrid perovskites (e.g., CH3NH3PbIxCl1-x) or mixed halide elpasolites.52,53 In these cases, mixing has produced

20


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beneficial changes resulting in better transport and luminescence properties in the former and latter, respectively. We have considered a similarly mixed compound Cs2HfCl3Br3. The intention here is to have a preliminary idea on possible alterations caused by mixing the two halogens. Mixing may cause a cubic structure to transform in to a tetragonal, orthorhombic or some other lower symmetry structure. In our calculations we have retained the original crystal symmetry in Cs2HfCl3Br3 and kept a fixed lattice constant of 10.85 Å, which is midway between the optimized lattice constants of CHC and CHB (Table 4). The Br atoms occupy either three equatorial sites (config. 1 in Table 4) or two apical and one equatorial site (config. 2 in Table 4) in a HfCl3Br3 octahedron. Energetically, both configurations are nearly degenerate and both have a band gap ~5.4 eV that is closer to CHB (~5.3 eV) than CHC (~6.3 eV). The atom projected DOS is shown in Figure 9, which shows the effect of Br mixing. The Br p levels primarily make up the top of the valence bands followed by a hybridization with the Cl p states. It is important to point out that Figure 9 shows the DOS without SOC. With heavier halogen, spin-orbit interaction increases the width of the valence band top. This further reduces the band gap by about 0.1-0.3 eV as shown in Table 4.11,48

CONCLUSIONS Recently, there have been a few remarkable developments among ionic-covalent halide compounds, for example CH3NH3PbI3 and TlBr that could have important application in the fields of photovoltaics and radiation detection. The emergence of covalency in these formally ionic compounds is often a result of “cross-band gap hybridization” and large static dielectric constants. Our current work provides us with an opportunity to explore these aspects and develop an understanding about the scintillation properties of CHC. The picture that emerges is similar to the related elpasolite compound Cs2LiYCl6. The large, approximately 6 eV band 21



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gap of CHC is a consequence of the insulating ionic character of the compound. We find some overlap between the Hf d and Cl p states as evidenced from the d character of the valence band density of states appearing between −2 to −4 eV in Figure 3. It does not however translate to lattice polarization or large effective Born charges. Unlike the aforementioned CH3NH3PbI3 or TlBr,33,54-55 in case of CHC we find only a nominal increase ∗ ∗ ∗ in Born charges ( = 1.3, = 4.1 and = −1.8) and a static dielectric constant (ionic

contribution) ε 0 = 3.1 using PBE functional. Compared to ε ∞ (dielectric constant at optical frequencies) a large static dielectric constant is often beneficial in screening carriers from charged defects in a crystal, resulting in a reduced carrier scattering or trapping. Reduced scattering can be instrumental in extended carrier diffusion lengths and larger µτ products in semiconductors. A comparatively low ε 0 of CHC may play a part in its defect chemistry and scintillation light yield and decay time. In CHC, the absorption and emission processes are dominated by the self-trapping of carriers. In this respect, it is similar to Cs2LiYCl6:Ce3+ which is also a commercially available scintillator.12-18 The narrow valence bands of CHC permit the self-trapping of holes as centers. The empty Hf d states making up the conduction band edge are similar to the Y d levels in Cs2LiYCl6,29 and they too allow formation of electron polarons. The trapped carriers may hop through the lattice and further bind with each other forming STEs. The two most stable structures named as STE1 and STE2 in Table 3 have similar binding energies and both are stable at room temperature. Their emission energies are also almost identical and agree with the observed experimental peak around 400 nm. The two structures are created by the occupation of two distinct nondegenerate t2g states and different relaxation of the surrounding six Cl ions (Table 3, Figure 8). It is possible that these structures are separated in our calculation by a small energy barrier and they would relax to the most stable structure under 22


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room temperature conditions. We find that these two STEs can also stabilize around a [ZrCl6] octahedron, if Zr is present as a substitutional defect. The emission energy of Zr-related STEs is about 2.4 eV which again agrees with a secondary broad emission peak at 480 nm.6 From our calculated formation energy of ZrHf defect, we find that Zr is easily soluble in CHC and therefore could be present as unintentional impurity. The extent to which Zr is responsible for scavenging some of the localized carriers that would have otherwise participated in a Hfcentered emission needs further investigation. It appears that the larger binding energy of an electron polaron at a Zr-site will interfere with and diminish emission from the Hf-centers. Some of the important activator doped scintillators currently being studied often suffer from problems associated with efficient energy transfer to the luminescent center. During excitation separate charge trapping at host and activator sites add typical fast and slow components in their decay profiles as seen for example in LaCl3:Ce3+ and Cs2LiYCl6:Ce3+.1218,56

Despite the similarities in the electronic structure of CHC and Cs2LiYCl6, it can be

argued that the time response in the latter is at least partially affected by the inefficient STE diffusion to the Ce3+ activators. There are also complexities involving spectral overlap between STE emission and activator absorption which may affect radiative energy transfer to the activator in Cs2LiYCl6. If the activator’s own absorption and emission wavelengths overlap, such as Eu2+ in Sr:Eu2+, it adds to light trapping and afterglow. Some of these inherent difficulties may be surpassed in an intrinsic scintillator like CHC because there is no explicit dependence on efficient energy transfer or spectral overlap. Both the electron and the hole can be trapped at a spatially localized level around a [HfCl6] octahedron and Hf acts as the luminescence center. It is likely one reason for its considerably higher light yield compared to Cs2LiYCl6:Ce3+. However, initial reports indicate scintillation decay time of CHC is on the same order as Cs2LiYCl6:Ce3+. It has a small fast-decay component accounting 23



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for ~5% at 0.3 µs, while the rest ~95% decays at 4.4 µs. Hence its time response is possibly due to long STE lifetime. Since dipole transitions from purely triplet to singlet states are forbidden, finite lifetimes of triplet STEs is often a result of mixing between the states caused by spin-orbit interaction. Indeed, shorter lifetimes due to stronger spin-orbit coupling parameter with heavier halogens has been discussed among the alkali halides.45,57 Assuming the slow response in CHC is related to STE lifetime, we may expect faster response in the order Cl→Br→I due to admixture of singlet and triplet states. Similar trend has been reported in K2LaCl5, Br5, I5 series of compounds.58 Additionally, it may not be out of place to study lighter alkali ions (e.g., Na) due to an opposite trend of shorter lifetime with decreasing atomic number among alkali halides.57 Therefore, possibility of smaller band gap, shorter STE lifetime using heavy halogen-light alkali metal and more mobile self-trapped holes ( ) in the mixed halide analogues could be ample reason for further studies of these intrinsic scintillators.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Phone: (870) 972-2427 Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This material is based upon work supported by the U.S. Department of Homeland Security under Grant Award Number, 2014-DN-077-ARI075-03. The support does not constitute an express or implied endorsement on the part of the Government. This research used resources 24


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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-AC0205CH11231. Computational resources at Arkansas State are partially funded from NSF Grant No. ECCS-1348341.

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Figure 1 277x193mm (150 x 150 DPI)



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Figure 7 931x719mm (120 x 120 DPI)



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Carrier Self-trapping and Luminescence in Intrinsically Activated

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