Hybrid Density Functional Study of the Local Structures and Energy

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A: Spectroscopy, Photochemistry, and Excited States

Hybrid Density Functional Study of the Local Structures and Energy Levels of CaAlO:Ce 2

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Bibo Lou, Weiguo Jing, Liren Lou, Yongfan Zhang, Min Yin, and Chang-Kui Duan J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01913 • Publication Date (Web): 12 Apr 2018 Downloaded from http://pubs.acs.org on April 12, 2018

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The Journal of Physical Chemistry

Hybrid Density Functional Study of the Local Structures and Energy Levels of CaAl2O4:Ce3+ Bibo Lou1, Weiguo Jing1, Liren Lou1, Yongfan Zhang2, Min Yin1,* and Chang-Kui Duan1,* 1

Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, School of

Physical Sciences, University of Science and Technology of China, Hefei, 230026, P. R. China. 2

Department of Chemistry, Fuzhou University, Fuzhou, Fujian 350002, People’s Republic of China

*

Corresponding authors: [email protected] (M. Yin) and [email protected] (CK. Duan)

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT:

First-principles calculations were carried out for the electronic structures of Ce3+ in calcium aluminate phosphors, CaAl2O4, and their effects on luminescence properties. Hybrid density functionals approaches were used to overcome the well-known underestimation of bandgaps of conventional density function approaches and to calculate the energy levels of Ce3+ ions more accurately. The obtained 4f-5d excitation and emission energies show good consistency with measured values. A detailed energy diagram of all three sites are obtained, which explains qualitatively all the luminescent phenomena. With the results of energy levels calculated by combining HSE06 and constraint occupancy approach, we are able to construct a configurational coordinate diagram to analyze the processes of capture of a hole or an electron, and luminescence. This approach can be applied for systematic high-throughput calculations in predicting Ce3+ activated luminescent materials with a moderate computing requirement.

1. Introduction Oxide-based inorganic phosphors, due to their excellent photo stability and low toxic level, have found many applications in scintillators, lasers, multicolor displays, lighting systems and biological and chemical sensing.1-5 Chemically stable alkaline earth aluminates MAl2O4 (M=Ca, Sr or Ba) have been used as a host material of phosphors.6-10 Among them, Ce3+ and Eu2+ doped CaAl2O4 have been extensively explored9-12 for their long-last persistent afterglow. The relative positions of the luminescent levels and other defect levels with respect to band edges are critical in determining the properties of scintillators13, thermal quenching of phosphors14 and persistent afterglow. For example, in the case of Ce-doped scintillators the 4f and 5d states of Ce3+ need reside in the band gap so as to trap a hole and an electron15, and in a phosphors the lowest 5d level needs to be lower than CBM considerably to allow a large quenching temperature. Considerable efforts, both experimentally and theoretically, have been made to determine the site 2


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occupancy16,17 of defects and their relative level positions etc.18-20, and first-principles calculation has emerged as a powerful tool to attack these problems.21,22

First-principles calculations based on density functional theory (DFT) have been extensively applied in material science, as they can provide useful insights into the chemical and electronic properties of materials and hence can aid in search of better materials or guide the modification of existing ones. Most of the first principle calculations on luminescent materials with doped ions are performed in either configuration interaction approach using a cluster model23-26 or solid-state band structural calculations based on supercell27-32. The former usually predicts excellent 4f → 5d transitions in consistent with the experimental values but is usually computational demanding. The latter has served as a powerful approach for assessing the properties of dopants and defects with low computational complexity. In the following we will focus on the supercell approach. Calculation of the energy difference from 4f to valence band edges (VBM) had been performed with DFT+U. 27 Furthermore, energies of 4f-5d transition have been investigated with ∆SCF (SCF: Self-Consistent Field) method27,28, where the excited state total energy is obtained by utilizing the constrained occupancy approach. 29 The results match well with experiments for a variety of Ce3+ activated luminescent materials.

The ∆SCF method together with the constrained occupancy approach for excited states has been shown to be effectively in previous calculations.27,28 However, when this method is applied to CaAl2O4:Ce3+, it is found that the 5d orbitals are all located in the conduction band (CB). This result conflicts with the observation of luminescence from the lowest 5d level of Ce3+, and makes further interpretations of calculated results difficult. The main reason is the underestimation of bandgap in DFT calculation. This lies in the lacking of the discontinuity of exchange-correlation potential in a practical Kohn-Sham formalism of DFT.30,31 Incorporate substantial amounts of exact exchange interaction, hybrid DFT can describe band gap of semiconductor and insulators more adequately. Recently, the hybrid functionals of Heyd, Scuseria, and 3



Ernzerhof (HSE06) and Perdew-Ernzerhof-Burke hybrid functional (PBE0) have been extensively adopted to provide more realistic GKS gaps and defect levels than PBE for typical semiconductors.33-35 And hybrid DFT could result in more accurate description if the parameters are optimized to fulfill the generalized Koopman’s Theroem.36,37 Hence, in the present study, we performed a first-principle study of CaAl2O4:Ce3+, aiming at predicting accurate defect level to analyze the luminescent processes. Our approach utilized constrained occupancy approach to obtain excited-state equilibrium configurations and HSE06 to calculate the band gap of the host and the defect levels relative to band edges.

2.

METHODOLOGY AND DETAILS

2.1 Structural calculations based on supercell.

The CaAl2O4 host has a monoclinic structure with space group P121/c1, and the unit cell with a = 8.7, b = 8.092, c = 15.191 Å, and β = 90°17′ contains twelve CaAl2O4.38 Ca atoms can occupy three different sites (figure 1), with Ca-I being coordinated with nine O atoms, while both Ca-II and Ca-III being coordinated with six O atoms. The mean distances between the Ca atoms and their nearest-neighbor O atoms are 2.784, 2.437 and 2.424 Å for Ca-I, Ca-II and Ca-III, respectively. The defect structural models were obtained through substitution of one of the Ca atoms with a Ce, and the Ce3+ ions occupying Ca-I, Ca-II, and Ca-III sites are named Ce-I, Ce-II, and Ce-III, respectively. Considering both the size of unit cell and computation cost, we constructed a supercell with a new base-vectors a - b, a + b, and c, which contains 168 atoms, to model the Ce-doped CaAl2O4.

Structural optimization was carried out with DFT calculations with generalized gradient approximation (GGA) PBE functionals, as implemented in the Vienna ab-initio Simulation Package (VASP).39,40 The projector augment wave (PAW) pseudopotentials were adopted to describe the interactions of atoms, where 4


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the valence configurations of O, Al, Ca and Ce were 2s22p4, 3s23p1, 3p64s2 and 5s25p64f15d16s2, respectively. The geometry optimizations were performed using the conjugate gradient technique, until the energy change was less than 1×10-6 eV and the Hellmann-Feynman forces on atoms were less than 0.01 eV/Å. Besides, only one K-point Γ was used to sample the Brillouin zone for defect-localized state supercell calculation,41 and the plane-wave cutoff energy of DFT calculation was set to 500 eV. For CaAl2O4, the artificial Madelung-type interaction of charged supercells42 is estimated to be of the order 0.1 eV, and exact correction values depend on the model applied. We will not apply the correction to the numerical data presented but discuss its effects briefly at the end. To determine the equilibrium configuration for the 5d-character excited state (Ce3+)* we perform a constrained GGA calculation by evacuating the 4f orbitals of Ce3+ and at the same time filling the lowest d character orbital of Ce3+ with one electron.

2.2 Energy levels calculations Although the electron structure and Kohn-Sham (KS) levels can be obtained in the above-mentioned calculations, it is noted that the Kohn-Sham (KS) levels obtained from a practical exchange-correlation functionals, which deviate considerably from an exact one, cannot be identified with any levels that are relevant to experimental measurements, even if there are no concerns about the accuracy of the KS band gap. The relative positions of the ground and excited states with respect to band edges can be calculated from difference in total energies (Sec. 2.2.1), which can be obtained with reasonable accuracy for ground state and approximately for excited state by using constraint occupancy approaches. Alternatively, in the generalized Kohn-Sham formalism, the defect levels can be identified approximate as the eigenvalues of generalized Kohn-Sham orbits (Sec. 2.2.2). 5



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2.2.1 Charge-state transition levels The defects energy levels can be calculated by the ∆SCF approach.21 The thermodynamic transition level ( ) is defined as the Fermi-level position for which the formation energies of charge states q1 and q2 are equal: ( ; ) ( ; ) =

(1)

where ( ; = 0) is the formation energy of the defect X in the charge state q when the Fermi level is at the VBM (EF = 0). The experimental significance of this level is that for Fermi-level positions below ( ), charge state q1 is stable, while for Fermi-level positions above ( ), charge state q2 is stable. 2.2.2 Band gap and hybrid DFT calculations The severe underestimation of the band gap in standard DFT causes significant uncertainties in the calculation of gap levels and the prediction of the electrical activity of defects in Ce-doped CaAl2O4, meanwhile all localized 5d states lie above the CBM, violating the observation of photon emission from the lowest 5d levels of Ce3+ in CaAl2O4.

Hybrid functionals have emerged as a useful alternative for precise band gap calculation, especially PBE0 and HSE06. PBE0 has 25% proportion of Hartree-Fock exchange α, while the HSE functionals43-45 include an additional short-range exchange screening µ. The case of α = 0.25 and µ = 0.2, termed HSE06, yields an excellent description of the electronic structure for both the perfect crystal and a wide range of the defects.30,46 A smaller cutoff energy of 400 eV was adopted to reduce the computational effort. In the calculation of bandgap, the coordinates of the high symmetry k-path in the Brillouin zones were chosen for K points.47 The 4f-VBM and CBM-5d energy differences were calculated using the HSE06. The 4f levels were obtained from the GKS eigenvalues of the filled 4f band at Γ point for the supercell that contained a 6


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Ce3+ ion. While for 5d levels, the same supercell was adopted, except that one electron was removed. It is noted that in the 5d case, the 5d band is empty and the evacuated 4f orbitals can be considered as frozen,48 and in order to simulate the Frank-Condon principle, the geometry coordinates are the same as the 4f case. To align the potentials in HSE06 calculations for different sites and charges, in analog to Ref. 49, a deep 2p state of Ca was referenced. The shifts due to such alignment were less than 0.1 eV in our calculations and negligible.

3.

RESULTS AND DISCUSSION

3.1 Equilibrium Structures and Band gap The structure of the pristine CaAl2O4 host was first optimized with GGA methods and the lattice parameters are shown in Table 1. The results show that the optimized lattice parameters of ground state are slightly larger than the experimental data by 0.89–1.5%. The discrepancy may be traced to the inherent imperfection of the DFT functional. The Ce-doped CaAl2O4 was modeled by an appropriate supercell. Table 2 presents the optimized bond-lengths of Ce3+-O2-. The substitution of Ce3+ at Ca2+ sites increases the distances to the nearest O2- ions, which is qualitatively consistent with the larger ion radius of Ce3+ than that of Ca2+ in the same coordination number. The average bond lengths for excited state are 0.6%, 2.0% and 1.5% shorter than those of the ground state for Ce-I, Ce-II and Ce-III, respectively. The optimized total energies relative to Ce-I are listed in Table 3, which shows that Ce-I is slightly more stable than Ce-II and Ce-III, agreeing with previous calculation in Ref. 9. This is expectable as Ce3+ is larger than Ca2+ and so tends to occupy a site with larger average bond lengths. It is expected that all the three Ce sites are presented in the phosphor due to small energy differences. Computed band structures, the total and partial densities of states (DOS and PDOS, respectively) for perfect CaAl2O4 are plotted in Figure 2. The bandgap obtained with PAW-PBE is only 4.35 eV, which is substantially underestimated. By trying the hybrid DFT including 7



HSE06 and PBE0, two kinds of parameters setting, the predicted band gap is 6.00 eV by HSE06 and 6.72 eV by PBE0. Experimentally, Hölsä et al. reported a bandgap of 6.7 eV for CaAl2O4 based on the UV−VUV synchrotron radiation excitation spectra,50 while D. Jia and W. M. Yen10 assigned it to be 5.8 eV based on the onset of interband absorption in the excitation spectrum. The actual band gap should be about 6.7 eV, as optical transitions tend to understate direct band gap due to the disturbance of various intrinsic defects or optically active dopants introduced unintentionally. In the following analysis we adopt HSE06 calculation and so use 6.00 eV for the band gap, but will discuss the impact of the band gap being larger.

3.2 Energy levels and transitions of Ce3+ ions 4f and 5d energy levels of Ce3+ doped supercell were obtained by DFT calculation with several choices of parameters. The results for Ce-II are plotted in Figure 3 (a). The occupied 4f level obtained via ∆SCF is about 0.4 eV higher than the HSE06 value, and similarly for the 5d state obtained by constraint occupancy approach. The 4f-VBM energy difference read off from KS eigenvalues is well known to be overestimated, but can be corrected by DFT+ U method.27 Here, instead of fine-tuning the parameter U in DFT+U calculations, we include its effect by lowering the KS 4f eigenvalue by Ueff /2= 1.25 eV, corresponding to the case of using Ueff = 2.5 eV. This matches well with the HSE06 result of 2.20 eV and PBE0 result of 2.19 eV. It is similar for the other two sites in Table 4. The empty 5d levels are located within the conduction bands of the host in GGA-PBE calculations, while the 5d levels of Ce3+ obtained with HSE06 calculations for the three sites are all localized in the gap. For each of the three Ce sites, the 4f-VBM and CBM-5d energies obtained with HSE06 are almost equal to those with PBE0. The main difference in the results of the two parameter choices is the band gap.

The energy levels calculated by HSE06 and their experimental counterparts for all the three sites are listed in Table 5. The calculated values match experimental measurements10 reasonably well, with less than 8


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10% underestimation. The agreement can be better by using a band gap of a few 0.1 eV larger. The results also show that the difference of 4f-5d excitation among the three sites is dominated by variation of 4f-VBM energy difference, as the variation of 5d1-CBM (5d1 being the lowest 5d level) among the three sites is much smaller. This is clearly shown in Figure 3 (b). The 4f energy level for Ce-I is 1.59 eV above the VBM, but is 2.2 eV and 2.24 eV for Ce-II and Ce-III. Ref. 10 shows that the emissions from Ce3+ ions in Ce-II and Ce-III are too close to allow accurate determination of their individual spectra. Because of the higher 4f-VBM energy difference compared with Ce-I, the Ce-II and Ce-III are more stable for the hole to reside, and hence both of them are more ready to accept an electron released or tunneled from shallow defects than Ce-I site. This explains why Ce-II or Ce-III is experimentally observed as the main site responsible for the afterglow10 despite that Ce-I is the most stable site. The position of 5d under CBM is similar for Ce-I and Ce-III, while for Ce-II it is 0.1 eV closer to CBM. This means a smaller ionization potential of Ce-II site, which will be discussed in next subsection.

3.3 Configuration coordinate diagram In order to analyze the processes of hole and electron captures and luminescence, a schematic configurational coordinate diagram is plotted in Figure 4. In the figure the curves denoted by Ce3+ and (Ce3+)* represent the potential surfaces corresponding to 4f and 5d levels, respectively, and (Ce3+)* is obtained by constraining the electron originally occupying the band with main character of 4f orbitals of Ce3+ to the lowest band with the main character of 5d orbitals of Ce3+; the potential surface of the system of Ce4+ together with a loose electron in CB is denoted as Ce4+ + e, sic passim. Concerning the process of producing electron-hole (e-h) pair and the trapping of a hole by Ce3+, two dash curves, representing respectively Ce3+ together with an e-h pair (Ce3+ + e + h) and Ce4+- h, are also added in the figure. F, D and C points represent the equilibrium configurations and the corresponding electronic energies for Ce3+, (Ce3+)*, and Ce4+ + e, respectively, and V0, F, D0, and C0 are points on different potential surfaces for the 9



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equilibrium geometry of the ground state. ϵ4f is the relative position of Ce3+ ground level with respect to VBM in terms of ionization energy difference. It equals the energy released when a Ce3+ at its equilibrium geometry captures a hole at VBM, and Eg -ϵ5d is the relative position of (Ce3+)* to CBM in terms of ionization to the conduction band calculated at the equilibrium geometry of Ce3+. The ionization potential ϵ0 decides the thermal ionization potential of an electron from 5d state. This is related to the activation energy of the luminescence’s thermal quenching. The host’s bandgap Eg is obtained via HSE06 from band structural calculation, and ϵ4f and Eg - ϵ5d are calculated with HSE06 using two supercells of the same atomic coordinates but containing Ce3+ (ϵ4f ) and Ce4+ (Eg - ϵ5d) ions. To depict the configuration coordinate diagram, we fixed the F, D0 and C0 points with the energy levels calculated by HSE06, and then the energy differences of F-F0, D-D0, and C-C0 from the calculations of the constrained occupancy approach. The calculated results are as follows. Eg = 6.00 eV fixes C0 relative to V0. ϵ4f = 2.2 eV specifies the energy difference between 4f and VBM, which corresponds to the energy released upon Ce3+ catching a hole from VBM before structural relaxation. The energy 0.06 eV between C and D illustrates the thermal ionization of the 5d excited state to conduction band. It is underestimated due to the neglect of the Madelung-type corrections for charged supercell, which would lower 5d energies by a few 0.1 eV, leading to an increase in predicted thermal stability of 5d luminescence. Such a downward revision of 5d energies will of course decrease the energy difference between 4f and 5d, but can be compensated by the fact that the actual band gap could be several 0.1 eV larger than 6.00 eV. Comparing to Ce-I and Ce-III, the 5d electron localized in 5d at Ce-II is slightly easier to be ionized to CB. Referencing to the theoretical criterion,51 the luminescent properties of a candidate Ce3+ doped material can be predicted with configuration coordination diagram and the calculations need include:

a. Good prediction of the bandgap with hybrid DFT such as HSE06 or PBE0;

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b. Geometry configurations for Ce3+, (Ce3+)* and Ce4+ in the supercell via conventional density functionals (Ce3+ and Ce4+) and the constrained occupancy approach [(Ce3+)*]; c. Hybrid DFT calculation at ground-state geometry to obtain ϵ4f (HOMO of the supercell with a Ce3+) and ϵ5d (LUMO of the supercell with a Ce4+ by disregarding evacuated 4f orbitals);

d. calculation of the relative energy in each potential surface via conventional DFT approach.

4. Conclusions Band structure level calculations by the combination of constrained occupancy approach and hybrid density functionals have been carried out on Ce3+ doped CaAl2O4. Firstly, geometry optimization of Ce3+ in three different sites was carried out and the calculation of the total energies show that Ca-I coordinated with nine O atoms is more stable than the other two sites coordinated with six O atoms; Secondly the 4f and 5d levels of Ce3+ in all the three sites are obtained by employing hybrid density functionals HSE06, which produces more realistic bandgap for the host than conventional density functionals. The obtained 4f and the lowest 5d levels are all in the bandgap, agreeing with experiments in which the phosphors show clearly 4f-5d absorption and 5d-4f emission. This is in severe contrast with those calculations employing conventional density functionals, which produce 5d levels in conduction bands, clearly in confliction with the fact that optical emission occurs from 5d levels. The localized 4f and 5d states are mostly matching well with the results of experiment, with the calculated absorption and emission energies being up to 10% lower than experimental measurements. The lowest 5d states of Ce in all the three sites are close to CBM, and it is mainly the position of 4f states that determine the difference in excitation and emission of Ce at three sites. Finally, we analyzed the calculated parameters combining with configurational coordinate. Applying the calculation scheme based on HSE06 and constrained occupancy approach, the absorption and emission 11



energies and reasonably accurate energy level position of defects were investigated in moderate calculation efforts, which indicated that the method used here was expected to be applied in discovering or screening out new scintillator and luminescence materials from large number of candidate materials.

ACKNOWLEDGEMENTS The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China. This work was financially supported by the National Key Research and Development Program of China (Grant No. 2016YFB0701001 and 2013CB921800), the National Natural Science Foundation of China (Nos. 61635012, 11574298, and 81788101), and Anhui Initiative in Quantum Information Technologies (Grant No. AHY050000).

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Table 1 Measured and calculated lattice parameters for CaAl2O4. Method

a(Å)

b(Å)

c(Å)

alpha

beta

gamma

Expta GGA

8.700 8.778

8.092 8.212

15.191 15.339

90.000 90.000

90.170 90.275

90.000 90.000

a

The experimental data are from Ref 10.

Table 2 Calculated bond-lengths of Ca2+-O2- and Ce3+-O2- in units of Å.

Bond M–O1 M–O2 M–O3 M–O4 M–O5 M–O6 M–O7 M–O8 M–O9

Ca-I site 2+

Ca -O

2-

2.352 2.393 2.403 2.807 2.893 2.904 3.039 3.088 3.175

Ca-II site

3+

2-

2+

2-

3+

Ce -O

Ca -O

Ce -O

2.387 2.406 2.420 2.799 2.811 2.826 2.911 3.057 3.140

2.310 2.351 2.356 2.400 2.444 2.680

2.333 2.362 2.384 2.426 2.443 2.686

Ca-III site 2-

2+

Ca -O2-

Ce3+-O2-

2.292 2.332 2.336 2.338 2.602 2.724

2.306 2.360 2.367 2.375 2.617 2.716

Table 3 Stabilities of three sites. Site Coordination Number Relative energy (eV)

Ce-I 9 0.00

Ce-II 6 0.27

Ce-III 6 0.33

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Table 4 Calculated energies of Ce3+ (4f) relative to VBM and (Ce3+)* (5d) relative to CBM in units of eV. 4f and 5d energies a Ce-I Ce-II Ce-III

ΔSCF 3.67 3.62 3.53

Δ(4f) 0.30 0.21 0.18

Δ(5d) 0.22 0.18 0.16

4f-VBM PBE+U b 1.64 2.18 2.15

ΔSCF 1.18 1.36 1.36

5d→CBM

HSE06 1.59 2.20 2.24

ΔSCF c -0.31 -0.41 -0.38

PBE0 1.58 2.19 2.23

HSE06 0.58 0.43 0.54

PBE0 0.55 0.40 0.51

a

Constrained occupation approach. ΔSCF: calculated energies for 4f→5d vertical transition; Δ(4f) and Δ(5d): energy changes of the ground and the excited states due to geometric relaxation, respectively. b Calculated as the difference of eigenvalues of 4f and VBM minus Ueff/2. c Calculated with Eg (PBE) –[∆SCF(5d←4f) + ΔSCF(4f-VBM)] with Eg (PBE)= 4.35 eV. Negative values mean 5d being higher than CBM.

Table 5 Calculated energy level position (in eV) of 4f relative to VBM and 5d relative to CBM by utilizing HSE06 approach, calculated and measured excitation and emission energies, and the ionization potential of 5d states to conduction band.

4f-VBM Ce-I

Ce-II

Ce-III a

Cal. Exp. Cal.

5d→CBM

Excitation

Emission

Ionization potential

0.58

3.83

3.45

0.39

4.15

3.82

1.59 a

2.20

0.43

Exp. Cal.

2.24

Exp.

0.54

3.37

2.85

3.43

3.00

3.22

2.89

3.38

3.16

The experimental data are from Ref 10.

18


0.06

0.15

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Fig 1

Figure 1. tic representations of CaAl2O4 and environment of Ca-I (in brown) coordinated with nine O atoms, and Ca-II (in yellow) and Ca-III (in purple) coordinated with six O atoms.

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Fig 2

Figure 2 Band structures and the total or partial densities of states (DOS and PDOS, respectively) of perfect CaAl2O4. (a) GGA: 4.35 eV (b) HSE06: 6.00 eV (c) PBE0: 6.72 eV.

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Fig 3

Figure 3. Bandgap and energy levels of impurities. (a) Energy level diagram of Ce-II in CaAl2O4:Ce3+ obtained by utilizing GGA, HSE06 and PBE0 approaches. The calculations are aligned with respect to the electrostatic potential of the pristine bulk: (1) VBM, 4f, 5d and CBM are their corresponding KS (or GKS for HSE06 and PBE0) eigenvalues; (2) 4f′ and 5d′ are calculated with ∆SCF method (see Table 2 for details). (b) VBM referred energy level diagram of three sites calculated by utilizing HSE06 approach.

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Fig 4

Figure 4. Schematic configurational coordinate diagram of the defect’s potential surfaces as a function of the generalized configuration coordinate: (1) Ce3+ and (Ce3+)* denote the ground and 4f-5d excited states of Ce3+ in the host, respectively; (2) Ce4+ + e simulates Ce4+ with a loose electron in CB, with a lower dash curve represents the case of the electron being trapped; (3) Two dashed curves are added to illustrate the processes of producing electron-hole (e-h) pair and the trapping of a hole and an electron.

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TOC Graphic

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Hybrid Density Functional Study of the Local Structures and Energy

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