Energetic, Optical, and Electronic Properties of Intrinsic Electron

Aug 8, 2014 - The nature of intrinsic defects in YAlO3 (YAP) has attracted ..... For example, the ε(0/−) level is related to trapping of an electro...
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Energetic, Optical, and Electronic Properties of Intrinsic ElectronTrapping Defects in YAlO3: A Hybrid DFT Study Lixin Ning,*,† Weiping Cheng,† Cuicui Zhou,† Changkui Duan,‡ and Yongfan Zhang§ †

Center for Nano Science and Technology, Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China § Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences, Fuzhou, Fujian 350002, China ‡

S Supporting Information *

ABSTRACT: The formation energies of cation antisite defects (YAl and AlY), oxygen vacancies (VO), and nearest-neighbor defect complexes (YAl−AlY and YAl− VO) in various charge states in the YAlO3 crystal are calculated using density functional theory (DFT) with a modified PBE0 hybrid functional containing 32% Hartree−Fock (HF) exchange. It is found that the formation of YAl is more energetically favorable than AlY under oxygen-poor condition, consistent with the fact that the latter was not observed in experiments. On the basis of calculated optical transition energies associated with the excitons trapped at YAl, VO, and YAl− VO, the two emission bands observed under excitonic excitation at low temperature are identified. Electronic properties of YAl−VO complexes in the neutral and singly negative charge states are finally investigated. It shows that the extra electron added into the negative charge state is mainly localized at 4d orbitals of YAl with a two-component feature of its density distribution extending axially along the YAl−VO direction.

1. INTRODUCTION The nature of intrinsic defects in YAlO3 (YAP) has attracted long-standing and continued interest because of important applications of the crystal in solid-state lasers and scintillators.1−3 For example, the Ce-doped YAP crystal has several favorable properties for scintillator applications in positron emission tomography and other medical imaging systems.4 The scintillation process involves the absorption of high-energy radiation by exciting electrons and holes into the conduction and valence bands, respectively, and the diffusion of these charge carriers to Ce3+ where radiative recombination occurs, leading to parity- and spin-allowed 5d → 4f emissions.5 However, the intermediate diffusion process may be hindered by electron trapping at intrinsic defects, among which the cation antisite defects (YAl or AlY), oxygen vacancies (VO), and their aggregates have been proposed as predominant ones, as a consequence of the high growth temperature (∼2000 °C) and the complex structure of the crystal.6 The origins and characteristics of intrinsic defects in YAP have been extensively studied using various experimental approaches.7−10 The nuclear magnetic resonance (NMR) method proved directly the existence of YAl defects.10 The electron paramagnetic resonance (EPR) measurements of the YAP crystal after X-ray or UV irradiation revealed that the YAl tends to form a defect complex (YAl−VO) with a nearestneighbor (NN) oxygen vacancy. This complex behaves as a trapping center of the electrons from the conduction band, though its electronic structure is not completely understood. By contrast, the presence of AlY has not been found by EPR © 2014 American Chemical Society

measurements. The hole-trapping centers have been attributed to regular oxygen ions (O2−), and several O−-type centers were detected by EPR and thermal stimulated luminescence (TSL) measurements of the UV-irradiated YAP crystal.7,10 The photoluminescence approaches have also been used to characterize the intrinsic defects in YAP. Under excitation in the exciton absorption region at 10 K, two emission bands that peaked at 5.9 and 4.2 eV were observed with a full width at halfmaximum (fwhm) of 0.7−0.9 eV.11 Different assignments have been made for the two emission bands. The higher-energy band has been ascribed to the YAl-trapped exciton,11,12 the YAl defect itself,13 or the self-trapped exciton,14 while the lower-energy one has been ascribed to the exciton trapped at the YAl−VO defect complex11 or at the isolated VO.15 A definite assignment of the emission bands is still not available. Theoretical studies have also been performed to understand the nature of intrinsic defects in YAP. Atomistic simulations using empirical pair-potentials proposed that the antisite pair, YAl−AlY, is the dominant intrinsic defect, followed by the Schottky disorder (cation and anion vacancies).16,17 Density functional theory (DFT) calculations using the local-density approximation (LDA) with a 40-atom supercell model18 predicted that both the single YAl and AlY defects have low formation energies with respect to Y2O3 and Al2O3 reserviors, and AlY induces a shallow electron trapping level below the Received: May 22, 2014 Revised: July 29, 2014 Published: August 8, 2014 19940

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conduction band edge as characterized by LDA eigenvalues. The YAl-induced trapping level was not predicted by the DFTLDA calculations, but the possibility for its observation in larger supercells was pointed out.18 These theoretical results differ from experimental observations in that the AlY defect was not detected by EPR measurements of the irradiated YAP crystal.10 The disparity underlines the need of more accurate calculations to clarify the origins of electron-trapping centers in YAP. In this respect, the hybrid DFT method using a sufficiently large supercell is expected to be helpful because it was shown to improve the results of the band gap and defect properties in oxides when compared with pure DFT methods.19−21 In this work, we have performed a hybrid DFT study on the isolated defects, YAl, AlY, and VO, and their associated NN complexes, YAl−AlY and YAl−VO, which could behave as electron-trapping centers in the YAP crystal. The defect formation energies, the optical transition energies associated with defect-trapped excitons, and the electronic structures of these defects have been investigated. The purpose of this study is to obtain a better understanding of the energetic and electronic properties of intrinsic electron-trapping defects in YAP, which is essential for a performance improvement of the crystal in practical applications. This paper is organized as follows. A brief description of the calculation method is outlined in section 2, and the results are presented and discussed in section 3, with the final conclusions collected in section 4.

ΔEf [Dq] = Etot[Dq] − Etot[perfect] +

∑ ΔnA μA A

+ q(εVBM + E F)

(1)

where Etot[Dq] and Etot[perfect] are the total energies of the defective and perfect supercells, respectively. ΔnA is the number of species A (=Y, Al, O) removed from the perfect supercell to introduce point defects, and μA is the corresponding atomic chemical potential. EF is the Fermi level measured from the valence band maximum (εVBM), which is aligned with that of the perfect system by the macroscopic averaging approach.28 We have not considered the effect of finite-cell size on the ΔEf of charged defects in the 160-atom supercells. On the basis of a recent study on the cell-size dependences of ΔEf of charged defects in LaAlO3,29 it is anticipated that the resulting errors are very small and will not significantly influence the present results. In the thermodynamic equilibrium, the atomic chemical potentials μA in eq 1 vary within the following correlation μ Y + μA1 + 3μO = μ YAP

(2)

where μYAP is the total energy per formula unit of the YAP crystal. The values of μA can be further determined by thermodynamic equilibrium conditions of various phases containing the three atomic species. Because the YAP crystal is usually grown from the melt in an oxygen-deficient atmosphere, we mainly focus on the following condition in the present work, described by μA1 = μA1(bulk) μ Y = μ Y(bulk) (3)

2. METHOD OF CALCULATIONS The DFT calculations were performed using a hybrid functional in the PBE0 scheme22 that admixes a fraction of Hartree−Fock (HF) exchange with PBE exchange, as implemented in the V ASP package. 2 3 , 2 4 The Y (4s24p64d15s2), Al (3s23p1), and O (2s22p4) were treated as valence electrons, and their interactions with the respective cores were described by the projected augmented wave (PAW) method.25 A 2 × 2 × 2 supercell, containing 160 atoms, was employed for the calculations of intrinsic defects. The geometries of supercells were fully optimized until the total energies and the Hellmann−Feynman forces on the atoms were converged to 10−5 eV and 0.02 eV Å−1, respectively. One kpoint Γ was used to sample the Brillouin zone, and the cutoff energy for the plane wave basis was set to 550 eV. The spinpolarized DFT calculations were empolyed for the systems with unpaired electrons. To check the convergence of the results with respect to the number of k points, we have performed test calculations on the lattice parameters of pure YAP, the defect formation energy of a VO in the charge state q = +2, and the electronic properties of the defect state in a neutral NN YAl−VO complex, using a 2 × 1 × 2 k-point grid for the 160-atom supercells. The comparison of the results with those obtained using a single k-point Γ shows that the deviations are at most 0.022 Å in the lattice parameters of pure YAP and ∼0.18 eV in the defect formation energy of VO2+, while the difference in the electronic properties of the defect state of the YAl−VO is negligible. These errors do not affect the conclusions of the present study. The formation energy (ΔEf) of a defect D in the charge state q can be calculated from the total energies of supercells using the standard formalism,26,27 that is,

In the above equilibrium state, the total energies of the bulk materials, YAP, Y(hcp), and Al(fcc) were calculated to determine atomic chemical potentials. Results under other thermodynamic equilibrium conditions (e.g., O-rich conditions) can be obtained in a similar way29,30 and are described briefly in the Supporting Information.

3. RESULTS AND DISCUSSION 3.1. Atomic and Electronic Structures of Perfect YAP. Before we present the results for intrinsic defects, we address briefly structural and electronic properties of the perfect YAP crystal. It has an orthorhombic structure of Pnma symmetry with four chemical formulas per unit cell31 (see Figure 1). There are two crystallographically different sites for the oxygen atoms, with point group symmetries of Cs and C1. They are located within the planes of Y and Al atoms, respectively, perpendicular to the b axis, and are indicated by OI and OII in Figure 1. Each oxygen is coordinated by four Y and two Al atoms. The Y atoms occupy the sites of Cs symmetry and are each coordinated by 12 O atoms. The Al atoms are located at the Ci symmetry sites, each with a coordination of six O atoms in the form of a distorted octahedron, which can be grouped into three pairs according to the Al−O bonding lengths, as shown in Figure 1. In the second coordination shell, each Al atom is surrounded by eight Y atoms, which can be classified into four NN Al−Y pairs according to their distances. The atomic structures of perfect YAP were optimized with the DFT-PBE0 method, and the results are in good agreement with experimental data31 (see Table 1). The results calculated with the PBE32,33 and HSE0634,35 functionals and those reported in ref 15 are also listed in the table for comparison. With the optimized geometry, the band gap energy (Eg) is 19941

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Figure 2. Total and orbital-projected DOS for the YAP unit cell calculated using DFT with the PBE0 hybrid functional containing 32% HF exchange and a 5 × 5 × 5 k-point grid to sample the Brillouin zone. The Fermi level is set at zero energy.

Figure 1. A schematic view of the geometric structure of the YAP crystal.

predicted to be 8.13 eV with the standard PBE0 that contains 25% HF exchange, larger than the values of 5.58 and 7.37 eV obtained with PBE and HSE06, respectively, but smaller than the experimental value of ∼8.8 eV, as determined from spectroscopic measurements.36,37 This experimental value can, however, be reached by increasing the fraction of HF exchange to 32% in the PBE0 functional. Because an accurate predication of Eg is a prerequisite for a proper determination of defect properties,21 we have employed the PBE0 functional with this adjusted amount of HF exchange in the following defect calculations. The calculated total and orbital-projected densities of states (DOSs) using the modified PBE0 functional for the YAP unit cell are plotted in Figure 2. The top of the valence band is composed of O 2p states with a dispersion of ∼7.5 eV, and the bottom of the conduction band is dominanted by Y 4d states with a bandwidth of ∼4.2 eV. 3.2. Formation Energies of Neutral and Charged Intrinsic Defects in YAP. In Table 2, we list the calculated formation energies (ΔEf) for the single defects YAl, AlY, and VO, and the NN complexes YAl−AlY, YAl−VO, and AlY−VO in their neutral charge states, under the O-poor condition imposed by eqs 2 and 3. It is shown that the ΔEf of YAl is much lower (by 2.173 eV) than that of AlY (3.737 eV). The value of ΔEf for AlY is rather high, and this may explain the fact that only YAl (but not AlY) was observed in EPR measurements of the YAP crystal grown in O-poor atmosphere.10,11 However, under O-rich condition, the relative order of magnitude of ΔEf for YAl and AlY is reversed, with a much smaller difference, as shown in Figure S2 of the Supporting Information. Similar variations of ΔEf with the growth environment were observed in DFT studies of LaAl and AlLa in LaAlO3.30 For the four NN antisite

Table 2. Calculated Formation Energies (ΔEf in eV) for the Isolated Defects, YAl, AlY, and VO, and their Associated NN Complexes, YAl−AlY, YAl−VO, and AlY−VO, in the Neutral Charge State in the YAP Crystal under the O-Poor Condition Imposed by Eqs 2 and 3a single defect YAl AlY defect complex

ΔEf

single defect

ΔEf

1.564 3.737

VOI (Cs) VOII (C1)

0.856 0.888 ΔEf

d

YAl−AlY1 YAl−AlY2 YAl−AlY3 YAl−AlY4 YAl−VOI YAl−VOII1 YAl−VOII2 AlY−VOI1 AlY−VOII AlY−VOI2

3.000 3.135 3.239 3.485 1.890 1.903 1.923 2.254 2.285 2.311

4.880 5.008 5.014 4.886 2.139 2.203 2.113 4.620 4.666 4.668

a

The unrelaxed distances (d in Å) between the two single defects in the complexes are indicated.

pairs YAl−AlY, their formation energies are smaller by 0.287− 0.422 eV than the sum of ΔEf for YAl and AlY, indicating an attractive interaction between the two neutral single defects, which might be due to beneficial elastic deformations around the two single defects. Nevertheless, the ΔEf of the antisite pairs are too high (4.880−5.014 eV) as a result of the large ΔEf of AlY, and thus, the probability of their formation is low. We

Table 1. Calculated and Experimental Lattice and Internal Parameters for the YAP Crystala PBEb HSE06b PBE0b PBE0*b LDAc exptd

a (Å)

b (Å)

c (Å)

xY

zY

xO (Cs)

zO (Cs)

xO (C1)

yO (C1)

zO (C1)

5.397 5.342 5.341 5.332

7.444 7.367 7.363 7.350

5.227 5.179 5.179 5.167

5.330

7.375

5.180

0.0549 0.0551 0.0549 0.0554 0.0562 0.0526

0.9872 0.9875 0.9876 0.9882 0.9868 0.9896

0.4763 0.4778 0.4778 0.4790 0.4756 0.475

0.0861 0.0839 0.0839 0.0827 0.0884 0.086

0.2944 0.2940 0.2939 0.2960 0.2949 0.2930

0.0453 0.0442 0.0442 0.0426 0.0465 0.0440

0.7052 0.7056 0.7056 0.7039 0.7045 0.7030

a

PBE0 and PBE0* denote the standard and modified PBE0 functionals with 25% and 32% HF exchange, respectively. Previous reported data are included for comparison. bThis work. cReference 18. dReference 31. 19942

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Figure 3. Calculated defect formation energies (ΔEf) for (a) YAl, (b) AlY, (c) VO, and (d) YAl−VO in different charge states, as a function of the Fermi level (EF) position in the fundamental band gap of YAP.

the figure, one sees that the neutral charge state is the most favorable when the EF level is located in the upper half of the band gap. The +1 charge state is preferred in a narrow range of EF position slightly lower than the middle position. The +2 and −2 charge states are the most favorable when EF is close to the VBM and conduction band minimum (CBM), respectively. Figure 3d presents the changes of ΔEf for YAl−VO in the charge states, q = +2, +1, 0, −1, averaged over the three NN YAl−VO complexes. It shows that the neutral charge state is the most stable when EF is located slightly higher than the middle position of the band gap. When the EF is near the VBM or CBM, the +2 or −1 charge state is preferred, respectively. These results are consistent with the variations of ΔEf for VO (Figure 3c) and YAl (Figure 3a). To summarize, for YAl, AlY, VO, and YAl−VO, the neutral charge states are the most stable when the EF is located in the intermediate reigon slightly above the middle position of the band gap, which is expected to be the case in reducing atmosphere. The positive and negative charge states will be favored if the EF is near the VBM or CBM, respectively. Figure 4 gives a schematic representation of the thermodynamic transition levels, as derived from the ΔEf values plotted in Figure 3a−d. These transition levels indicate the Fermi levels at which the formation energies of a defect in two charge states become equal. From the figure, one sees that YAl, AlY, VO, and

mention that the values of ΔEf for the antisite pairs are independent of the crystal-growth environment because the stoichiometry of the system is maintained after their formation. As for isolated oxygen vacancies, Table 2 shows that the ΔEf for VOI (Cs) and VOII (C1) are similar, with the latter being slightly higher by 0.032 eV. Under O-rich condition, the ΔEf become much larger (∼7.0 eV), and thus, their formations are unlikely; see Figure S2 of the Supporting Information. There are three distinct NN YAl−VO complexes according to the different Al−O bonding lengths within the distorted AlO6 octahedron in perfect YAP. The calculated ΔEf values for the three complexes are similar, with the differences being no larger than 0.090 eV. Furthermore, the ΔEf for each complex is smaller than the sum of those for the single YAl and VO by 0.249−0.339 eV, indicating an additional stabilization provided by the formation of an NN complex, presumably because of the strain relaxation. In O-rich condition, Figure S2 of the Supporting Information shows that the ΔEf for YAl−VO are much higher (>9.0 eV) as a result of the large ΔEf for VO, thus excluding the formation of these defect complexes in such a growth environment. We have also calculated ΔEf values for three NN AlY−VO complexes, which are much higher than those of NN YAl−VO in O-poor condition. This is similar to the comparison described above for ΔEf values of AlY and YAl. Overall, the above results show that the neutral intrinsic defects, YAl, VO, and YAl−VO, are most likely formed in YAP in O-poor atomosphere. Because charged defects can also occur under certain experimental conditions, we have calculated ΔEf for YAl, AlY, VO, and YAl−VO in several charge states. In Figure 3a and b, the ΔEf for YAl and AlY in the charge states, q = +1, 0, −1, are depicted, respectively, as a function of the EF position within the band gap. It shows that for both defects the neutral charge state is the most stable at most of the EF positions, but when EF is near the VBM or CBM, the +1 or −1 charge state is, respectively, preferred. Figure 3c plots the variations of ΔEf for VO in the five charge states, q = +2, +1, 0, −1, −2, averaged over the values at VOI and VOII sites in view of their close proximity. The triplet state has been considered for q = −2, which was found to be more stable than the singlet state. From

Figure 4. Summary of derived thermodynamic transition energy levels for YAl, AlY, VO, and YAl−VO in YAP. 19943

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YAl−VO can behave as trapping centers of the electrons from the conduction band. For example, the ε(0/−) level is related to trapping of an electron by a neutral defect and changing its charge state to −1, which is paramagnetic and could be detected by EPR. The ε(0/−) level of YAl−VO is deeper than those of YAl or VO, which can be understood by the additional stability gained by formation of the YAl−VO complex. The YAl and AlY produce shallow hole-trapping levels (denoted by ε(+/ 0)) with depths of 0.768 and 0.986 eV, respectively. 3.3. Optical Transition Energies of Defect-Trapped Excitons. The energetic calculations for defects in different charge states can be correlated with optical transitions of defect-trapped excitons. A defect-trapped excitonic state is an excited state in which an electron in the CBM (eCBM) is bound to a positively charged defect (Dq+1, q ≥ 0), as indicated by Dq+1 + eCBM in Figure 5. This excited state can be produced by

Figure 5. Their values for YAl, VO, and YAl−VO are summarized in Table 3. From the Eem values listed in the last column of the Table 3. Calculated Optical Transition Energies Associated with the Excitons Trapped at YAl, VO, and YAl−VO Defects in YAPa YAl VOI VOII YAl−VOI YAl−VOII1 YAl−VOII2 a

q + 1/q

Eabs

EZPL

Eem

+1/0 +1/0 +2/+1 +1/0 +2/+1 +1/0 +2/+1 +1/0 +2/+1 +1/0 +2/+1

8.28 5.05 5.88 5.01 5.85 4.94 5.88 4.90 5.95 5.01 6.14

8.08 3.91 4.57 3.89 4.55 3.92 4.78 3.82 4.74 3.96 4.94

7.71 3.08 3.79 3.09 3.78 3.20 4.13 3.11 4.18 3.27 4.36

See Figure 5 for the meaning of the symbols Eabs, EZPL, and Eem.

table, we find that the broad-band emssion observed at 4.2 eV under excitonic excitation of YAP at 10 K can be ascribed to the excitons trapped at (YAl−VO)2+ with Eem = 4.13−4.36 eV, confirming the experimental assignment on the basis of spectroscopic analyses.11 The excitons localized at VO2+ with Eem ∼ 3.78 eV might also contribute to this emission band in view of its large fwhm. For the higher-energy emission band observed experimentally at 5.9 eV, the assigment to the excitons localized at isolated YAl defects11,12 is not supported by the present calculations. This emission band could be due to the self-trapped excitons or to the YAl defect itself, as proposed in refs 13 and 14. The present optical transition energies were estimated using the calculated ground-state energetic properties. A more accurate determination should require excited-state calculations using, for example, the many-body GW method38 or the Bethe-Salpeter equation,39 in which the electron−hole interaction in the excitonic state is taken into account. 3.4. Electronic Properties of YAl−VO Defect Complexes. The presence of YAl−VO defects has been evidenced by EPR measurements on the irradiated YAP crystal grown in Opoor atmosphere10 and is also confirmed by the present DFT calculations. The local atomic structures of these defects are plotted schematically in Figure 6, and the values of selected bond distances in the neutral and singly negative charge states are listed in Table 4, along with the corresponding values in perfect YAP for comparison. 3.4.1. Neutral YAl−VO Complexes. Table 4 shows that the incorporation of YAl−VO in perfect YAP causes structural rearrangements of the atoms around the VO sites, which is especially significant for the antisite YAl atom. In the neutral charge state, the YAl moves radially toward the VO sites by 0.077−0.116 Å, as expected from the much larger ionic radius of Y3+ (1.040 Å40) than that of Al3+ (0.675 Å40) in the 6-fold coordination. The Al atoms on the opposite side of YAl also shift slightly toward the VO sites by 0.029−0.061 Å. With the inward movements of YAl and Al, the other four adjacent Y atoms (Y1−Y4) move outward by 0.059−0.204 Å because of steric interactions. In addition, the YAl−O and Al−O bond lengths are increased by 0.206−0.285 Å and 0.026−0.058 Å, respectively (not shown in Table 4). The presence of a neutral VO produces a doubly occupied defect state within the band gap. Figure 7 plots the density of

Figure 5. Schematic configuration coordinate diagram of the optical transitions associated with an excitonic state localized at a defect (D) in the charge state q + 1. The upper curve denotes the Dq+1-trapped excitonic state with the electron at the CBM, and the lower one indicates the ground state of the defect Dq.

removing an electron from the valence band to the CBM with the hole left behind relaxed into a defect state (Dq) giving rise to Dq+1 or from a defect state (Dq) to the CBM by absorption of an energy of Eabs (see Figure 5). After structural relaxation, the excited state has a finite probability to return to the ground state (Dq) by emitting a photon with the energy of Eem. The EZPL denotes the transition energy of the zero-phonon line in the absorption or emission spectrum, corresponding to the difference between the energies of the excited and ground states at their equilibrium geometries, as denoted by Qq+1 and Qq in the figure, respectively. It corresponds to the energy difference between the thermodynamic transition level and the CBM (see Figure 4). The Eem (Eabs) is equal to EZPL minus (plus) the structural relaxation energy in the ground (excited) state and corresponds to the energy difference between the optical transition level (not shown) and the CBM. The optical transition energies related to a defect-trapped exciton can be calculated by using the total energies of the defective supercells in the charge states q + 1 and q, with the expression q+1 q Etran = Etot(Dq + 1) − Etot(Dq) + (q + 1)εVBM − qεVBM

+ Eg q where εq+1 VBM and εVBM represent the VBM energies of the two systems. Depending on the structures used to calculate the total energies, Etran will denote EPL, Eem, or Eabs, as is evident from

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Figure 6. Schematic representations of the local coordination structures of the three defect complexes (a) YAl−VOI, (b) YAl−VOII1, and (c) YAl−VOII2 in YAP.

Figure 7. Total DOS of the YAP supercell containing a single (a) YAl− VOI, (b) YAl−VOII1, or (c) YAl−VOII2 defect complex in the neutral charge state. The insets show the electron density projected onto the occupied defect states. The zero energy has been set at the top of the O 2p valence band. The Fermi levels are indicated by the dashed lines.

Table 4. Calculated Distances (in Å) of the VO Sites to the Y and Al Cations in the First Coordination Shells before and after the Incorporation of the NN YAl−VO Complexes in the Neutral (q = 0) and Singly Negative Charge (q = −1) States in the YAP Supercella perf.b VOI−YAl Al Y1 Y2 Y3 Y4 VOII1−YAl Al Y1 Y2 Y3 Y4 VOII2−YAl Al Y1 Y2 Y3 Y4

1.890 1.890 2.311 3.112 2.978 2.254 1.903 1.923 2.285 3.266 2.475 2.548 1.923 1.903 2.285 3.266 2.475 2.548

q = 0c 1.813 1.829 2.448 3.171 3.069 2.392 1.813 1.894 2.362 3.386 2.679 2.663 1.807 1.857 2.355 3.364 2.604 2.730

(−0.077) (−0.061) (+0.137) (+0.059) (+0.091) (+0.138) (−0.090) (−0.029) (+0.077) (+0.120) (+0.204) (+0.115) (−0.116) (−0.046) (+0.070) (+0.098) (+0.129) (+0.182)

magnetic ground state. Addition of the extra electron leads to a structural relaxation around the VO site, which is again the most pronounced for the antisite YAl atoms, as shown in Table 4. Compared with the structure in the neutral charge state, the YAl atoms move further toward the VO site by 0.127−0.135 Å because of the filling of a bonding band state (see below), with slight structural rearrangements of the other neighboring Y atoms. The Al atoms also exhibit an inward relaxation by 0.047−0.084 Å. The YAl−O and Al−O bonds are elongated by 0.017−0.120 Å and 0.011−0.101 Å, respectively, together with the movements of YAl and Al (not shown in Table 4). Figures 8 and 9 display the DOSs of the supercells containing the negatively charged YAl−VO. Because of the different numbers of spin-up and spin-down electrons, the doubly

q = −1d 1.685 1.782 2.488 3.090 3.080 2.295 1.686 1.810 2.294 3.394 2.695 2.644 1.672 1.803 2.284 3.368 2.622 2.710

(−0.128) (−0.047) (+0.040) (−0.081) (+0.011) (−0.097) (−0.127) (−0.084) (−0.068) (+0.008) (+0.016) (−0.019) (−0.135) (−0.054) (−0.071) (+0.004) (+0.018) (−0.020)

a

See Figure 6 for the definition of atomic labels. bIn the perfect YAP crystal. cThe values in parentheses are the differences taken with respect to the data in the perf. column. dThe values in parentheses are the differences taken with respect to the data listed in the q = 0 column.

states (DOSs) for the defective supercells, and in the insets, the isosurfaces of the electron density projected onto the occupied defect states. These defect states are located at 3.32−3.45 eV above the top of O 2p valence band and are highly localized at the VO sites with some density on nearby Y, Al, and O atoms. These states exhibit a typical structure for a neutral oxygen vacancy41,42 and are mainly contributed by the p- and d-type orbitals of Y atoms and the s- and p-type orbitals of Al atoms. 3.4.2. Singly Negatively Charged YAl−VO Complexes. By trapping an electron from the conduction band, the neutral YAl−VO defect becomes negatively charged, with a para-

Figure 8. Total DOS of the YAP supercell containing a single YAl−VOI defect complex in the singly negative charge state. The insets show the electron density projected onto the occupied defect states. The zero energy has been set at the top of the O 2p valence band. The Fermi level is indicated by the dashed line. 19945

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The Journal of Physical Chemistry C

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YAl dxy, dyz, and dz2 orbitals, are bonding with the Y4 dyz and Y3 dxy orbitals, respectively. For YAl−VOII2, the mixing of the YAl dx2−y2, dz2, dyz, and dxy orbitals yields the two components, which build bonds with the dx2−y2 orbitals of Y4 and Y1 and the dyz orbital of Y3, respectively, as shown in the inset of Figure 9b. Thus, in the given coordinate system, the electronic structure of the defect state occupied by the extra electron in (YAl−VO)− is dependent on the YAl−VO orientation. The electron density projected onto this state displays a two-component pattern with a near-axial symmetry along the YAl−VO direction and may as well be described as a dxy-type, in support of the model analysis presented in ref 10.

4. CONCLUSIONS We have studied theoretically energetic and electronic properties of the isolated defects, YAl, AlY, VO, and the NN complexes, YAl−AlY and YAl−VO, in various charge states in YAP. The DFT calculations with a modified PBE0 hybrid functional have been employed, and the fraction of HF exchange in the functional has been increased to 32% to reproduce the experimental band gap energy of perfect YAP. The results of defect formation energies show that the YAl antisite defect is much more stable than AlY in O-poor atomosphere, excluding the formation of AlY, AlY−VO, and YAl− AlY in such a condition, in agreement with experimental observations. On the basis of energetic calculations of the defects in different charge states, the optical transition energies of excitons trapped at YAl, VO, and YAl−VO were derived and compared with experimental data to help in clarifying the origins of the emission bands observed under excitonic excitation at low temperature. Finally, electronic properties of the occupied defect states in neutral and singly negatively charged YAl−VO complexes have been discussed. It was found that, in (YAl−VO)−, the extra electron is mainly localized at YAl 4d orbitals with some density on 4d orbitals of other Y atoms near the VO. The electron density exhibits a two-component distribution with a near-axial symmetry along the YA1−VO direction. The results of the present work complement earlier experimental and theoretical studies on the nature of intrinsic electron-trapping defects in the YAP crystal.

Figure 9. Total DOS of the YAP supercell containing a single (a) YAl− VOII1 or (b) YAl−VOII2 defect complex in the singly negative charge state. The insets show the electron density projected onto the occupied defect states. The zero energy has been set at the top of the O 2p valence band. The Fermi levels are indicated by the dashed lines.

occupied defect state splits into two spin-resolved ones separated by 0.37−0.40 eV, with an average energy position similar to those observed in the neutral YAl−VO. At 1.82−1.86 eV above, a spin-up defect state emerges and is occupied by the extra electron. In the insets of the two figures, the isosurfaces of the electron density projected onto the occupied defect states are plotted. In the lower pair of states, the electron density distributions are similar to those of the doubly occupied defect states of the neutral YAl−VO (see Figure 7) and are highly localized at the VO sites. The insets of Figures 8 and 9 show that the electron density distribution projected onto the highest occupied defect state in (YAl−VO)− is quite different from those projected onto the lower two states. Although localized at the VO site, the distribution exhibits two components with a near-axial symmetry along the YAl−VO direction. It involves mainly 4d orbitals of YAl, which are bonding with 4d orbitals of other Y atoms around the VO. For YAl−VOI, the inset of Figure 8 indicates that the YAl dxy orbital forms bonds with the Y2 dxz orbital for one component and the Y1 dx2−y2 orbital for the other component and a weak bond with the Y4 dxz orbital. For YAl−VOII1, the inset of Figure 9a shows that the two components, which are mainly derived from a mixing of the

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ASSOCIATED CONTENT

S Supporting Information *

Calculated defect formation energies for the neutral VO, YAl, AlY, YAl−VO, AlY−VO, and YAl−AlY defects in YAP under various thermodynamic equilibrium conditions. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the National Natural Science Foundation of China (Grant Nos. 11174005, 11274299, and 21373048). L.N. acknowledges support from the Special and Excellent Research Fund of Anhui Normal University. 19946

dx.doi.org/10.1021/jp5050404 | J. Phys. Chem. C 2014, 118, 19940−19947

The Journal of Physical Chemistry C

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Article

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dx.doi.org/10.1021/jp5050404 | J. Phys. Chem. C 2014, 118, 19940−19947