Interaction between Bi Dopants and Intrinsic Defects in LiNbO3 from

Feb 7, 2019 - Three charge-compensated defect clusters, BiLi4+ + NbLi4+ + 8VLi–, BiLi4+ + 4VLi–, and BiLi4+ + BiNb0 + 4VLi–, are modeled in this...
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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Interaction between Bi Dopants and Intrinsic Defects in LiNbO3 from Local and Hybrid Density Functional Theory Calculations Lili Li, Yanlu Li,* and Xian Zhao

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State Key Lab of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China ABSTRACT: The interactions between Bi dopants including Bi-substituting Li (BiLi) and Bi-substituting Nb (BiNb) and the intrinsic antisite defects (NbLi) and Li vacancies (VLi) in LiNbO3 are investigated using local and hybrid density functional theories. Three charge-compensated defect clusters, BiLi4+ + NbLi4+ + 8VLi−, BiLi4+ + 4VLi−, and BiLi4+ + BiNb0 + 4VLi−, are modeled in this work to investigate the effects of the Bi concentration. The most stable cluster configurations, the Bi-doping stability in the clusters, and the electronic state interaction between Bi and intrinsic defects have been studied in detail. It is found that BiLi4+ has a stronger electron-capturing ability than NbLi4+ in Bidoped congruent LiNbO3. The BiLi-doping-induced local lattice distortion and the electron-trapping behavior remain unchanged with increasing Bi-doping concentration. However, the position of the Bi defect states in the band gap is found to be shifted in congruent LiNbO3. This is mainly attributed to the large lattice relaxation induced by the large number of Li vacancies instead of the ionic level redistribution caused by the direct interaction between Bi and intrinsic defects.

1. INTRODUCTION Lithium niobate (LiNbO3, LN) is a promising photorefractive (PR) crystal1 with many important applications in holographic data storage, phase-conjugated mirrors, optical communications, and demultiplexers.2−4 Dopants such as Fe3+/2+, Ce3+/2+, Mn3+/2+, and Cu2+/+ could be incorporated into the LiNbO3 lattice to enhance the PR effect of the material.5 In particular, recent research has found that Bi-doped LiNbO3 (Bi:LiNbO3) shows better PR performance than the more common Fedoped LiNbO3 (Fe:LiNbO3), showing, for example, an acceleration in the PR response and increased PR sensitivity.6 The PR process in LiNbO3 refers to the photoexcitation of the electron carriers from the trapped state to the conduction band (CB) and the recapture of the carriers in the CB by the trapped states. During this process, charge transport can be described as occurring via small polarons.7,8 In general, the polaron, a quasiparticle composed of electron carriers, can distort the surrounding lattice and create a local potential well through interaction with the lattice. In our previous work, we verified that the Bi 6s2 lone electron pair has a major impact on the structural distortion and electron-trapping behavior in Bi:LiNbO3.9 Although stoichiometric LiNbO3 (SLN) crystals have been grown recently, the most widely used material for practical applications is congruent LiNbO3 (CLN),10,11 which contains a large number of intrinsic point defects such as Nb antisites (NbLi) and Li vacancies (VLi).12,13 The photoexcitation of CLN involves the intrinsic Nb Li small polarons and bipolarons.14,15 Bi has previously also been found by us to introduce small polarons.9 The coexistence of intrinsic and extrinsic polarons could lead to different electron excitation process from the case of Bi in stoichiometric LiNbO3.16,17 © XXXX American Chemical Society

Therefore, it is of great importance to study the local lattice distortion, the relative position of the defect states, and the complicated electron-trapping behavior introduced by the interaction of intrinsic and extrinsic polarons. The intrinsic defects interact with the Bi dopants in both electronic and configurational respects. First, the electron carriers in the crystal could be trapped in either the NbLi polarons or the BiLi polarons. This results in varying photorefractivity with respect to a single PR center. Second, the Bi dopants could be charge compensated for by the dominant intrinsic defects, NbLi4+ and VLi−, in congruent LiNbO3. The form of the defect clusters could be changed with increasing Bi concentration. For example, Bi could coexist with NbLi and VLi defects as BiLi4+ + NbLi4+ + 8VLi− clusters when the Bi concentration is very low. Such large defect clusters would lead to huge lattice relaxation with respect to the single defect18 and thus significantly affect the electron distribution around the Bi dopants. The present work aims to understand the mechanism of interaction between Bi dopants and the intrinsic defects using density functional theory (DFT).19,20 The strategy to find the most stable defect cluster configurations is illustrated in detail. Based on the experimentally observed variation in defect species with increasing Bi concentration, five chargecompensated defect cluster models including BiLi4+ + NbLi4+ + 8VLi−, BiLi4+ + 4VLi−, BiLi4+ + BiNb0 + 4VLi−, 2BiLi2+ + BiNb2− + 2VLi−, and BiLi2+ + BiNb2− were constructed. We mainly focus on the first three defect clusters, which will be formed in congruent crystals with low Bi concentration, to understand Received: November 11, 2018

A

DOI: 10.1021/acs.inorgchem.8b03167 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry 2 O5 2Δμ(Nb) + 5Δμ(O) = −ΔH Nb f

the interaction mechanism between Bi and intrinsic defects. The energetics and electronic structures of these clusters were also examined. To obtain more reliable defect formation energies and electron distributions, hybrid DFT, rather than a (semi)local functional, was used in most of the calculations, except for the neutral defect clusters calculated in 540-atom supercells, despite its computational expensive.21−26 The accuracy of the hybrid functional in describing the energetics and electronic structures of point defects in LiNbO3 has been proved in our previous work.9,17,27,28

(4)

Details of calculation models, parameters, equations, and calculated formation enthalpies can be found in our previous work.9,17,28 Here, we quote Figure 2 of ref 9 to visualize the range of stable chemical potentials of the components in LiNbO3 calculated using HSE06, as shown in Figure 1. The shaded region enclosed by lines connecting

2. METHODOLOGY The present calculations were carried out in the Vienna ab initio Simulation Package (VASP)29,30 implementation of DFT in conjunction with the projector-augmented-wave (PAW) formalism.31 Thereby the Li 2s1, Nb 4p65s14d4, O 2s22p4, and Bi 6s26p3 states are treated as valence electrons. The electronic wave functions are expanded as plane waves using an energy cutoff of 400 eV. The electron exchange and correlation (XC) of the generalized gradient approximation (GGA)32 functional of Perdew, Burke, and Ernzerhof (PBE)33 was used to optimize the configurations under constant volume, and the force convergence criterion for the structural relaxation was set to 0.01 eV/Å. Except for the energetics of the charge-neutral defect clusters, all the other energetic and electronic property calculations were performed using the screened hybrid functional (HSE06) proposed by Heyd, Scuseria, and Ernzerhof.34,35 In this approach, the long-range exchange potential and the correlation potential are calculated using the PBE functional, whereas the short-range exchange potential is calculated by mixing a fraction of nonlocal Hartree−Fock exchange with that of PBE. The screening length and mixing parameter were fixed at 10 Å and 0.25, respectively. Hexagonal 2 × 1 × 1 supercells containing 120 atoms were used to model the defect pairs in congruent LiNbO3, whereas hexagonal 3 × 2 × 2 supercells containing 540 atoms were used to model the chargeneutral defect clusters composed by Bi dopants (BiLi4+ and BiNb0) and intrinsic point defects (NbLi4+ and VLi−). A 4 × 4 × 4 Monkhorst− Pack k-point mesh was used for the PBE calculations in the 120-atom supercells, and a 2 × 2 × 2 Monkhorst−Pack k-point mesh was used for the HSE06 calculations in the 120-atom supercells. A Γ-point for PBE calculations in the 540-atom supercells. The formation energy of dopant X with charge state q dependent on the Fermi level position is calculated as36−38

Ef (X q) = Etot(X q) − Etot(pristine) +

Figure 1. Stability range of the chemical potential (in eV) of the components in LiNbO3 calculated at the HSE06 level. The region enclosed between points B, D, and F satisfies eq 3, while the region enclosed between points A, C, E, and G satisfies eq 4. The shaded region enclosed between points B, C, E, and F represents the thermodynamically allowed range of the chemical potentials.9 points B, C, E, and F indicates the LiNbO3 stability range, and values outside this region lead to the precipitation of the secondary phases. A different choice of the reference state will modify the relative stability of the investigated doping defects. Line BF in Figure 1 corresponds to the Li-rich condition, and line CE indicates the Li-deficient condition. To reproduce the experimental conditions,6 the chemical potential of Bi should satisfy the requirement for forming its oxide, Bi2O5:

2Δμ(Bi) + 5Δμ(O) = −ΔHf Bi2O5

The chemical potentials of Li, Nb, O, and Bi calculated by DFTPBE and HSE06 under Li-rich and Li-deficient conditions are listed in Table 1. It should be noted that the deviations between the values

Table 1. Calculated Chemical Potentials (eV) of Li, Nb, O, and Bi at the DFT-PBE and HSE06 Levels under Li-Rich and -Deficient Conditions in LiNbO3

∑ niμi i

+ q(E F + E V + ΔV ) tot

q

(5)

(1)

DFT-PBE

tot

where E (X ) and E (pristine) are the total energies derived from a supercell with and without doping of ion X of charge state q. In addition, ni indicates the number of atoms of species i that have been added or removed upon doping, and μi is the corresponding chemical potential, which depends on the preparation conditions. EF is the Fermi level with respect to the valence-band maximum (VBM, EV) of the pristine material, and ΔV is a correction term38 to align the electrostatic potentials between the defect supercell and the bulk. The latter can be obtained by inspecting the potential in the supercell far from the impurity, and aligning it with the electrostatic potential of bulk LiNbO3. The thermodynamic considerations restrict the accessible range of the μi if one requires the LiNbO3 to be stable with respect to decomposition into its single components and binary oxides (Li2O and Nb2O5). We define Δμ as the discrepancy between the bulk values of the chemical potential of the corresponding component. They should satisfy the following relationships: Δμ(Li) + Δμ(Nb) + 3Δμ(O) = −ΔHfLiNbO3

(2)

2Δμ(Li) + Δμ(O) = −ΔHfLi2O

(3)

HSE06

chemical potentials

Li-rich

Li-deficient

Li-rich

Li-deficient

Li Nb O Bi

−2.58 −21.57 −5.22 −6.56

−4.37 −20.19 −5.08 −6.77

−2.62 −22.51 −8.90 −8.68

−3.45 −21.68 −8.98 −8.56

obtained by DFT-PBE and HSE06 are much larger for O compared to those of the other components. This is because the chemical potential of O is obtained by using eqs 2−4 and thus exhibits a large deviation by summing the deviations for Li, Nb, Li2O, Nb2O5, and LiNbO3. In this work, we use the chemical potentials calculated using HSE06 under Li-deficient condition to reproduce the experimental environment of the congruent LiNbO3 material. Furthermore, we define the binding energy of the defect pair X1X2 as the difference between the formation energies of the defect pairs and the sum of the formation energies of the isolated constituents:38−40 E b[(X1X 2)q ] = Ef [(X1X 2)q ] − Ef [(X1)q1 ] − Ef [(X 2)q2 ] B

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DOI: 10.1021/acs.inorgchem.8b03167 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry where q = q1+ q2. Here, the formation energy of a defect pair is defined in the same way as for isolated defects by eq 1. The negative binding energy corresponds to a preference for the defects to cluster; that is, the interaction between defect X1 and X2 is attractive, and the formation of defect pairs becomes thermodynamically favorable. To assess the formation energetics of defect clusters at finite temperatures, we considered the free energy, F = E − TS, rather than the total energy, E. The electronic entropy, the lattice vibrations, and the configurational entropy all contribute to the free energy, F. Here, the electronic entropy is negligible because of the large LiNbO3 band gap. The contribution of the vibrational zero energy to F can also be neglected at low temperature.36 In contrast, the configurational entropy can be expected to be the most important contribution in the present context, where structures with significantly different numbers and configurations of point defects must be compared. The configurational entropy is calculated in this work according to Boltzmann’s entropy formula:

S = kB ln W

3. RESULTS AND DISCUSSION 3.1. Association of Bi with Intrinsic Defects. According to the calculated formation energies in ref 9, Bi dopants are stable in BiLi4+ and BiNb0 when the Fermi level locates at the half lower part of the band gap. However, the Fermi level can be close to the conduction band in the Bi-doped LiNbO3, since Bi is a donor. In this case, BiLi2+ and BiNb2− become more stable. Therefore, we first investigated the association between the Bi dopants, including BiLi4+, BiLi2+, BiNb0, and BiNb2−, and the intrinsic point defects NbLi4+ and VLi− by calculating the binding energies of each defect pair as a function of distance. In Figure 2a,b, we show the locations and the distances of the

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where kB is the Boltzmann constant and W is the number of defect cluster configurations in the LiNbO3 lattice. W is approximated here by multiplying the number of possible combinations of each defect type in the cluster. In this work, we have considered the defect repulsive interactions within a certain range to reduce the error in the supercell size on the configurational entropy.41 Because the size of investigated defect clusters reaches 1 nm, we only consider the possible arrangements of each defect for clusters built within a circle with a radius of 1 nm. These clusters contain 61 Li, 60 Nb, and 169 O atoms. Therefore, W is calculated with the binomial coefficients Cnk as

Figure 2. Schematic locations of the nearest-neighbor (NN) Li sites to XLi (a) and XNb (b). Nb atoms have been hidden for simplification. Gray balls indicate Li atoms. Dark green, dark yellow, purple, blue, and pink balls indicate the FNN, SNN, 3NN, 4NN, and 5NN sites, respectively. Atoms in the same NN site are numbered. Distances are given in the angstrom units (Å).

W (BiLi 4 + + NbLi 4 + + 8VLi−) = C611C601C598 W (BiLi 4 + + 4VLi−) = C611C60 4 W (BiLi 4 + + BiNb0 + 4VLi−) = C611C601C60 4 W (BiLi 2 + + NbLi 4 + + 6VLi−) = C611C601C596

first-, second-, third-, fourth-, and fifth-nearest-neighbor (FNN, SNN, 3NN, 4NN, and 5NN) Li sites to a XLi defect center (BiLi, or NbLi), as well as to a XNb center (BiNb) in LiNbO3, respectively. Taking Bi as an example, BiLi (BiNb) has 6 (1) equivalent FNN sites, 6 (3) equivalent SNN sites, 6 (3) equivalent 3NN sites, 6 (1) equivalent 4NN sites, and 2 (6) equivalent 5NN sites on the Li (Nb) sublattice. The distancedependent binding energies of BiLi4+ + NbLi4+, BiLi4+ + VLi−, NbLi4+ + VLi−, and BiLi2+ + VLi− defect pairs are shown in Figure 3a, and BiNb0 + VLi−, BiNb0 + BiLi4+, and BiNb2− + BiLi2+ defect pairs are shown in Figure 3b. The distances in the figure are measured by taking the highly charged Bi defect as the reference and then changing the position of another defect.

W (BiLi 2 + + 2VLi−) = C611C60 2 W (BiLi 2 + + BiNb0 + 2VLi−) = C611C601C60 2 W (2BiLi 2 + + BiNb2 − + 2VLi−) = C612C601C59 2 W (BiLi 2 + + BiNb2 −) = C611C601

(8)

and result in S values of 0.0026, 0.0015, 0.0018, 0.0022, 0.0010, 0.0014, 0.0016, and 0.00071 eV/K respectively. The calculated configurational entropy values for the above defect clusters under room temperature (300 K) and annealing temperature (1423 K)6 are listed in Table 2.

Table 2. Calculated Configurational Entropy Values for the Defect Clusters in LiNbO3 under Room Temperature (300 K) and Annealing Temperature (1423 K) configurational entropy (eV) cluster

T = 300 K

T = 1423 K

BiLi4+ + NbLi4+ + 8VLi− BiLi4+ + 4VLi− BiLi4+ + BiNb0 + 4VLi− BiLi2+ + NbLi4+ + 6VLi− BiLi2+ + 2VLi− BiLi2+ + BiNb0 + 2VLi− 2BiLi2+ + BiNb2− + 2VLi− BiLi2+ + BiNb2−

0.77 0.44 0.55 0.67 0.30 0.41 0.49 0.21

3.64 2.11 2.61 3.17 1.42 1.92 2.34 1.01

Figure 3. Calculated distance-dependent binding energies of defect pairs obtained by taking the (a) BiLi or NbLi and (b) BiNb defect centers as the reference position. Calculations are performed at the HSE06 level. The Fermi energy is assumed to correspond to the VBM. C

DOI: 10.1021/acs.inorgchem.8b03167 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry The NbLi4+ + VLi− pair is taken as a reference to measure the distances. The BiLi4+ + VLi−, BiLi2+ + VLi−, and NbLi4+ + VLi− defect pairs have negative binding energies, indicating that they prefer to cluster together. The binding energies of BiLi4+ + VLi− are overall 0.25 eV higher than those of NbLi4+ + VLi− because of the higher electronegativity of Bi than that of Nb. It can be seen that VLi− prefers to bond to the SNN site rather than the FNN site of both BiLi4+, BiLi2+ and NbLi4+; that is, the placement of VLi− in the same xy-plane as the positive defects is favorable. In contrast, the BiLi4+ + NbLi4+ and BiLi4+ + BiNb0 defect pairs have positive binding energies, illustrating that they do not tend to cluster together. In particular, the largest binding energies of the BiLi4+ + NbLi4+ defect pairs among all the investigated defect pairs indicate that BiLi4+ and NbLi4+ should be treated as isolated defects because of the strong Coulomb repulsion between the same highly positive charged defects. Moreover, the BiNb0 + VLi− defect pair could also be clustered when VLi− locates at the FNN site of BiNb0 on the basis of its negative binding energy. Furthermore, BiNb2− and BiLi2+ defects could be stably clustered when BiLi2+ locates at the FNN site of BiNb2−. These conclusions could all be treated as the basis to construct complicated defect cluster models. As revealed in our previous study,9 the photoexcitation process in Bi-doped congruent LiNbO3 refers to the intrinsic NbLi bipolaron and BiLi small polaron. The polarons are formed by trapping two electrons at the NbLi4+ and BiLi4+ defects. The question is whether the presence of NbLi defects will influence the BiLi small polaron. Therefore, we constructed a BiLi4+ + NbLi4+ defect pair model in the 120-atom supercell by placing BiLi4+ and NbLi4+ separately at a distance of ca. 8 Å to prevent interactions with each other. Then, we added two and four electrons, respectively, to the BiLi4+ + NbLi4+ pair and examined the lattice distortion and where the electrons were trapped. The calculated charge density distribution maps are shown in Figure 4. Figure 4a shows that when the BiLi4+ +

similar map as that for a single BiLi2+ defect.9 The electrontrapping at BiLi causes the local lattice distortion of the nearestneighboring O atoms, which is consistent with the features of the small polaron. In the BiLi2+ + NbLi4+ defect pair, the Bi−O bond lengths are 2.19 and 2.09 Å, which are quite similar to those (2.18 and 2.09 Å) of the single defect.9 Therefore, we can conclude that the presence of NbLi defects will not influence the features of the BiLi2+ small polaron. When BiLi2+ + NbLi4+ defect pair captures two additional electrons, all the electrons locate near the Bi closest to its nearest-neighbor O atoms in the z-direction, as is shown in Figure 4b. The Coulomb repulsion between the trapped electrons and the neighbor O atoms also leads to the local lattice distortion of the nearest-neighbor O atoms. Thus, the BiLi defect is pushed in the opposite z-direction, and the Bi−O bond lengths are elongated by 7.18%. The local lattice distortion of BiLi0 in the defect pair is also similar to that for the single BiLi0 defect, and the lattice environment of NbLi remains almost unchanged during electron capture. This result further confirms that BiLi has stronger electron capture ability compared to that of the NbLi defect. Therefore, the defect pair could be treated as BiLi0 + NbLi4+. Because the trapping of electron carriers in the crystal is more favorable around BiLi, the intrinsic photorefractivity induced by NbLi could be suppressed to some extent. However, because Bi prefers to substitute NbLi4+ rather than the normal Li site,9 the number of intrinsic NbLi4+/2+ PR centers in the crystal will decrease with increasing Bi concentration. This will also suppress the intrinsic photorefractivity of the LiNbO3 crystals. Therefore, the interaction between Bi and intrinsic defects could influence the PR properties of LiNbO3 by affecting the electron-trapping and changing the ratio of the two PR centers. 3.2. Structure and Energetics of the Defect Clusters. According to the well-accepted Li-vacancy model, CLN contains many intrinsic NbLi4+ and VLi− point defects. In Bi:CLN, these intrinsic defects might be charge compensated by Bi dopants to maintain the electrical neutrality of the whole system. Both experiment and theory indicate that Bi prefers to substitute NbLi first, and with increasing Bi concentration, all the NbLi sites disappear. Bi prefers to be located at the normal Li site and then at Nb sites.6,9 Therefore, at lower concentration, BiLi4+, NbLi4+, and VLi− could coexist in the crystal and form a BiLi4+ + NbLi4+ + 8VLi− charge-neutral cluster in CLN. When the Bi concentration increases to the point that all NbLi sites disappear, the defect cluster becomes BiLi4+ + 4VLi−. It is also possible to form BiLi4+ + BiNb0 + 4VLi− defect clusters when Bi begins to substitute Nb in the lattice. It should be noted that NbLi2+ was not used to form the defect cluster models because NbLi4+ has been found to have a weaker electron capturing ability than BiLi4+; thus, the formation of BiLi2+ is more favorable than that of NbLi2+ in the Bi-doped CLN crystals. Furthermore, we also constructed chargecompensated cluster models composed of BiLi2+ and the intrinsic defects and compared their formation energies with the clusters composed of BiLi4+ and the intrinsic defects, as shown in Table 3. Overall, the BiLi4+-related clusters have lower formation energies per defect than the BiLi2+-related clusters, indicating that the BiLi2+-related clusters are less stable. It should be noted that the present formation energies include the configurational entropies at 300 K, which is 0.77, 0.44, 0.55, 0.67, 0.30, and 0.41 eV for BiLi4+ + NbLi4+ + 8VLi−, BiLi4+ + 4VLi−, BiLi4+ + BiNb0 + 4VLi−, BiLi2+ + NbLi4+ + 6VLi−, BiLi2+ + 2VLi−, and BiLi2+ + BiNb0 + 2VLi− clusters. At the annealing

Figure 4. Charge density difference maps of BiLi4+ + NbLi4+ defect pairs after the capture of two (a) and four (b) electrons calculated at the HSE06 level. Blue and yellow regions represent electron depletion and accumulation respectively. The distances between BiLi(NbLi) and its neighboring O atoms are presented in angstrom units (Å).

NbLi4+ pair captures two electrons, the electrons mainly distribute around the BiLi defect rather than NbLi defect, indicating that BiLi4+ has stronger electron capture ability. In this case, the defect pair can be treated as BiLi2+ + NbLi4+. The captured electrons are found to fill the space between Bi and its nearest-neighbor O atoms along the z-direction, resulting in a D

DOI: 10.1021/acs.inorgchem.8b03167 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 3. Comparison of the Formation Energies (eV) of the Clusters and the Values Per Defect for the Charge-Compensated Defect Clusters Composed of +4 or +2Charged BiLi and Intrinsic Defects Calculated at the DFT-PBE Level formation energy clusters

T = 300 K

BiLi4+ + NbLi4+ + 8VLi− BiLi4+ + 4VLi− BiLi4+ + BiNb0 + 4VLi−

17.21 8.262 7.925

BiLi2+ + NbLi4+ + 6VLi− BiLi2+ + 2VLi− BiLi2+ + BiNb0 + 2VLi−

14.22 5.239 5.555

formation energy per defect T = 1423 K

BiLi4+-Related Clusters 20.08 9.932 9.985 BiLi2+-Related Clusters 16.73 6.359 7.065

T = 300 K

T = 1423 K

1.721 1.652 1.321

2.008 1.986 1.664

1.778 1.746 1.388

2.091 2.120 1.766

NbLi4+ + (BiLi4+ + 8VLi−) and BiLi4+ + (NbLi4+ + 8VLi−), respectively. The dependence of the formation energies of these two extreme cases on the number of VLi− located at SNN sites is plotted in Figure 5. χSNN (χ = 2−6) in this figure

temperature of 1150 °C (1423 K) experimentally,6 the contribution of configurational entropy to the formation energies is increased to 3.64, 2.11, 2.61, 3.17, 1.42, and 1.92 eV. Therefore, the calculated formation energies at annealing temperature will be 1−3 eV higher than those at room temperature. The influence of configurational entropy at annealing temperature is larger for the clusters with more single defects. For example, the calculated configurational entropy for BiLi4+ + NbLi4+ + 8VLi− is 3.64 eV at 1423 K, which is almost twice the value of BiLi2+ + 2VLi− (1.92 eV). However, from Table 3 we can see that such an increase of formation energies (even at high temperature) does not change the relative stability of the BiLi4+- and BiLi2+-related clusters at high temperature. Moreover, in our previous work, we have found that BiLi4+ is much more stable than BiLi2+ in the majority of LiNbO3 samples.9 Therefore, we preferentially discuss the BiLi4+ + NbLi4+ + 8VLi−, BiLi4+ + 4VLi−, and BiLi4+ + BiNb0 + 4VLi− defect clusters in the subsequent sections. The Fermi level can be closer to the conduction band in the Bi-doped LiNbO3, since Bi is assumed to be a donor. In this case, Bi can also be located at Nb-site for the formation of acceptor-like BiNb2− defect according to the calculated formation energies of Bi dopants in our previous study.9 According to the experiments, Bi dopants begin to substitute Nb sites only when all the NbLi defects disappear. Therefore, the 2BiLi2+ + BiNb2− + 2VLi− and BiLi2+ + BiNb2− defect clusters could also be formed and have been considered in this work. For large models that contain at least five single defects, finding the most energetically preferable configuration is challenging because the large number of cluster configurations does not allow for a complete energy comparison of all conceivable structural models. In this work, we constructed three cluster models in a step-by-step manner by considering the binding ability of single defects and checking if the new structure is more stable than that of the last step. We take BiLi4+ + NbLi4+ + 8VLi− as an example to show the steps for identifying the most stable cluster configuration. First, we examine the distribution of VLi− around the two positive BiLi4+ and NbLi4+ charge centers. By comparing the binding energies in Figure 3a, the VLi− defects are found to bond preferably with BiLi4+ and NbLi4+, first at the SNN site and then at the FNN site. Therefore, we only consider adding eight VLi− at the SNN or FNN sites of BiLi4+ and NbLi4+ in the following steps. The single defects in the clusters including BiLi4+, NbLi4+, and VLi− all lie in the Li sublattice. As shown in Figure 2a, BiLi4+ and NbLi4+ all have six equivalent FNN sites, labeled A1A2 ... A6 and A1′A2′ ... A6′, and six equivalent SNN sites, labeled B1B2 ... B6 and B1′B2′ ... B6′. We first consider two extreme cases, namely, eight VLi− all locate around BiLi4+ or NbLi4+, which are marked

Figure 5. Defect formation energies of BiLi4+ + (NbLi4+ + 8VLi−) and NbLi4+ + (BiLi4+ + 8VLi−) as a function of the number of VLi− located at the SNN sites calculated at the DFT-PBE level.

indicates that there are χVLi− at the SNN sites and (8 − χ)VLi− at the FNN sites. We found that both NbLi4+ + (BiLi4+ + 8VLi−) and BiLi4+ + (NbLi4+ + 8VLi−) clusters have the lowest formation energies when five VLi− locate at the SNN sites. This indicates that it is also energetically favorable to locate VLi− at the SNN sites of BiLi4+ or NbLi4+ in the cluster models, which is a trend similar to that observed for the defect pairs. Next, we determined how to distribute the eight VLi− to obtain the most stable cluster configuration. We use (BiLi4+ + χVLi−) + [NbLi4+ + (8 − χ)VLi−] to express the VLi− distribution, where χ represents the number of VLi− located around BiLi4+. We first consider the SNN location of BiLi4+ or NbLi4+ and, then, the FNN sites according to our previous calculation results. The final calculated formation energies of the most stable (BiLi4+ + χVLi−) + [NbLi4+ + (8 − χ)VLi−] clusters are shown in Figure 6. When the VLi− defects are evenly distributed around BiLi4+ and NbLi4+ (χ = 4), the defect cluster is the most stable. In this case, the BiLi4+ + NbLi4+ + 8VLi− cluster could be treated as a combination of the NbLi4+ + 4VLi− and BiLi4+ + 4VLi− clusters. Because we have obtained the most stable configuration of the NbLi4+ + 4VLi− cluster as three VLi− at the SNN sites and one VLi− at the FNN site in our previous work,17 we fixed the structure of NbLi4+ + 4VLi− E

DOI: 10.1021/acs.inorgchem.8b03167 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

BiLi4+ and NbLi4+, we obtained the most stable configuration of the BiLi4+ + NbLi4+ + 8VLi− cluster, as shown in Figure 7a. As

Figure 6. Defect formation energies of (BiLi4+ + χVLi−)+[NbLi4+ + (8 − χ)VLi−] clusters as a function of the number of VLi− calculated at the DFT-PBE level. Figure 7. Configurations of the energetically most favored defect clusters: (a) BiLi4+ + NbLi4+ + 8VLi−, (b) BiLi4+ + 4VLi−, (c) BiLi4+ + BiNb0 + 4VLi−, (d) 2BiLi2+ + BiNb2− + 2VLi−, and (e) BiNb2− + BiLi2+. The gray, dark gray, light blue, and purple balls indicate Li, Nb, O, and Bi, respectively. The black dashed circles and blue dashed circles represent VLi and NbLi. The distances indicated in the figures are all in angstrom units (Å).

cluster and then changed the location of the remaining four VLi− around BiLi4+. In Table 4, we list all the possible configurations and formation energies for the (BiLi4+ + 4VLi−) + (NbLi4+ + 4VLi−) Table 4. Possible VLi− Locations around BiLi4+ and NbLi4+ and the Corresponding Formation Energies, Ef, of the (BiLi4+ + 4VLi−) + (NbLi4+ + 4VLi−) Cluster Calculated at the DFT-PBE Levela VLi− distribution around BiLi4+ 3FNN+1SNN

2FNN+2SNN

1FNN+3SNN

4SNN

VLi− location

Ef (in eV)

A4A5A6B1 - B1′B3′B5′A4′ A4A5A6B2 - B1′B3′B5′A4′ A4A5A6B3 - B1′B3′B5′A4′ B1B4A1A4 - B1′B3′B5′A4′ B1B5A1A4 - B1′B3′B5′A4′ B1B4A4A6 - B1′B3′B5′A4′ B1B5A5A6 - B1′B3′B5′A4′ B1B3B5A4 - B1′B3′B5′A4′ B1B3B5A5 - B1′B3′B5′A4′ B1B3B5A6 - B1′B3′B5′A4′ B1B3B6B4 - B1′B3′B5′A4′ B1B2B3B4 - B1′B3′B5′A4′ B1B2B3B5 - B1′B3′B5′A4′

17.68 17.57 17.56 17.40 17.39 17.48 17.50 17.34 17.35 17.35 17.30 17.20 17.24

shown, the cluster reaches 1 nm in size. The whole cluster suffers a large lattice deformation, breaking the C3 symmetry of the LiNbO3 crystal. The formation energy is thus reduced by 5.4 eV compared to the dilute limit, and such a large energy reduction makes the single defects cluster together stably. We noticed that the increase of formation energies (even at high temperature) owing to the configurational entropy could not compensate to the energy reduction owing to the defect clustering. Therefore, such defect cluster is also stable in the high-temperature process from the aspect of energetics. To construct the BiLi4+ + 4VLi− cluster, VLi− are added to the BiLi4+ + VLi− defect pair one by one to guarantee that the energy of this structure is lower than the former. This procedure is the same as that used to construct the NbLi4+ + 4VLi− defect cluster in ref 17. In addition, only the FNN and SNN sites of BiLi4+ are considered. The most stable configuration of the BiLi4+ + 4VLi− cluster is shown in Figure 7b. One VLi− is located at the FNN site of BiLi4+, whereas three VLi− are located at the SNN sites. This cluster shows the same defect location as that of the NbLi4+ + 4VLi− cluster. To construct the BiLi4+ + BiNb0 + 4VLi− cluster model, we added one BiNb0 to the FNN and SNN sites of one VLi− in the most stable BiLi4+ + 4VLi− cluster configuration according to the binding energies of BiNb0-VLi− in Figure 3b. As shown from Figure 7c, the whole cluster becomes most stable when BiNb0 is located at the FNN site of VLi−. The introduction of BiNb0 does not cause further large lattice distortion with respect to the BiLi4+ + 4VLi− cluster. This is because charge-neutral BiNb0 can bond weakly with the BiLi4+ + 4VLi− cluster via a VLi− defect. We construct the 2BiLi2+ + BiNb2− + 2VLi− cluster by treating the cluster as (BiLi2+ + 2VLi−) + (BiLi2+ + BiNb2−). We first find the most stable BiLi2+ + 2VLi− cluster by comparing the formation energies of all possible arrangements of putting two VLi− at the FNN and SNN sites of BiLi2+. On the basis of the most stable BiLi2+ + BiNb2− defect pair, we have found in Figure 3b, we tested the distance between the two BiLi2+ defects to

a

The configurational entropy at T = 300 K has been included in the calculation of formation energies. A1A2 ... A6 and A1′A2′ ... A6′ indicate the FNN sites of BiLi4+ and NbLi4+, whereas B1B2 ... B6 and B1′B2′ ... B6′ represent the corresponding SNN sites.

cluster. We found that the formation energies of the BiLi4+ + NbLi4+ + 8VLi− clusters were lower when more VLi− sites occupied the SNN position of BiLi4+. It should be noted that the calculated formation energies include the configurational entropies at 300 K, which is 0.77 eV for this cluster. The calculated formation energies at annealing temperature will overall be ∼3 eV higher than those at room temperature. The relative stability of different arrangements for the (BiLi4+ + 4VLi−) + (NbLi4+ + 4VLi−) cluster will not be changed because the contribution of configurational entropy is same. We obtained the most stable configuration of the BiLi4+ + NbLi4+ + 8VLi− cluster as that having four VLi− located at the SNN sites of BiLi4+, three VLi− located at the SNN sites of NbLi4+, and one VLi− located at the FNN site of NbLi4+. Finally, after testing the dependence of the formation energies on the distance between F

DOI: 10.1021/acs.inorgchem.8b03167 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry ensure the lowest energy of 2BiLi2+ + BiNb2− + 2VLi− cluster. The most stable configurations of the 2BiLi2+ + BiNb2− + 2VLi− and BiLi2+ + BiNb2− defect clusters are shown in Figure 7d,e. Because we focus on the interaction mechanism between Bi dopants and the intrinsic defects rather than the interaction between Bi dopants, we therefore discuss the stability and electronic structures of the BiLi4+ + NbLi4+ + 8VLi−, BiLi4+ + 4VLi−, and BiLi4+ + BiNb0 + 4VLi− clusters in the subsequent sections. 3.3. Bi-Doping Stability in CLN. The complexity of Bidoping also varies in SLN and CLN crystals because of the intrinsic defects. To evaluate the influence of the intrinsic defects on the relative stability of the most stable BiLi4+ dopant, we compared the formation energies for BiLi4+ in a perfect LiNbO3 lattice (SLN) and those of crystals with the above investigated defect clusters (CLN). The formation energies of BiLi4+ were calculated using eq 1, and the results are listed in Table 5. The calculated formation energies are dependent on

calculated the partial density of states (PDOSs) for BiLi4+, BiNb0, and the defect clusters composed of Bi and intrinsic NbLi4+ and VLi− defects, as shown in Figure 8. To reduce the

Table 5. Comparison of the Defect Formation Energies of BiLi4+ in SLN and CLNa Bi location BiLi4+@SLN BiLi4+@[BiLi4+ + NbLi4+ + 8VLi−] BiLi4+@[BiLi4+ + 4VLi−] BiLi4+@[BiLi4+ + BiNb0 + 4VLi−]

formation energy (in eV) 4EF 4EF 4EF 4EF

− − − −

3.80 2.45 1.67 1.48

Figure 8. PDOSs of (a) pristine LiNbO3; crystals with (b) BiLi4+, (c) BiNb0, (d) BiLi4+ + NbLi4+ + VLi−, (e) BiLi4+ + VLi−, and (f) BiLi4+ + BiNb0 + VLi− defects determined from DFT-HSE06 calculations. Only the dominant atomic state contributions are shown.

a

EF indicates the Fermi level.

the Fermi level. The symbols BiLi4+@SLN, BiLi4+@[BiLi4+ + NbLi4+ + 8VLi−], BiLi4+@[BiLi4+ + 4VLi−], and BiLi4+@[BiLi4+ + BiNb0 + 4VLi−] in the table represent the BiLi4+ in SLN and in LiNbO3 crystals with BiLi4+ + NbLi4+ + 8VLi−, BiLi4+ + 4VLi−, and BiLi4+ + BiNb0 + 4VLi− defect clusters. As shown, the incorporation of BiLi4+ into SLN has the lowest formation energy, and the formation energy difference between SLN and CLN is as large as 1.35−2.32 eV. Thus, it is more energetically favorable to incorporate BiLi4+ into SLN than CLN. In CLN crystals, a large number of VLi− is needed to compensate for the two highly charged NbLi4+ and BiLi4+ defects if we take the BiLi4+ + NbLi4+ + 8VLi− cluster as an example. In this case, the absence of many Li atoms significantly reduces the energy of the whole system. However, the large lattice relaxation caused by the BiLi4+ + NbLi4+ + 8VLi− cluster could further reduce the system energy. However, the energy gain due to the intrinsic defects cannot compensate the increase in energy caused by the formation of the defect cluster. Therefore, the formation energy of BiLi4+ in SLN is still smaller than those in CLN. As expected, it becomes more difficult to incorporate Bi into the CLN lattice with increasing Bi concentration. The formation energy of BiLi4+@[BiLi4+ + NbLi4+ + 8VLi−] is found to be about 1 eV lower than those of BiLi4+@[BiLi4+ + 4VLi−] and BiLi4+@[BiLi4+ + BiNb0 + 4VLi−]. The energy gain of 1 eV mainly arises from the larger lattice relaxation of the NbLi4+ defect and more VLi− sites. In our previous study, we found that a single VLi defect has little influence on both the lattice relaxation and energetics of LiNbO3, but the impact of a large number of VLi sites in the defect clusters cannot be ignored. Therefore, in the next section, we will focus on the influence of both NbLi and VLi on the electronic structures of Bi:LiNbO3. 3.4. Interaction of Bi Electronic States with Intrinsic Defects. To understand the effect of the interaction between Bi and the intrinsic defects on the electronic structures, we

influence of the number of single defects on the electronic structures, we did not use the above investigated chargecompensated cluster models. Instead, we used the defect cluster models that contain each kind of defect. Compared with the pristine LiNbO3 (Figure 8a), it can be seen that BiLi4+ and BiNb0 defects could all introduce one empty Bi 6s0 defect state at 2.88 and 3.45 eV in the band gap, as shown as the Figure 8b,c. When BiLi4+ interacts with intrinsic defects to form a BiLi4+ + NbLi4+ + VLi− cluster (Figure 8d), the defect state downshifts by 0.26 eV with respect to that of BiLi4+. To understand the origin of the defect state movement, we broke down the relaxation of the whole cluster to the relaxation of one or two single defects in the cluster and identified the relaxation of which defect is responsible for the defect state movement. The calculated PDOSs are shown in Figure 9. Compared to the BiLi4+ + NbLi4+ + VLi− cluster (Figure 9a), the defect level does not move as VLi− is relaxed, including the cases modeling the relaxation of both BiLi4+ + VLi− and NbLi4+ + VLi− pairs (Figure 9b,c) or VLi− alone (Figure 9g). In contrast, if we keep V Li − unrelaxed (Bi Li 4+ or Nb Li 4+ individually or both relaxed, Figures 9d−f), the defect state downshifts by 0.27 eV. Therefore, the relaxation of VLi− is one of the key factors that account for the defect state downshift of the BiLi4+ + NbLi4+ + VLi− cluster. This conclusion is contrary to our inference that NbLi4+ may be the main influencing factor, because it induces large lattice relaxation, and introduces the Nb 4d electronic state at the conduction band minimum (CBM). We believe that NbLi4+ does not have an effect because it is located far from BiLi4+, and the interaction of their electronic states is thus avoided. For BiLi4+ + VLi−, Figure 10a,b shows that the defect state downshifts by 0.15 eV with respect to that of BiLi4+. In Figure 10c−e, we also calculated the PDOSs of fully and partly G

DOI: 10.1021/acs.inorgchem.8b03167 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Similarly, we investigated the interaction of the electronic states of the single defects in BiLi4+ + BiNb0 + VLi− cluster. We found that the introduced defect states can be treated as the sum of those of independent BiLi4+ and BiNb0 defects, whereas the effect of VLi− is relatively weak. Notably, the defect state of BiLi4+ is deeper than that of BiNb0. Therefore, when the cluster captures electrons, the electrons prefer to fill in the defect state of BiLi4+ first. Therefore, BiLi4+/2+ is also the dominant PR center when the Bi concentration is high. However, the interaction of the single defects makes the Nb 4d states below the CBM downshift somewhat, leading to a reduction in the electron transition energy from the defect states to the conduction band.

4. CONCLUSION In conclusion, we have investigated the interactions between the Bi dopants and the intrinsic defects in LiNbO3, including the charge compensated configurations, the relative stability, and the electronic structures. We constructed BiLi4+ + NbLi4+ + 8VLi−, BiLi4+ + 4VLi−, and BiLi4+ + BiNb0 + 4VLi− charge-neutral cluster models to include the effect of Bi concentration. By starting with the binding ability between the single defects in the clusters, we obtained the most stable configurations for each cluster step-by-step. We found that when more VLi− sites are needed to compensate the positively charged defects such as the BiLi4+ + NbLi4+ + 8VLi− cluster the formation energy of Bi is dramatically reduced because of the large lattice deformation compared to those of other clusters. However, VLi− is found to be the main source of the defect level movement in the clusters with respect to that of BiLi4+. Our research results show that BiLi4+ has a stronger electron capture ability than NbLi4+ in Bi:CLN. The features of the BiLi polaron remain unchanged in the congruent crystals. This is important for the practical applications of Bi:LiNbO3 because doping in stoichiometric crystals has not been realized yet.

Figure 9. PDOSs of fully and partly relaxed BiLi4+ + NbLi4+ + VLi− clusters calculated at the DFT-HSE06 level.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yanlu Li: 0000-0002-1983-0368 Xian Zhao: 0000-0002-1523-4534 Notes Figure 10. PDOSs of fully and partly relaxed BiLi4+ + VLi− clusters calculated at the DFT-HSE06 level.

The authors declare no competing financial interest.

relaxed BiLi4+ + VLi− clusters at the DFT-HSE06 level to understand the origin of the defect state movement. As shown in Figure 10e, when VLi− relaxes alone, the position of the defect level is the same as that of the BiLi4+ + VLi− pair, further confirming that the relaxation of VLi− is the main reason for the downshift in the defect state. Such an effect could be amplified in the charge-neutral clusters because of the large number of VLi− defects. In contrast, we found that the defect level of BiLi4+ + VLi− is 0.11 eV higher than that of BiLi4+ + NbLi4+ + VLi−. This shift should be due to NbLi4+. However, in the discussion above, we have confirmed that the interaction of the electronic states of BiLi4+ and NbLi4+ can almost be ignored. Therefore, the lattice relaxation of NbLi4+ may contribute to the further redshift of the BiLi4+ + NbLi4+ + VLi− defect state compared to that of BiLi4+ + VLi−.

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ACKNOWLEDGMENTS

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REFERENCES

We gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant No. 51502158).

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