Microscopic Properties of Mg in Li and Nb Sites of LiNbO3 by First

Article pubs.acs.org/JPCC

Microscopic Properties of Mg in Li and Nb Sites of LiNbO3 by FirstPrinciple Hybrid Functional: Formation and Related Optical Properties Yanlu Li, Lili Li, Xiufeng Cheng,* and Xian Zhao* State Key Lab of Crystal Materials, Shandong University, Jinan 250100, China S Supporting Information *

ABSTRACT: As the traditional and basic doping ion, Mg is found to strongly lower the photorefractivity of LiNbO3 when it reaches the threshold concentration, and it is always used to codope with other functional ions to improve both the photorefractive and nonphotorefractive properties of LiNbO3. Thereby we investigate the basic characteristic of Mg doping, such as the local distortion produced by Mg substitution and the related electronic structures, which mainly determine a broad range of optical properties of LiNbO3 by employing density functional theory (DFT) within hybrid exchange-correlation functional. The effect of Mg concentration and the interaction of Mg with intrinsic point defects according to the Li-vacancy model are also examined. It is found that, when Li is deficient, MgLi with +1 charge state (MgLi+) and MgNb with −3 charge state (MgNb3−) are energetically preferable with the increase of Fermi energy. Overall, MgNb3− exhibits much more contributions than MgLi+ to the electronic structure and optical properties of LiNbO3; however, their interaction with intrinsic point defects NbLi4+ and VLi− is limited. According to our calculation results, we expect to codope Mg with photorefractive ions such as Fe, Cu, etc. to reduce the electron−hole combination and change the photorefractive properties of LiNbO3 by controlling Mg doping concentration.

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INTRODUCTION Bulk crystals of doped LiNbO3 are important for a variety of applications using nonlinear optical,1 ferroelectric,2 and photorefractive effects.3 It is well-demonstrated that LiNbO3 can be modified for a specific application by controlling the extrinsic and intrinsic defect structures in crystal through doping and composition modification.4−7 Specifically, the optical damage in the visible and near-infrared (IR) is significantly suppressed by high doping of 4.6 mol % Mg in a congruent melt,4,5,8−10 and on the contrary, the photorefractivity and the light-induced absorption change in highly Mg-doped LiNbO3 (Mg:LiNbO3) are greatly enhanced in the ultraviolet (UV).6,7 Such threshold behavior in the visible and near-IR is phenomenologically ascribed to the increase of photoconductivity due to the disappearance of Nb antisite NbLi4+ defect in highly doped Mg:LiNbO3,5 while the mechanism for the opposite threshold behavior in the UV is not clear up to now. It is rather well admitted that the dependence of optical properties on defect content is linked to the site incorporation of Mg2+ ions in the lattice. It was demonstrated in various literature articles that Mg2+ ions first substitute at Li sites, thereby preventing the formation of Nb antisites until no antisites are left, and then Mg begins to incorporate on the Nb sites at larger concentration.11−15 Also, Donnerberg et al.16,17 have determined by lattice energy minimization calculations that the possible incorporation on interstitial sites can be discarded and only Li and Nb sites are energetically favorable for Mg impurities. © 2017 American Chemical Society

Generally, the incorporation of Mg in LiNbO3 was experimentally studied mostly concerning the Mg incorporation process and the nonphotorefractive properties of Mg:LiNbO3.14−18 More importantly and quite surprisingly, there have been few experimental and theoretical studies19,20 reporting on the direct investigation of the most basic characteristics of Mg doping such as the lattice location and the feature of electronic structure, which mainly determines a broad range of optical properties of LiNbO3. On the other hand, Mg is always used as basic ion codoping with other functional ions, such as photorefractive ion Fe, Cu, etc. to make LiNbO3 crystals own both nonphotorefractive and photorefractive properties; therefore, it becomes important to first understand well how the Mg doping influences the photorefractive and nonphotorefractive properties of LiNbO3. Besides, the widely used LiNbO3 samples contain plenty of intrinsic point defects, such as Nb antisite NbLi and Li vacancy VLi according to the Li-vacancy defect model.21 We thus also focus on the interaction of Mg impurity with these intrinsic point defects in this work. A state-of-the-art first-principles approach based on density functional theory (DFT) offers an alternative method for such quantitative studies, which is highly complementary to experimental studies. To our knowledge, the reported firstReceived: February 8, 2017 Revised: March 30, 2017 Published: April 4, 2017 8968

DOI: 10.1021/acs.jpcc.7b01274 J. Phys. Chem. C 2017, 121, 8968−8975

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The Journal of Physical Chemistry C

is modeled by replacing one, two, three, and four isolated Li or Nb ions by Mg, which corresponds to 0.83, 1.67, 2.50, and 3.33 atom % and 4.16, 8.33, 12.5, and 16.6 mol %, respectively. The atom concentration is used in the following discussion. Monkhorst−Pack43 k-point meshes (4 × 4 × 4 and 2 × 2 × 2) are employed to sample the Brillouin zones for PBE and HSE calculations, respectively. The calculated electronic band gap of LiNbO3 by HSE is 5.07 eV, which is a little smaller than the calculated value of 5.21 eV in our previous paper28 due to the larger supercell used here. We calculate the formation energy of doping ion X with charge state q dependent on the Fermi level position according to44,45

principle studies on Mg:LiNbO3 up to now are limited to the stability and the optical absorption by using a (semi)local generalized gradient approximation (GGA) functional.22−24 The electronic structure and the interaction of Mg with intrinsic point defects were not discussed. On the other hand, the (semi)local functional always underestimates the band gaps of semiconductors and insulators,25 which severely affects the predictive power of the approximation when applied to defect levels26,27 and is particularly severe in cases of strong correlations such as those occurring in the highly localized Nb d states.28,29 Besides, GGA suffers from the self-interaction error, which can also affect the position of defect levels with respect to the band edges. In the present work, the energetics, electronic, and optical properties of Mg:LiNbO3 are studied with hybrid DFT calculations, such as the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional proposed by Heyd et al.30,31 In this approach the electron exchange and correlation functionals contain some amount of exact exchange from Hartree−Fock theory, and it is demonstrated to result in a reliable description of defect formation energies, defect levels, and the localization of the electron distribution in wide-bandgap semiconductors.32−37

Ef (X q) = Etot(X q) − Etot(bulk) +

∑ niμi + q(EF + Ev + ΔV ) i

(1)

where Etotal(Xq) is the total energy derived from a supercell with doping ion X, Etotal(bulk) is the total energy of the perfect supercell, ni indicates the number of atoms of species i that have been added or removed upon doping process, and μi are the corresponding chemical potentials. EF is the Fermi level with respect to the bulk valence-band maximum (VBM) Ev, and ΔV is a correction term46 that aligns the reference potential in the doping supercell with that in the bulk. The chemical potentials μi depend on the preparation conditions. A different choice of the reference state will modify the relative stability of the investigated doping defects. In the following we assume Nb-rich conditions (line CE in Figure 2 in ref 27), consistent with the Li-deficient composition of congruent samples. On this basis, we repeat the calculation of the chemical potentials with the same considerations as our previous work28 but by HSE hybrid functional instead of (semi)local PBE functional. The requirements by HSE calculations are visualized in Figure 2, and line CE shows the chemical potentials of Li and Nb in Li-deficient condition to be −3.45 and −21.68 eV, respectively. The chemical potential of Mg should meet the requirement to form its oxide MgO as in the following relation:

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COMPUTATIONAL DETAILS The present calculations employ the Vienna ab initio simulation package (VASP)38,39 implementation of DFT in conjunction with the projector-augmented-wave (PAW) formalism.40 Thereby the Li 2s1, Nb 4p65s14d4, O 2s22p4, and Mg 3s2 states are treated as valence electrons. The electronic wave functions are expanded in plane waves using an energy cutoff of 400 eV. The electron exchange and correlation (XC) within GGA of Perdew, Burke, and Ernzerhof (PBE)41 functional is used to optimize the configurations, and the force convergence criterion for the structural relaxation is set to 0.01 eV/Å. All other properties were performed by the screened hybrid functional HSE.30,31,42 In this approach, the long-range exchange potential and the correlation potential are calculated with the PBE functional, while the short-range exchange potential is calculated by mixing a fraction of nonlocal Hartree−Fock exchange with PBE. The screening length and mixing parameter are fixed at 10 Å and 0.25, respectively. Hexagonal supercells containing 120 atoms are used to model the isolated Mg substitution at Li sites MgLi and Nb site MgNb, as shown in Figure 1, as well as the clusters composed by Mg impurities and intrinsic defects NbLi and VLi. Mg concentration

Figure 2. Stability range of the chemical potentials (in eV) of the LiNbO3 constituents. Lines BF and CE correspond to the Li2O and Nb2O5 reference states, respectively. The green shaded region enclosed between points B, C, E, and F represents the thermodynamically allowed range of the chemical potentials.

Figure 1. Ball-and-stick models for defect-free LiNbO3 (a) and material with Mg substitutional Li (b) and Mg substitutional Nb (c). 8969


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The Journal of Physical Chemistry C Δμ(Mg) + Δμ(O) = −ΔHfMgO

notation,48 [Kr]3s0) is most favored for the electron chemical potential in the lower half of the band gap, while MgNb3− is most preferable for the electron chemical potential in the higher half of the band gap. The transition of relative stability from MgLi+ to MgNb3− occurs at EF = 2.32 eV. When the Fermi level is in the very lower part of the band gap, the neutral MgNb transfers to MgNb− at 0.14 eV and then transfers to the most stable −3 state directly at 0.34 eV, while when the Fermi energy lies near the minimum of conduction band (CBM), the stable MgLi+ transfers to its neutral state. However, in the majority of LiNbO3 samples, the Fermi energy lies in the lower part of the fundamental band gap. Our results thus support the experimental observations12,14−18 that Mg impurities mainly incorporate into Li sites as MgLi+, and MgNb3− defects are also detected in the LiNbO3 samples. Interestingly, when we compared the formation energies of Mg substitution with the intrinsic point defects in the samples, we found that only the most stable state of MgLi and MgNb (MgLi+ and MgNb3−) may have lower formation energies than the intrinsic point defects NbLi4+ and VLi− when Fermi energy lies in the half lower part of band gap. This indicates the coexistence of the stable MgLi+ and MgNb3− with the intrinsic point defects NbLi4+ and VLi− in the samples. Due to the strong Coulomb repulsion of MgLi+ and NbLi4+, they will be isolated in LiNbO3, whereas the Coulomb attraction between MgLi+ and VLi− may modify the charge redistribution, which will be discussed in the next section. It is reported experimentally that MgNb3− are only formed after the antisites NbLi4+ are fully replaced by Mg. Combining with our results in Figure 3, we infer that both MgLi+ and MgNb3− could be formed at high Mg concentration, and in such an environment, it is impossible for MgNb3− to interact with any intrinsic point defects. We then present the local structures of the preferable MgLi+ and MgNb3− in Figure 4 in comparison with the defect NbLi4+ and bulk material. It is found that MgLi+ only leads to quite slight local distortion of its first-next-neighboring atom shell due to the movement of Mg along the z direction. Such movement leads to the shortening of the Mg−O bonds and the distance between Mg and its neighboring Nb along the z direction. The distortion caused by Mg substitution is too slight to be ignored compared to the case of NbLi4+, however, due to the similar valent electronic configuration and ionic radius between Li and Mg ions. Then it is inferred that the electronic structure and optical property of LiNbO3 will not be changed

(2)

The enthalpy of MgO is calculated by using the face-centered cubic MgO lattice with Fm3̅m space group. The calculated chemical potential of Mg is −8.04 eV here. The potential correction described by eq 5 of ref 28 is applied in order to account for the effect of charged supercells. Thereby, the weighted average of the experimental values of the 33 static dielectric tensor components ε11 s = 84 and εs = 29 given in ref 47 are used. Also, only the leading correction term is considered in this work as the higher-order terms could be neglected due to the high dielectricity of LiNbO3.

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RESULTS AND DISCUSSION A. Preferable Substitutional Sites of Mg in LiNbO3. As mentioned in the Introduction, Mg impurities prefer to incorporate into Li site to form Mg substitutional Li MgLi at lower concentration, while at higher concentration Mg begins to substitute Nb site to form MgNb defect. Therefore, we first investigate the local structures and the relative stabilities of Mg preferable doping sites in LiNbO3. The calculated formation energies of MgLi and MgNb with possible charge states are shown in Figure 3 in comparison with those of the dominant

Figure 3. Formation energies of Mg incorporation into Li and Nb sites as well as the main intrinsic point defects NbLi and VLi in LiNbO3 as a function of the Fermi energy under Li-deficient condition. Only the most stable charge states of each defect are indicated. The Fermi energy range corresponds to the fundamental band gap of LiNbO3.

point defects NbLi and VLi under Li-deficient condition. It is seen that MgLi with +1 charge state (MgLi+, Kröger−Vink

Figure 4. Local structures of the stable Mg substitutional configurations in LiNbO3 in comparison with the bulk material and the material with Nb antisite defect. The white, green, red, and yellow balls indicate Li, Nb, O, and Mg, respectively. The distances between the defect or the corresponding atoms in the bulk material (noted by the green dashed cycles) and its neighboring ions are presented in the figures (with the unit of Å). The arrows indicate the movement of the ions. 8970


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whole Fermi energy region, which represents (3s0) electronic configuration. One empty shallow impurity state is introduced near the CBM (see Figure 6), leading to the slight shift of the

too much by Mg incorporation into Li sites. Considering that MgLi+ induces small local distortion and is energetically stable in almost the whole range of Fermi energy, electrons could not be trapped at MgLi+ site to form MgLi0. It is noted that the doping concentration considered here is as small as 0.83 atom % and that the lattice distortion of the material may be enlarged or modified by the increase of doping concentration. Besides, in congruent LiNbO3 that contains intrinsic point defects, the local structure around MgLi+ center may also be affected by the attraction of the positive MgLi+ with negative VLi− defects. On the other hand, MgNb3− presents absolutely different local structural relaxation with MgLi+: As a large amount of electrons aggregate around MgNb3−, MgNb3− does not only repulse its first-next-neighboring O atoms back to the doping center but also leads to the attractive movement of Mg with its neighboring Li along the negative direction of the z axis to each other. The Mg−O bond length is therefore enlarged by 7.40%, and the distance between Mg and its neighboring Li is shortened by 6.27%. In fact, the large lattice relaxation is not only found in MgNb with the stable −3 charge state but also with its 0, −1, and −2 charge states. The large lattice distortion is expected to largely affect the electronic structure and the optical response of Mg:LiNbO3. B. Electronic Structures and Related Optical Response of Mg:LiNbO3. To better understand the electronic properties of Mg-doped LiNbO3, we have calculated the partial electronic density of states (PDOS) for the most stable Mg substitutional Li and Nb sites as compared with the bulk crystal (0.83 atom %; see Figure 5a−c). Only the electronic states that mainly contribute to the chemical bonding are shown in the figures. MgLi is found to be stable at the +1 charge state during the

Figure 6. Schematic diagram of impurity levels of MgLi and MgNb with different charge states as well as the clusters formed by Mg and intrinsic point defects NbLi and VLi. For the case of NbLi, only the lowest impurity states for the +2 and +4 charge states are shown. The small blue balls on the black lines represent the electrons on the impurity levels.

conduction band of 0.05 eV to the low energy direction as compared with the bulk material. Due to the strong metallic characteristic, Mg does not introduce any deep and localized impurity state in the electronic band gap. In this case, when MgLi+ captures one electron, the electron is hard to localize in the Mg 3s impurity state but transfers to the empty states in the CBM, such as O 2p and Nb 4d states. This is confirmed by the calculation of the electron density difference of the neutral MgLi as seen in Figure S1 in the Supporting Information, from which we can see that the captured electron is localized at the 2p orbitals of the first-next-neighboring O atoms and the 4d orbitals of the second-next-neighboring Nb atoms. By increasing the MgLi+ concentration from 0.83 to 3.33 atom %, we found more impurity levels generated near the CBM without introducing any deep states in the band gap (see Figure S2). From this point of view, we could conclude that Mg doping with lower concentration (only from MgLi+ defects) could not introduce a new photorefractive center in the crystals and thus influence the photorefractive properties of LiNbO3. When Mg reaches the threshold concentration, MgNb begins to form in the crystal. As shown in Figure 6, a half-occupied state and an unoccupied state are introduced at 0.03 and 0.36 eV, respectively, above the VBM for the neutral MgNb. When neutral MgNb captured one electron to form MgNb−, the halfoccupied state became full-occupied with 0.03 eV downshift to the VBM, while further capturing of one electron (MgNb2−) led to the unoccupied state becoming half-occupied with 0.05 eV downshift to the VBM. Finally, MgNb is stable at its −3 charge state with two degenerated full-occupied impurity states located at 0.13 eV above the VBM. As shown from Figures S3 and S4, these impurity states mainly come from the neighboring O 2p states of MgNb, while the charge distributes to the O atoms of the second-next-neighboring and even farther shell when MgNb exists in its highly charged negative states. We can see that, although Mg substitutional Nb with 0, −1, and −2 charge states

Figure 5. Partial density of states of Mg doping in LiNbO3, including single Mg substitution at Li and Nb sites, as well as the clusters of Mg with intrinsic point defects. Only the dominant contributions of atomic states are shown in the figures. The contribution of Mg is indicated by the green shadow. 8971


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bulk one because of the disappearance of the highest O 2p occupied states and the reduction of the Nb 4d unoccupied states between 5 and 6 eV, which thus reduces the electron transition between them. Another extra optical absorption for MgNb3− occurs at 9−9.5 eV, and it comes from the electron transition of O 2p states of impurity bands near VBM to Nb 4d states at 9.5−10 eV in the conduction band. The same reason accounts for the reduction of the absorption peak at 9.5−10 eV in Figure 7. We also examined the effect of Mg Li + and Mg Nb 3− concentrations on the imaginary part of the dielectric function along the polarization direction as shown in Figure 8. We

introduces some half-occupied and unoccupied impurity states in the electronic band gap that may trap electrons, these states are so close to the VBM (0.03−0.36 eV) that the electrons trapped in these states could easily be recombined with the holes in the VBM. For the most stable −3 charge state, the shallow impurity states are all full-occupied to enhance the electron transition energy and reduce the electron−hole recombination. Therefore, we conclude that MgNb cannot introduce a new photorefractive center in LiNbO3 samples either. From Figure 5 we can see that the formation of MgNb3− leads to the reduction of 0.33 eV of band gap as compared to the bulk material. It should be noted that the energy gap between the impurity states near the VBM to the CBM is 4.75 eV, and the electron transition between them will cause new optical absorption in the UV region. It might be a possible explanation to the phenomenon that the optical absorption is changed in highly doped Mg:LiNbO3 in the UV.6,7 By examining the effect of Mg concentration, we found that, although more impurity states are introduced with the increase of MgNb3− concentration from 0.83 to 3.33 atom %, they are also very close to the VBM and will not seriously influence the photorefractive character of the crystal. Now we turn to the linear optical response of LiNbO3 with Mg doping. In Figure 7 we plot the imaginary part of the

Figure 8. Imaginary part of the dielectric function along the polarization direction of MgLi+ and MgNb3− with increasing doping concentration.

notice that the magnitude and shape of optical absorption peaks of MgLi+-doped LiNbO3 do not change with the increase of the doping concentration up to 3.33 atom %, while there is an obvious break for the case of MgNb3− between the doping concentration of 1.67 and 2.50 atom %: a 0.3 eV redshift of the absorption curves and the combination of two sharp absorption peaks at 5.6 and 6.8 eV to a single one at ∼6.4 eV for the highly doped crystals (see Figure 8). Combining with the PDOS analysis in Figure S4, we infer that the slight red-shift of the absorption curves is due to the additional MgNb3− impurity bands generated above the VBM corresponding to the high MgNb3− concentration. From Figure S4 we found that, when MgNb3− is in its lowest concentration of 0.83 atom %, the conduction band between 5 and 7.5 eV is split into two parts, 5−6 eV and 6−7.5 eV. The electron transitions from VBM to these two sub-bands lead to the two sharp absorption peaks at 5.6 and 6.8 eV as shown in Figure 8. When MgNb3− doping concentration increases up to 2.50 atom %, Nb 4d states in CBM become so weak that the sub-bands are combined to form a whole band that spans into a broad energy region in the conduction band. Therefore, for the MgNb3− doping concentration higher than 2.50 atom %, the electron transitions from

Figure 7. Imaginary part of the dielectric function along the polarization direction of the most stable Mg substitutional configurations (0.83 atom %) and their clusters with intrinsic point defects.

dielectric function of the above considered Mg doping configurations along the polarization direction with Mg concentration of 0.83 atom %. It is not surprising that MgLi+ has little influence on the curve of the imaginary part of the dielectric function due to the similar electronic properties as compared to the bulk crystal, as discussed in the section on electronic structures. The main optical absorption peaks between 5.5 and 7.5 eV come from the electronic transitions from VBM to the lower conduction bands of 5−7.5 eV, while those peaks between 9.5 and 12 eV come from the electronic transitions from VBM to the higher conduction bands of 9−11 eV. On the other hand, MgNb3− leads to a 0.3 eV redshift of the absorption edge as compared to the bulk crystal due to the introduction of the impurity bands above the VBM. Therefore, the absorption edge of MgNb3− is referred to the electronic transition from the impurity bands to the CBM. Besides, the first main absorption peak of MgNb3− becomes weaker than the 8972


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The Journal of Physical Chemistry C VBM to such a broad band in the conduction band leads to just one broad absorption peak at 6.4 eV. It should be illustrated that, when we constructed the highly doped configurations, we put each MgNb3− far away from each other to avoid unreasonable lattice relaxation according to the strong repulsion between them. This means that the optical absorption characteristic of Mg:LiNbO3 can be modified only by the ionic level redistribution caused by the superimposed effect of local lattice relaxation with extreme highly doping. It is essentially different from controlling the optical properties by introducing new electronic states. More importantly, such relaxationinduced modification of optical response can easily be changed if there are other impurities or intrinsic point defects existing in the crystals, and it is known that LiNbO3 is such a kind of crystal with plenty of intrinsic point defects in its congruent melt. Therefore, it becomes important to understand well the microscopic properties of Mg interacted with the intrinsic point defects NbLi and VLi in LiNbO3 crystals. C. Interaction of Mg with Intrinsic Point Defects. In this section, we will discuss the interaction of Mg with intrinsic point defects in LiNbO3 based on the well-known Li-vacancy model, in which it is referred to the Nb antisite NbLi4+ and Li vacancy VLi− as the dominant point defects in the crystals. Here we only focus on how the interaction of Mg with single point defect influences the electronic and optical properties of LiNbO3 and ignore the charge compensation between them. As much research on the Mg doping process indicates, Mg first substitutes the antisite NbLi until there are no antisite in the crystals at all, and then substitutes the normal Li while at the same time Mg substitutional Nb begins to form. It should be noted that, according to the Li-vacancy model, one NbLi4+ defect is charge compensated by four VLi−, and therefore, when Mg occupies all the antisite sites, there are still lots of VLi− defects left in the crystals. Therefore, we consider the interactions of MgLi+ with both NbLi4+ and VLi− as well as with only VLi−, and the interaction between MgLi+ and MgNb3− is also investigated. We first construct all possible cluster configurations of MgLi++NbLi4++VLi−, MgLi++VLi−, and MgLi++MgNb3− in LiNbO3 (labeled as (MgLi++NbLi4++VLi−)@LiNbO3, (MgLi++VLi−)@ LiNbO3, and (MgLi++MgNb3−)@LiNbO3) and examine their relative stabilities in order to find the energetically preferable configuration of three kinds of clusters. The optimized cluster configurations are shown in Figure 9. We found that both NbLi4+ and MgLi+ prefer to locate at the second-nextneighboring sites of VLi− in Li-sublattice but with opposite direction, while MgNb3− at the first-next-neighboring sites of MgLi+ has the lowest formation energy. The MgLi++NbLi4++VLi− cluster reduces the band gap of 0.45 eV as compared with the bulk mainly due to the introduction of impurity bands below the CBM, as shown in Figure 5d. From Figure 5 we also find that the PDOS shape of O 2p states is changed as compared to MgLi+; for example, the sharp O 2p peak at 0.3 eV below the VBM disappears due to the hybridization of 2p states from the neighboring O atoms of both MgLi+ and NbLi4+. Besides, as the CBM of (MgLi++NbLi4++VLi−)@LiNbO3 is mainly contributed from the 4d states of NbLi4+ and its neighboring Nb, the PDOS sharp peak at CBM is obviously changed with respect to the case of MgLi+. It is also found that the small shape PDOS peak at 9−9.5 eV also disappears due to the interaction of MgLi+ with NbLi4+ and VLi−. These electronic characteristics thus exhibit corresponding changes on the linear optical response caused by the electron transitions (see Figure 7): The absorption edge of

Figure 9. Local structures of MgLi++NbLi4++VLi− (a), MgLi++VLi− (b), and MgLi++MgNb3− (c) clusters in LiNbO3. The distances between the defects in each cluster are noted. Li vacancy is labeled by the blue circles.

(MgLi++NbLi4++VLi−)@LiNbO3 has a red-shift of 0.4 eV with respect to the bulk system due to the reduction of band gap. The strengthening of the main peak at 5.5 eV is obviously weakened as the density of electron transition that is responsible for such a peak is reduced due to the disappearance of the O 2p peak near the VBM; in a similar way, the strengthening of the small peak at 8.8 eV also becomes weak due to the disappearance of Mg 3s states at 9−9.5 eV, and the optical absorption around the small peak at 8.8 eV is enhanced due to the new electron transitions from VBM to Nb 4d states at 8.6 eV and Mg 3s states at 9.3 eV. We then compare the results of electronic structures and linear optical response for the MgLi++NbLi4++VLi− cluster and for the three isolated defects (in this work and our previous work28,29). It is found that three kinds of defects have almost “independent” effects on the electronic and optical properties of (MgLi++NbLi4++VLi−)@ LiNbO3. As shown in Figure 6, the impurity states introduced by the MgLi++NbLi4++VLi− cluster can be treated as the sum of the impurity states introduced by MgLi+, NbLi4+, and VLi−, respectively. As discussed above and in our previous work,28 MgLi+ and VLi− all have little contribution to the electronic structure of Mg:LiNbO3, and therefore, the effect of the MgLi++NbLi4++VLi− cluster on the electronic and optical properties of Mg:LiNbO3 is predominantly from the contribution of NbLi4+. According to the above analysis and conclusion, we infer that it is also impossible for the MgLi++VLi− cluster to introduce any deep impurity states in the band gap, and this has been proven by our calculation results in Figures 5 and 6. As MgLi+ and VLi− all have little influence on the electronic structure and optical properties of LiNbO3, we could conclude that the electronic and optical properties of (MgLi++VLi−)@LiNbO3 are similar to those of the bulk crystal (also proved in Figures 5 and 6); the band gap is only reduced by 0.11 eV when introducing the MgLi++VLi− cluster. In a similar way, the electronic structure and optical properties of (MgLi++MgNb3−)@LiNbO3 are brought into correspondence with those of MgNb3−. The band gap of (MgLi++MgNb3−)@LiNbO3 is reduced by 0.34 eV as compared to the bulk material by introducing shallow impurity states above the VBM. The band gap of such a cluster is only 0.01 eV smaller than that of MgLi+, further verifying the 8973


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The Journal of Physical Chemistry C little contribution of MgLi+ in the clusters. It is thus expected to use MgLi+ to charge-compensate with other negative defects including intrinsic point defects and other doping ions to maintain the charge neutrality of Mg:LiNbO3 without introducing any extra huge change of electronic structures. It is found that, no matter whether Mg ions substitute at Li or Nb sites, the interaction of Mg with intrinsic point defects is too limited to change the photorefractive properties of LiNbO3. The changing photorefractive properties of Mg:LiNbO3 are due to the reduction of the NbLi4+/2+ photorefractive center by Mg substituting NbLi. Just due to such “stable” properties, Mg could codope with some photorefractive ions like Fe, Cu etc. to improve both the photorefractive and nonphotorefractive properties of LiNbO3. On the one hand, when there are more than one photorefractive centers in the crystal, Mg could reduce the number of photorefractive centers by replacing the photorefractive ions and thus change the photorefractive properties of LiNbO3. On the other hand, in highly Mgdoped LiNbO3 crystal, the metastable MgNb (q = 0, −1) introduces shallow unoccupied and half-occupied impurity states, which could capture electrons from the valence band, and thus effectively passivates the recombination of electrons in the photorefractive centers and the holes in the valence band.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Xian Zhao: 0000-0002-1523-4534 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant no. 51502158) and the Fundamental Research Funds of Shandong University (Grant no. 2015TB008).

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REFERENCES

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CONCLUSION In conclusion, the stable Mg doping sites in LiNbO3 and their influence on the electronic structure and optical properties such as photorefractive center and optical absorption have been examined by using hybrid density functional theory. The interaction of Mg with the dominant intrinsic point defects according to the Li-vacancy model is also investigated. It is found that under Li-deficient environment MgLi with +1 charge state is the most stable doping configuration when the Fermi level lies in the lower half of the electronic band gap, while MgNb with −3 charge state is energetically preferable when the Fermi level is in the higher half of the band gap. Both MgLi+ and MgNb3− introduce shallow impurity states near the CBM/VBM and will not introduce a new photorefractive center in LiNbO3 crystals due to their closed-shell electronic configurations. Therefore, the photorefractive properties of Mg:LiNbO3 are changed by reducing the NbLi4+/2+ photorefractive center due to the Mg substitution instead of the interaction between Mg and NbLi. Overall, MgLi+ has little influence on the electronic structure and optical properties of LiNbO3 while the effect of MgNb3− is much larger. Although MgLi+ and MgNb3− could form clusters with intrinsic point defects NbLi4+ and VLi−, the interaction between them is quite limited. The effect of the whole cluster on the electronic and optical properties of LiNbO3 could be treated as the sum of the isolated components. We therefore expect to codope Mg with other photorefractive ions such as Fe, Cu, etc. to reduce the electron−hole combination and to change the photorefractive properties of LiNbO3 by controlling Mg doping concentration.

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ence for Mg substitutional Nb in its 0, −1, −2, and −3 charge states, and partial density of states of MgNb3− with different doping concentrations (PDF)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b01274. Isosurface of the electron density difference for Mg substitutional Li in its +1 and 0 charge states, total density of states of MgLi+ with different doping concentrations, isosurface of the electron density differ8974


Article


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Microscopic Properties of Mg in Li and Nb Sites of LiNbO3 by First

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