Tailoring Bandgap of Perovskite BaTiO3 by Transition Metals Co-Doping for Visible-Light Photoelectrical Applications: A First-Principles Study

The physical and chemical properties of V-M″ and Nb-M″ (M″ is 3d or 4d transition metal) co-doped BaTiO3 were studied by first-principles calculation based on density functional theory. Our calculation results show that V-M″ co-doping is more favorable than Nb-M″ co-doping in terms of narrowing the bandgap and increasing the visible-light absorption. In pure BaTiO3, the bandgap depends on the energy levels of the Ti 3d and O 2p states. The appropriate co-doping can effectively manipulate the bandgap by introducing new energy levels interacting with those of the pure BaTiO3. The optimal co-doping effect comes from the V-Cr co-doping system, which not only has smaller impurity formation energy, but also significantly reduces the bandgap. Detailed analysis of the density of states, band structure, and charge-density distribution in the doping systems demonstrates the synergistic effect induced by the V and Cr co-doping. The results can provide not only useful insights into the understanding of the bandgap engineering by element doping, but also beneficial guidance to the experimental study of BaTiO3 for visible-light photoelectrical applications.

Inorganic oxide perovskites ABO 3 have been investigated for photovoltaic applications due to their tunable bandgap [23], wide range of possibilities for switchable component [24], low cost [8], and high chemical stability.Recently, the potential of this class of materials for photovoltaic applications has been demonstrated by several theoretical and experimental studies.However, it is also known that these materials usually have limited light absorption due to the wide bandgaps and poor electrical conductivity [25].Currently, the most common method used to overcome these problems is doping with either metal or non-metal elements.In terms of the feasibility and effectiveness, element doping is one of the most important strategies to regulate the bandgap of oxide perovskites at the atomic scale structure modification.
In one of our previous papers, we have systematically investigated the effects of single element doping with various metals on the performance of BaTiO 3 [26].We showed that impurity levels could be introduced in the bandgap by the metal doping.These impurity levels can act as recombination centers for electrons and holes, which are harmful for the performance of the materials for photovoltaic applications.In general, wide bandgap semiconductors with doping may exhibit some unwanted properties or behaviors [27]: (i) desirable impurities may have limited solubility; (ii) for those impurities that have sufficient solubility, they may form deep levels that are not effective for carrier transitions; and (iii) spontaneous formation of compensating defects.In the literature, it has been shown that some of these unwanted features could be avoided by co-doping two different types of elements [28].Ishii et al. [29] reported that Cr 3+ and Ta 5+ co-doped SrTiO 3 can improve photocatalytic activities.Kako et al. [30] reported a visible-light sensitive TiO 2 with Fe-Ta co-doping ((Fe,Ta) x Ti 1−x O 2 , 0 ≤ x ≤ 1) that has a higher photocatalytic activity than the Fe 3+ doped TiO 2 .Masahiro et al. [31] also reported that N and La co-doped SrTiO 3 had better visible-light absorption (≥400 nm) compared with the pure SrTiO 3 .
In this paper, we screened out the suitable co-doped elements by studying the defect formation energy and electronic properties of the transition metals co-doping on the Ti-site in BaTiO 3 .In comparison to the results of single doping, we evaluated the synergistic effects between the two co-doping elements and tried to use co-doping to overcome the shortcomings of single metal doping and avoid the formation of the deep levels in the bandgap, so as to promote the separation of photogenerated electron-hole pairs and expand the visible-light absorption range.Such information can provide beneficial guidance for the experimental regulation of the BaTiO 3 bandgap at atomic scale for visible-light utilization.

Calculation Details
In order to avoid the strong interaction between the co-doping elements and obtain a relatively reasonable doping concentration, the co-doping system was modelled using a 2 × 2 × 3 (60 atoms) supercell of the cubic BaTiO 3 unit cell, as shown in Figure 1a.The dopant concentration was 3.3%.Two Ti atoms are substituted by two different transition metals (M and M ) and the chemical formula can be expressed as Ba 8 (M M ) Ti 6 O 24 , where M refers to V or Nb, while M includes 3d transition metals (Cr, Mn, Fe, Co and Ni) and 4d transition metals (Mo, Tc, Ru and Pd).There are three kinds of possible substitution.These doping situations are schematically shown in Figure 1b-d and the lowest energy situation is described in Figure 1b.The pure BaTiO 3 system was modelled using a 1 × 1 × 1 supercell.To keep the doping concentration similar between the single doping and co-doping systems, the single doping system was modelled using 2 × 2 × 2 supercell.The atomic percentage of the impurity was 2.5%.

Structure
The calculated lattice parameter of pure BaTiO3 is 4.03 Å, which is in good agreement with the experimental value of 4.0 Å (within an error of 0.07%) [39].The lattice parameter of the transition metal co-doped BaTiO3 was also obtained after geometric structure optimization.The volume of the co-doped structure is not only dependent on the radii of the doped elements, but related to the interaction between atoms.As shown in Figure S1, after co-doping, the lattice constants a and b decrease slightly (except V-Ni and Nb-Ni) while c increases and oscillates.It indicates that the crystal cell is slightly enlarged in the c direction.As shown in Tables S2 and S3, the interatomic bond length varies due to the lattice distortion after co-doping.This means that the center of the positive charge after metal co-doping into the octahedral does not coincide with the center of the negative charge, resulting in the internal dipole moment.Since different elements co-doping causes a different interaction force, the deformation degree of the octahedral is different and the lattice constant accordingly changes.In this study, we chose V or Nb as one of the co-doping elements.Namely, the co-doping systems can be divided into two groups: V-M″ and Nb-M″.On one hand, V and Nb are typical 3d and 4d transition metals, respectively.On the other hand, the locations of V and Nb in the periodic table of elements are close to Ti, and their atomic radii are similar.Thus, it is more suitable for V and Nb to replace Ti.In addition, the radius of V is less than Nb, so the volume of the V-M″ co-doping system is smaller than that of the Nb-M″ co-doping system.Also, the volume of the 3d transition metals co-doping systems is usually smaller than that of the 4d transition metals co-doping systems.

Structure
The calculated lattice parameter of pure BaTiO 3 is 4.03 Å, which is in good agreement with the experimental value of 4.0 Å (within an error of 0.07%) [39].The lattice parameter of the transition metal co-doped BaTiO 3 was also obtained after geometric structure optimization.The volume of the co-doped structure is not only dependent on the radii of the doped elements, but related to the interaction between atoms.As shown in Figure S1, after co-doping, the lattice constants a and b decrease slightly (except V-Ni and Nb-Ni) while c increases and oscillates.It indicates that the crystal cell is slightly enlarged in the c direction.As shown in Tables S2 and S3, the interatomic bond length varies due to the lattice distortion after co-doping.This means that the center of the positive charge after metal co-doping into the octahedral does not coincide with the center of the negative charge, resulting in the internal dipole moment.Since different elements co-doping causes a different interaction force, the deformation degree of the octahedral is different and the lattice constant accordingly changes.In this study, we chose V or Nb as one of the co-doping elements.Namely, the co-doping systems can be divided into two groups: V-M and Nb-M .On one hand, V and Nb are typical 3d and 4d transition metals, respectively.On the other hand, the locations of V and Nb in the periodic table of elements are close to Ti, and their atomic radii are similar.Thus, it is more suitable for V and Nb to replace Ti.In addition, the radius of V is less than Nb, so the volume of the V-M co-doping system is smaller than that of the Nb-M co-doping system.Also, the volume of the 3d transition metals co-doping systems is usually smaller than that of the 4d transition metals co-doping systems.

Defect Formation Energy
The defect formation energy (E Form ) of transition metals co-doping BaTiO 3 can be calculated according to the formulas: where E co-doped is the energy of the co-doped BaTiO 3 system, E pure is the total energy of pure BaTiO 3 supercell, µ M and µ M are the chemical potentials of the co-doping metal elements, and µ Ti is the chemical potential of Ti.The µ M and µ M are defined and calculated from Equation (2), and the µ Ti is defined by Equation (3).The µ ( M /M ) m O n is the energy of the most stable oxide of the doping metal atom.µ O can be calculated from the ground state energy of O 2 .Under the equilibrium condition, the concentrations of point defects are controlled by their formation energies, which rely on the chemical potentials of impurity atoms and host [6].Thus, the smaller the defect formation energy value is, the more stable the co-doped BaTiO 3 is.The defect formation energies of all co-doped BaTiO 3 are shown in Figure 2. In comparison, the defect formation energies of Nb-M co-doping are energetically more favorable than V-M co-doping.It is difficult to find the tendency of E Form with the increase of the atomic number of M .The formation energies of V-M (Cr, Fe and Ni) and Nb-M (Cr, Mn, Fe, Co, Ni, Mo, Tc, Ru, and Pd) are negative, which means that the co-doping system is energetically favorable and could be easily prepared in the experiment.From Tables S2 and S3, the average bond length of Nb-O appears identical with that of Ti-O.Therefore, the influence of Nb doping into the structure of BaTiO 3 is smaller, and thus the formation energy is smaller and the structure is more stable.The deformation of the octahedral in the V-M co-doping system is thus more serious, corresponding to the stronger internal stress and unstable structure.

Defect Formation Energy
The defect formation energy ( orm F E ) of transition metals co-doping BaTiO3 can be calculated according to the formulas: where Eco-doped is the energy of the co-doped BaTiO3 system, Epure is the total energy of pure BaTiO3 supercell, μM′ and μM″ are the chemical potentials of the co-doping metal elements, and μTi is the chemical potential of Ti.The μM′ and μM″ are defined and calculated from Equation (2), and the μTi is is the energy of the most stable oxide of the doping metal atom.O  can be calculated from the ground state energy of O2.Under the equilibrium condition, the concentrations of point defects are controlled by their formation energies, which rely on the chemical potentials of impurity atoms and host [6].Thus, the smaller the defect formation energy value is, the more stable the co-doped BaTiO3 is.The defect formation energies of all co-doped BaTiO3 are shown in Figure 2. In comparison, the defect formation energies of Nb-M″ co-doping are energetically more favorable than V-M″ co-doping.It is difficult to find the tendency of EForm with the increase of the atomic number of M″.The formation energies of V-M″ (Cr, Fe and Ni) and Nb-M″ (Cr, Mn, Fe, Co, Ni, Mo, Tc, Ru, and Pd) are negative, which means that the co-doping system is energetically favorable and could be easily prepared in the experiment.From Tables S2  and S3, the average bond length of Nb-O appears identical with that of Ti-O.Therefore, the influence of Nb doping into the structure of BaTiO3 is smaller, and thus the formation energy is smaller and the structure is more stable.The deformation of the octahedral in the V-M″ co-doping system is thus more serious, corresponding to the stronger internal stress and unstable structure.

Electronic Properties
Figure 3 shows the calculated band structure and density of states (DOS) of pure cubic BaTiO3.The band structure shows an indirect bandgap of 1.56 eV, which is smaller than the experimental value (3.2 eV) as the small calculated bandgap is a systematic error in the DFT calculation [40].However, the DFT calculation can still give a reliable description of the result on the trend of bandgap variation due to doping.The valence band maximum (VBM) is mainly derived from the Ti 3d and O 2p states [41].The conduction band minimum (CBM) is derived from the Ti 3d states.Ba does not contribute to the VBM and CBM, although it does provide electrons to balance the system charge [42].Therefore, the bandgap value of BaTiO3 depends on the relative energy positions of the

Electronic Properties
Figure 3 shows the calculated band structure and density of states (DOS) of pure cubic BaTiO 3 .The band structure shows an indirect bandgap of 1.56 eV, which is smaller than the experimental value (3.2 eV) as the small calculated bandgap is a systematic error in the DFT calculation [40].However, the DFT calculation can still give a reliable description of the result on the trend of bandgap variation due to doping.The valence band maximum (VBM) is mainly derived from the Ti 3d and O 2p states [41].The conduction band minimum (CBM) is derived from the Ti 3d states.Ba does not contribute to the VBM and CBM, although it does provide electrons to balance the system charge [42].Therefore, the bandgap value of BaTiO 3 depends on the relative energy positions of the Ti 3d and O 2p states.However, as a light absorbing material, the bandgap of BaTiO 3 is too large to efficiently absorb the visible light.In order to clarify the co-doping effects with different transition metals on the electronic properties of the cubic BaTiO3, we systematically and carefully compared the band structures and density of states of the different co-doping systems.The co-doping systems can be divided into two types: BVM″TO and BNbM″TO.M″ includes 3d transition metals (Cr, Mn, Fe, Co, and Ni) and 4d transition metals (Mo, Tc, Ru, and Pd).Accordingly, the classified discussion is conducted in detail as follows.Although there exist the spin channels, the magnetic properties of the system have not been discussed in the article.The main reason is that this article mainly focuses on the change of the bandgap in the co-doped system and the effect on the absorption of light.
3.3.1.V and 3d M″ Co-Doping (Cr, Mn, Fe, Co and Ni) Figure 4 reveals that the bandgap of BaTiO3 after co-doping is narrowed due to the introduction of the impurity energy levels (IELs).It is noticed that BaTiO3, after V-M″ co-doping, exhibits ferromagnetism, except for V-Co co-doping.The ferromagnetism caused by transition metal doping is also found in other doped semiconductors, such as V-Cr co-doped ZnO [43], Mn doped GaN [44], and Mn doped AIN [45].The majority spin (up-spin) DOS has a smaller bandgap than the minority spin (down-spin) DOS.The bandgaps on both spin states are formed by the interaction of the V 3d or M″ 3d states with the O 2p states.The electronic structure of BaTiO3 is significantly modified by the dopants.The V 3d states are located at the bottom of the conduction band (CB), while the 3d states of Cr, Mn, Fe, Co, and Ni show up at the top of valence band (VB) (V-Cr, V-Mn and V-Fe co-doping) or in the middle of the bandgap (V-Co and V-Ni co-doping).Thus, the energy states from the dopants form new CBM, VBM, or a transition state in the bandgap, leading to a relatively narrow bandgap.Figure 4 shows that the IELs (from Cr, Mn, Co, and Ni) move from left to right, which means the highest occupied energy level of the 3d states is arranged in the order of Cr < Mn < Co < Ni from lower to higher energy, consistent with the number of the d electrons in these atoms.
For further analysis of the effect of IELs in the co-doping systems, we compared the band structures of the V-Cr (a) and V-Co (b) co-doping systems (Figure 5).The bandgaps of V-Cr (a) and V-Co (b) are 0.4 eV and 1.46 eV, respectively.The V 3d and Cr 3d states make the VBM and CBM In order to clarify the co-doping effects with different transition metals on the electronic properties of the cubic BaTiO 3 , we systematically and carefully compared the band structures and density of states of the different co-doping systems.The co-doping systems can be divided into two types: BVM TO and BNbM TO.M includes 3d transition metals (Cr, Mn, Fe, Co, and Ni) and 4d transition metals (Mo, Tc, Ru, and Pd).Accordingly, the classified discussion is conducted in detail as follows.Although there exist the spin channels, the magnetic properties of the system have not been discussed in the article.The main reason is that this article mainly focuses on the change of the bandgap in the co-doped system and the effect on the absorption of light.
3.3.1.V and 3d M Co-Doping (Cr, Mn, Fe, Co and Ni) Figure 4 reveals that the bandgap of BaTiO 3 after co-doping is narrowed due to the introduction of the impurity energy levels (IELs).It is noticed that BaTiO 3 , after V-M co-doping, exhibits ferromagnetism, except for V-Co co-doping.The ferromagnetism caused by transition metal doping is also found in other doped semiconductors, such as V-Cr co-doped ZnO [43], Mn doped GaN [44], and Mn doped AIN [45].The majority spin (up-spin) DOS has a smaller bandgap than the minority spin (down-spin) DOS.The bandgaps on both spin states are formed by the interaction of the V 3d or M 3d states with the O 2p states.The electronic structure of BaTiO 3 is significantly modified by the dopants.The V 3d states are located at the bottom of the conduction band (CB), while the 3d states of Cr, Mn, Fe, Co, and Ni show up at the top of valence band (VB) (V-Cr, V-Mn and V-Fe co-doping) or in the middle of the bandgap (V-Co and V-Ni co-doping).Thus, the energy states from the dopants form new CBM, VBM, or a transition state in the bandgap, leading to a relatively narrow bandgap.Figure 4 shows that the IELs (from Cr, Mn, Co, and Ni) move from left to right, which means the highest occupied energy level of the 3d states is arranged in the order of Cr < Mn < Co < Ni from lower to higher energy, consistent with the number of the d electrons in these atoms.
For further analysis of the effect of IELs in the co-doping systems, we compared the band structures of the V-Cr (a) and V-Co (b) co-doping systems (Figure 5).The bandgaps of V-Cr (a) and V-Co (b) are 0.4 eV and 1.46 eV, respectively.The V 3d and Cr 3d states make the VBM and CBM shift to the middle and result in a smaller bandgap.But the Co 3d states are located in the middle of the bandgap, forming an intermediate level.Such a level in the bandgap usually plays two roles.One is to form a step for the electron transition and the other is to work as the electron-hole recombination center when the doping concentration is too high.The former is beneficial to visible light absorption, but the latter hinders electron-hole separation.Therefore, combining Figures 4 and 5, the results show that V-Cr, V-Mn, and V-Fe co-doping should have suitable bandgap and better visible light absorption than V-Co and V-Ni.One is to form a step for the electron transition and the other is to work as the electron-hole recombination center when the doping concentration is too high.The former is beneficial to visible light absorption, but the latter hinders electron-hole separation.Therefore, combining Figure 4 and Figure 5, the results show that V-Cr, V-Mn, and V-Fe co-doping should have suitable bandgap and better visible light absorption than V-Co and V-Ni.One is to form a step for the electron transition and the other is to work as the electron-hole recombination center when the doping concentration is too high.The former is beneficial to visible light absorption, but the latter hinders electron-hole separation.Therefore, combining Figure 4 and Figure 5, the results show that V-Cr, V-Mn, and V-Fe co-doping should have suitable bandgap and better visible light absorption than V-Co and V-Ni.As shown in Figure 6, the IELs introduced by V-4d M co-doping emerges in the middle of bandgap and CB.Compared with Figure 4, the IELs of the 4d metals are even closer to the CB than the IELs of 3d metals.The reason is that the 4d states have higher energy than the 3d states of the transition metals.Therefore, the IELs of V co-doping with the 4d transition metals are closer to the conduction band and belong to the significant n-doping.The Fermi level (E F ) gradually shifts from the conduction band to the valence band with the increase of the atomic number of the M elements.The definition of the Fermi level is the highest energy level of the electron at the absolute zero degree, which corresponds to the energy state at 0 eV.It can act as a reference to discuss the effects of the transition metal co-doping on the band edge modification and the bandgap variation.The IELs in the bandgap and near the bottom of the CB partially (V-Tc, V-Ru and V-Pd co-doping systems) or wholly overlap with the CBM (V-Mo co-doping system).Both cases can lead to the CBM downward shifting, while the valence bands remain barely unchanged upon the co-doping.The Fermi levels of the V-M (Mo, Tc, Ru and Pd) co-doping systems pass through the IELs, that is to say, the electrons can occupy the IELs below the Fermi level in the ground state.Due to the small distance between this energy level and the bottom of the CB, electrons can be excited by absorbing small photon energy [46,47].As shown in Figure 6, the IELs introduced by V-4d M″ co-doping emerges in the middle of bandgap and CB.Compared with Figure 4, the IELs of the 4d metals are even closer to the CB than the IELs of 3d metals.The reason is that the 4d states have higher energy than the 3d states of the transition metals.Therefore, the IELs of V co-doping with the 4d transition metals are closer to the conduction band and belong to the significant n-doping.The Fermi level (EF) gradually shifts from the conduction band to the valence band with the increase of the atomic number of the M″ elements.The definition of the Fermi level is the highest energy level of the electron at the absolute zero degree, which corresponds to the energy state at 0 eV.It can act as a reference to discuss the effects of the transition metal co-doping on the band edge modification and the bandgap variation.The IELs in the bandgap and near the bottom of the CB partially (V-Tc, V-Ru and V-Pd co-doping systems) or wholly overlap with the CBM (V-Mo co-doping system).Both cases can lead to the CBM downward shifting, while the valence bands remain barely unchanged upon the co-doping.The Fermi levels of the V-M″ (Mo, Tc, Ru and Pd) co-doping systems pass through the IELs, that is to say, the electrons can occupy the IELs below the Fermi level in the ground state.Due to the small distance between this energy level and the bottom of the CB, electrons can be excited by absorbing small photon energy [46,47].Figure 7 shows that the effects of this series of co-doping are similar to the V-M″ (Cr, Mn, Fe, Co and Ni) co-doping described in Figure 4.The only difference is that the energy of the Nb 4d states is higher than that of the V 3d states.Consequently, the V 3d states are located at the CBM but the Nb 4d states are in the upper CB.Therefore, the Nb 4d states have little effect on the bandgap and there is no synergistic effect between the co-dopants.The Fermi level moves from CB to VB with the increase of the atomic number of M″ elements.The Cr, Mn, and Ni 3d states occur in the middle of the bandgap and become the intermediate level.The intermediate state might be beneficial to the electron transition under visible-light irradiation.However, it might not be  Figure 7 shows that the effects of this series of co-doping are similar to the V-M (Cr, Mn, Fe, Co and Ni) co-doping described in Figure 4.The only difference is that the energy of the Nb 4d states is higher than that of the V 3d states.Consequently, the V 3d states are located at the CBM but the Nb 4d states are in the upper CB.Therefore, the Nb 4d states have little effect on the bandgap and there is no synergistic effect between the co-dopants.The Fermi level moves from CB to VB with the increase of the atomic number of M elements.The Cr, Mn, and Ni 3d states occur in the middle of the bandgap and become the intermediate level.The intermediate state might be beneficial to the electron transition under visible-light irradiation.However, it might not be conducive to the effective separation of the electron-hole since it could also act as the recombination centers on the other hand.In addition, the Fe and Co 3d states are divided into two parts, where the high energy part is weak at the bottom of the CB, and the low energy part is strong, which is located at the top of the VB.Both cases can lead to the bandgap narrowing and are beneficial to visible-light absorption.
In these Nb-M co-doping systems, we chose two typical doping forms, the Nb-Mn and Nb-Co co-doping systems, to further investigate their band structures, as shown in Figure 8.The bandgaps are found to be 1.2 and 0.96 eV, respectively.In the Nb-Mn co-doping system, the IELs in the middle of bandgap are contributed by the Mn 3d states.However, in the Nb and Co co-doping system, the Co 3d and O 2p states form the p-d hybridization and locate above the original VB or partly coincided with the bottom of the CB.Overall, both co-doping could reduce the bandgap effectively but with different causes.It is also necessary to consider that Nb and Mn heavy co-doping might lead to a serious recombination due to the IELs in the bandgap.
conducive to the effective separation of the electron-hole since it could also act as the recombination centers on the other hand.In addition, the Fe and Co 3d states are divided into two parts, where the high energy part is weak at the bottom of the CB, and the low energy part is strong, which is located at the top of the VB.Both cases can lead to the bandgap narrowing and are beneficial to visible-light absorption.
In these Nb-M″ co-doping systems, we chose two typical doping forms, the Nb-Mn and Nb-Co co-doping systems, to further investigate their band structures, as shown in Figure 8.The bandgaps are found to be 1.2 and 0.96 eV, respectively.In the Nb-Mn co-doping system, the IELs in the middle of bandgap are contributed by the Mn 3d states.However, in the Nb and Co co-doping system, the Co 3d and O 2p states form the p-d hybridization and locate above the original VB or partly coincided with the bottom of the CB.Overall, both co-doping could reduce the bandgap effectively but with different causes.It is also necessary to consider that Nb and Mn heavy co-doping might lead to a serious recombination due to the IELs in the bandgap.conducive to the effective separation of the electron-hole since it could also act as the recombination centers on the other hand.In addition, the Fe and Co 3d states are divided into two parts, where the high energy part is weak at the bottom of the CB, and the low energy part is strong, which is located at the top of the VB.Both cases can lead to the bandgap narrowing and are beneficial to visible-light absorption.In these Nb-M″ co-doping systems, we chose two typical doping forms, the Nb-Mn and Nb-Co co-doping systems, to further investigate their band structures, as shown in Figure 8.The bandgaps are found to be 1.2 and 0.96 eV, respectively.In the Nb-Mn co-doping system, the IELs in the middle of bandgap are contributed by the Mn 3d states.However, in the Nb and Co co-doping system, the Co 3d and O 2p states form the p-d hybridization and locate above the original VB or partly coincided with the bottom of the CB.Overall, both co-doping could reduce the bandgap effectively but with different causes.It is also necessary to consider that Nb and Mn heavy co-doping might lead to a serious recombination due to the IELs in the bandgap.As shown in Figure 9, Nb-Mo, Nb-Tc, Nb-Ru, and Nb-Pd co-doping have very little influence on the top of valence band, but it changes the distribution of the electron states at the bottom of the conduction band.The Nb 4d states are in the middle of the conduction band, while the Mo, Tc, Ru, and Pd 3d states are located at the conduction band bottom or in the bandgap.Hence this series of co-dopings have no synergistic influence, and the doping effects around the bandgap are similar to the individual Mo, Tc, Ru, or Pd doping.Generally, according to the results above, transition metal co-doping can have three effects on reducing the bandgap.Firstly, the IELs appear below the CB, partially or wholly overlap with the bottom of the CB, and eventually cause the CBM to move downward.Secondly, the IELs are located above the VB, overlap with the top of VB in different degrees, and make the VBM move up.Thirdly, the IELs lie in the middle of the bandgap to form the intermediate energy level.In the actual co-doping system, two or more effects can coexist to modify the energy bandgap.
In order to further study the difference between the single doping and co-doping systems, we calculated the band structures and total and partial DOS of V doped BaTiO3, Nb doped BaTiO3, and Cr doped BaTiO3, as shown in Figure 10.The band structures clearly show that V doping reduces the bandgap to 1.15 eV since the V 3d states appear at the bottom of CB and form a new CBM.But the bandgap after Nb doping is 1.63 eV, which is even a bit larger than pure BaTiO3 (1.56 eV).The reason is that the Nb 4d states are located in the CB and far away from CBM, which have little effect on the bandgap.Thus, in the Nb-M″ co-doping system, the doping effect mostly depends on the single M″ doping.In the Cr-doped BaTiO3, an IEL emerges in the bandgap, which is quite different from the V and Nb doping systems.Generally, according to the results above, transition metal co-doping can have three effects on reducing the bandgap.Firstly, the IELs appear below the CB, partially or wholly overlap with the bottom of the CB, and eventually cause the CBM to move downward.Secondly, the IELs are located above the VB, overlap with the top of VB in different degrees, and make the VBM move up.Thirdly, the IELs lie in the middle of the bandgap to form the intermediate energy level.In the actual co-doping system, two or more effects can coexist to modify the energy bandgap.
In order to further study the difference between the single doping and co-doping systems, we calculated the band structures and total and partial DOS of V doped BaTiO 3 , Nb doped BaTiO 3 , and Cr doped BaTiO 3 , as shown in Figure 10.The band structures clearly show that V doping reduces the bandgap to 1.15 eV since the V 3d states appear at the bottom of CB and form a new CBM.But the bandgap after Nb doping is 1.63 eV, which is even a bit larger than pure BaTiO 3 (1.56 eV).The reason is that the Nb 4d states are located in the CB and far away from CBM, which have little effect on the bandgap.Thus, in the Nb-M co-doping system, the doping effect mostly depends on the single M doping.In the Cr-doped BaTiO 3 , an IEL emerges in the bandgap, which is quite different from the V and Nb doping systems.In addition, we compared the band structure and DOS of V, Cr, and V-Cr doped BaTiO3.In the V-doped BaTiO3, the IELs are located at the bottom of the CB.In the Cr-doped BaTiO3, the IELs appear in the middle of the bandgap and form the intermediate energy level.But in the V-Cr -4 In addition, we compared the band structure and DOS of V, Cr, and V-Cr doped BaTiO 3 .In the V-doped BaTiO 3 , the IELs are located at the bottom of the CB.In the Cr-doped BaTiO 3 , the IELs appear in the middle of the bandgap and form the intermediate energy level.But in the V-Cr co-doped BaTiO 3 as shown in Figure 4, the IELs divided into two parts.One was situated at the bottom of the CB, and the other at the top of the VB.Finally, as the intermediate energy level raised from the single Cr, doping disappeared, as confirmed in Figure 5a.Thus, the V-Cr co-doping can overcome the shortcoming of the single Cr doping and combine the advantages of the V and Cr doping in reducing the bandgap to effectively shift the CBM and VBM toward the bandgap.Through such synergistic effect, the light absorption range could be expanded and the visible-light photoelectrical activity is expected to improve.
Furthermore, the charge density distribution was investigated for the V-doped, Cr-doped, and V-Cr co-doped BaTiO 3 as shown in Figure 11, which indicates that Ti-O, Cr-O, and V-O form covalent bonds.Due to different electronegativity (Ti < V < Cr < O), the covalent bond strength is different.The greater the metal electronegativity is, the smaller the electronegativity difference between the metal and oxygen atoms, and the more uniform is the charge density distribution.According to an effective empirical determining method, the electronic energy level of an element is usually inversely proportional to its electronegativity.That is to say, the higher the electronegativity, the lower the position of the energy level and the lower the position of the corresponding energy band [48].Therefore, when Cr or V with larger electronegativity was doped into BaTiO 3 , the IELs with a relatively low energy position were introduced around the CBM or in the bandgap, leading to a narrower bandgap after doping.The results are verified by the line profile of the charge density as displayed in Figure 11a-c.The charge density of Ti, O, Cr, and V is slightly decreased in various degrees after Cr-V co-doping compared to the single Cr or V doping.It can be found that in comparison to the single doping, where the charge density is more localized around the atoms, V-Cr co-doping could result in a relatively evener charge distribution.This not only causes the hybridization of the newly introduced IELs and the initial CBM or VBM of the pure BaTiO 3 , but is associated with the interaction among the newly introduced energy states due to the V-Cr synergistic effect, which accounts for the bandgap engineering by the co-doping for visible-light activation.Through such synergistic effect, the light absorption range could be expanded and the visible-light photoelectrical activity is expected to improve.Furthermore, the charge density distribution was investigated for the V-doped, Cr-doped, and V-Cr co-doped BaTiO3 as shown in Figure 11, which indicates that Ti-O, Cr-O, and V-O form covalent bonds.Due to different electronegativity (Ti < V < Cr < O), the covalent bond strength is different.The greater the metal electronegativity is, the smaller the electronegativity difference between the metal and oxygen atoms, and the more uniform is the charge density distribution.According to an effective empirical determining method, the electronic energy level of an element is usually inversely proportional to its electronegativity.That is to say, the higher the electronegativity, the lower the position of the energy level and the lower the position of the corresponding energy band [48].Therefore, when Cr or V with larger electronegativity was doped into BaTiO3, the IELs with a relatively low energy position were introduced around the CBM or in the bandgap, leading to a narrower bandgap after doping.The results are verified by the line profile of the charge density as displayed in Figure 11a-c.The charge density of Ti, O, Cr, and V is slightly decreased in various degrees after Cr-V co-doping compared to the single Cr or V doping.It can be found that in comparison to the single doping, where the charge density is more localized around the atoms, V-Cr co-doping could result in a relatively evener charge distribution.This not only causes the hybridization of the newly introduced IELs and the initial CBM or VBM of the pure BaTiO3, but is associated with the interaction among the newly introduced energy states due to the V-Cr synergistic effect, which accounts for the bandgap engineering by the co-doping for visible-light activation.In order to further analyze the charge density near the bandgap, we calculated the distribution of the partial charge density from the top of the valence band to the bottom of the conduction band, as shown in Figure 12, which could reveal the visual information of the electron densities mainly derived from the doped/co-doped atoms.The calculated partial electron density in the V-Cr co-doped BaTiO3 distributed around the V and Cr dopants is shown in Figure 12a, and is mainly In order to further analyze the charge density near the bandgap, we calculated the distribution of the partial charge density from the top of the valence band to the bottom of the conduction band, as shown in Figure 12, which could reveal the visual information of the electron densities mainly derived from the doped/co-doped atoms.The calculated partial electron density in the V-Cr co-doped BaTiO 3 distributed around the V and Cr dopants is shown in Figure 12a, and is mainly derived from the Cr 3d isolated non-bond states and the hybrids between the V 3d and O 2p electronic states, as suggested by Figures 4 and 5. Figure 12b presents the partial electron density on Cr in the Cr doped BaTiO 3 , which consists significantly of the isolated Cr 3d orbitals confirmed by Figure 10f.From Figure 12c, the partial electron density calculated in the V doped BaTiO 3 distributed around the V atom, which primarily originates from V-O bonds arising from the hybridization of the O 2p and V 3d orbitals.As such, the doped/co-doped atoms play a key role in narrowing the bandgap of BaTiO 3 .These results also reveal that the appropriate selection of co-doping elements, such as V-Cr co-doping, can result in synergistic effects by the two co-dopants that can effectively manipulate the bandgap.Before choosing the pair of dopants for co-doping, it is important to examine the electronic structures of the individual doping and their interaction so that the pair of dopants in the co-doping system can coexist to properly modify the bandgap edge and improve the visible-light adsorption properties.Besides the electronic structure, charge mobility and surface properties/states also play important roles in the photoelectric behavior, which should be addressed in the future.derived from the Cr 3d isolated non-bond states and the hybrids between the V 3d and O 2p electronic states, as suggested by Figures 4 and 5. Figure 12b presents the partial electron density on Cr in the Cr doped BaTiO3, which consists significantly of the isolated Cr 3d orbitals confirmed by Figure 10f.From Figure 12c, the partial electron density calculated in the V doped BaTiO3 distributed around the V atom, which primarily originates from V-O bonds arising from the hybridization of the O 2p and V 3d orbitals.As such, the doped/co-doped atoms play a key role in narrowing the bandgap of BaTiO3.These results also reveal that the appropriate selection of co-doping elements, such as V-Cr co-doping, can result in synergistic effects by the two co-dopants that can effectively manipulate the bandgap.Before choosing the pair of dopants for co-doping, it is important to examine the electronic structures of the individual doping and their interaction so that the pair of dopants in the co-doping system can coexist to properly modify the bandgap edge and improve the visible-light adsorption properties.Besides the electronic structure, charge mobility and surface properties/states also play important roles in the photoelectric behavior, which should be addressed in the future.

Conclusions
In summary, the formation energy and electronic properties of the transition metal V-M″ and Nb-M″ co-doped BaTiO3 have been studied by first-principles calculations.The results indicate that the V-M″ co-doping is more suitable than the Nb-M″ co-doping for narrowing the bandgap of BaTiO3 and increasing the absorption of visible light, since the V-M″ co-doping can form shallow levels around the bandgap edge while those energy levels induced by the Nb-M″ co-doping are usually deep levels in the energy band or bandgap.The optimal co-doping model is proposed as the V-Cr co-doped BaTiO3, which not only has favorable defect formation energy, but also significantly reduce the bandgap.Simultaneous introduction of V and Cr results in a synergistic effect, which has been demonstrated by the detailed analysis of the density of states, band structure, and charge-density distribution of the doping systems.V-Cr co-doping could overcome the shortcoming of the single Cr doping and combine the advantages of both the V and Cr doping.For this optimal co-doped BaTiO3 system, the Cr 3d states are located just above the VBM and the V 3d states occupied band just below the CBM, corresponding to a bandgap narrowing of about 0.4 eV, which is beneficial for efficient visible-light adsorption.The results can provide an important guideline for future experiments to modify the wide BaTiO3 bandgap for visible-light driven solar applications.

Supplementary Materials:
The following are available online at www.mdpi.com/link, Figure S1: The lattice constants of transition metals co-doped cubic BaTiO3, Table S1: The special K points coordinates, Table S2: The average bond length obtained after optimization of the V-M″ co-doping system, Table S3: The average bond length obtained after optimization of the Nb-M″ co-doping system.

Conclusions
In summary, the formation energy and electronic properties of the transition metal V-M and Nb-M co-doped BaTiO 3 have been studied by first-principles calculations.The results indicate that the V-M co-doping is more suitable than the Nb-M co-doping for narrowing the bandgap of BaTiO 3 and increasing the absorption of visible light, since the V-M co-doping can form shallow levels around the bandgap edge while those energy levels induced by the Nb-M co-doping are usually deep levels in the energy band or bandgap.The optimal co-doping model is proposed as the V-Cr co-doped BaTiO 3 , which not only has favorable defect formation energy, but also significantly reduce the bandgap.Simultaneous introduction of V and Cr results in a synergistic effect, which has been demonstrated by the detailed analysis of the density of states, band structure, and charge-density distribution of the doping systems.V-Cr co-doping could overcome the shortcoming of the single Cr doping and combine the advantages of both the V and Cr doping.For this optimal co-doped BaTiO 3 system, the Cr 3d states are located just above the VBM and the V 3d states occupied band just below the CBM, corresponding to a bandgap narrowing of about 0.4 eV, which is beneficial for efficient visible-light adsorption.The results can provide an important guideline for future experiments to modify the wide BaTiO 3 bandgap for visible-light driven solar applications.

Supplementary Materials:
The following are available online at http://www.mdpi.com/2079-4991/8/7/455/s1, Figure S1: The lattice constants of transition metals co-doped cubic BaTiO 3 , Table S1: The special K points coordinates, Table S2: The average bond length obtained after optimization of the V-M co-doping system, Table S3: The average bond length obtained after optimization of the Nb-M co-doping system.
Author Contributions: S.L. conceived and designed the experiments; F.Y., L.Y., C.A. and P.X.performed the theoretical; F.Y., C.W. and X.L. analyzed the data; F.Y. wrote the paper.

3 of 15 15 Figure 1 .
Figure 1.Models for the calculation.(a) the structure of 2 × 2 × 3 supercell model of BaTiO3; (b-d) configurations for transition metals co-doping in BaTiO3.The purple and green spheres indicate the transition metal dopants.The pink, blue and red spheres indicate Ba, Ti and O atoms, respectively.

Figure 1 .
Figure 1.Models for the calculation.(a) the structure of 2 × 2 × 3 supercell model of BaTiO 3 ; (b-d) configurations for transition metals co-doping in BaTiO 3 .The purple and green spheres indicate the transition metal dopants.The pink, blue and red spheres indicate Ba, Ti and O atoms, respectively.

Figure 2 .
Figure 2. The defect formation energies of transition metals co-doped cubic BaTiO3.(a) V or Nb with 3d metal M″ (Cr, Mn, Fe, Co, and Ni); (b) V or Nb with 4d metal M″ (Mo, Tc, Ru, and Pd).

Figure 2 .
Figure 2. The defect formation energies of transition metals co-doped cubic BaTiO 3 .(a) V or Nb with 3d metal M (Cr, Mn, Fe, Co, and Ni); (b) V or Nb with 4d metal M (Mo, Tc, Ru, and Pd).

Nanomaterials 2018, 8 ,
x FOR PEER REVIEW 5 of 15 Ti 3d and O 2p states.However, as a light absorbing material, the bandgap of BaTiO3 is too large to efficiently absorb the visible light.

Figure 3 .
Figure 3. Band structure, total and partial density of states of pure cubic BaTiO3.

Figure 3 .
Figure 3. Band structure, total and partial density of states of pure cubic BaTiO 3 .

Figure 4 .
Figure 4.The total and partial density of states of the V-M″ (3d metal elements: Cr, Mn, Fe, Co, and Ni) co-doped BaTiO3.The black dashed line indicates the position of the Fermi level.

Figure 5 .Figure 4 .
Figure 5.The band structures of the V-Cr (a) and V-Co (b) co-doped BaTiO3.The red lines indicate Cr 3d states or Co 3d states.The blue lines indicate V 3d states.

Figure 4 .
Figure 4.The total and partial density of states of the V-M″ (3d metal elements: Cr, Mn, Fe, Co, and Ni) co-doped BaTiO3.The black dashed line indicates the position of the Fermi level.

Figure 5 .Figure 5 .
Figure 5.The band structures of the V-Cr (a) and V-Co (b) co-doped BaTiO3.The red lines indicate Cr 3d states or Co 3d states.The blue lines indicate V 3d states.

Figure 6 .
Figure 6.The total and partial density of states of the V-M″ (4d metal elements: Mo, Tc, Ru and Pd) co-doped BaTiO3.The black dashed line indicates the position of the Fermi level.

Figure 6 .
Figure 6.The total and partial density of states of the V-M (4d metal elements: Mo, Tc, Ru and Pd) co-doped BaTiO 3 .The black dashed line indicates the position of the Fermi level.

Figure 7 .
Figure 7.The total and partial density of states of the Nb-M″ (3d metal elements: Cr, Mn, Fe, Co, and Ni) co-doped BaTiO3.The black dashed line indicates the position of the Fermi level.

Figure 8 .
Figure 8.The band structures of Nb-Mn (a) and Nb-Co (b) co-doped BaTiO3.The red lines indicate Mn 3d states (a) and Co 3d states (b).

Figure 7 .
Figure 7.The total and partial density of states of the Nb-M (3d metal elements: Cr, Mn, Fe, Co, and Ni) co-doped BaTiO 3 .The black dashed line indicates the position of the Fermi level.

Figure 7 .
Figure 7.The total and partial density of states of the Nb-M″ (3d metal elements: Cr, Mn, Fe, Co, and Ni) co-doped BaTiO3.The black dashed line indicates the position of the Fermi level.

Figure 8 .
Figure 8.The band structures of Nb-Mn (a) and Nb-Co (b) co-doped BaTiO3.The red lines indicate Mn 3d states (a) and Co 3d states (b).

Figure 8 .
Figure 8.The band structures of Nb-Mn (a) and Nb-Co (b) co-doped BaTiO 3 .The red lines indicate Mn 3d states (a) and Co 3d states (b).

3. 3 . 4 . 15 3. 3 . 4 .
Nb-4d M Co-Doping (Mo, Tc, Ru and Pd) As shown in Figure9, Nb-Mo, Nb-Tc, Nb-Ru, and Nb-Pd co-doping have very little influence on the top of valence band, but it changes the distribution of the electron states at the bottom of the conduction band.The Nb 4d states are in the middle of the conduction band, while the Mo, Tc, Ru, and Pd 3d states are located at the conduction band bottom or in the bandgap.Hence this series of co-dopings have no synergistic influence, and the doping effects around the bandgap are similar to the individual Mo, Tc, Ru, or Pd doping.Nanomaterials 2018, 8, x FOR PEER REVIEW 9 of Nb-4d M″ Co-Doping (Mo, Tc, Ru and Pd)

Figure 9 .
Figure 9.The total and partial density of states of the Nb-M″ (4d metal elements: Mo, Tc, Ru and Pd) co-doped BaTiO3.The black dashed line indicates the position of the Fermi level.

Figure 9 .
Figure 9.The total and partial density of states of the Nb-M (4d metal elements: Mo, Tc, Ru and Pd) co-doped BaTiO 3 .The black dashed line indicates the position of the Fermi level.

Nanomaterials 2018, 8 ,
x FOR PEER REVIEW 11 of 15 co-doped BaTiO3 as shown in Figure4, the IELs divided into two parts.One was situated at the bottom of the CB, and the other at the top of the VB.Finally, as the intermediate energy level raised from the single Cr, doping disappeared, as confirmed in Figure5a.Thus, the V-Cr co-doping can overcome the shortcoming of the single Cr doping and combine the advantages of the V and Cr doping in reducing the bandgap to effectively shift the CBM and VBM toward the bandgap.

Figure 12 .
Figure 12.Partial charge-density distribution calculated from the top of the valence band to the bottom of the conduction band: (a) V and Cr co-doped BaTiO3; (b) Cr-doped BaTiO3; and (c) V-doped BaTiO3.

Author
Contributions: S.L. conceived and designed the experiments; F.Y., L.Y., C.A. and P.X.performed the theoretical; F.Y., C.W. and X.L. analyzed the data; F.Y. wrote the paper.

Figure 12 .
Figure 12.Partial charge-density distribution calculated from the top of the valence band to the bottom of the conduction band: (a) V and Cr co-doped BaTiO 3 ; (b) Cr-doped BaTiO 3 ; (c) V-doped BaTiO 3 .
Nanomaterials 2018, 8, x FOR PEER REVIEW 6 of 15 shift to the middle and result in a smaller bandgap.But the Co 3d states are located in the middle of the bandgap, forming an intermediate level.Such a level in the bandgap usually plays two roles.