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Jun 21, 2018 - State Key Laboratory of Marine Resource Utilization in South China Sea, ... Ames Laboratory, U. S. Department of Energy, and Department of ...
nanomaterials Article

Tailoring Bandgap of Perovskite BaTiO3 by Transition Metals Co-Doping for Visible-Light Photoelectrical Applications: A First-Principles Study Fan Yang 1,2 , Liang Yang 2 , Changzhi Ai 1,2 , Pengcheng Xie 1,2 , Shiwei Lin 1,2, *, Cai-Zhuang Wang 3 and Xihong Lu 4 1

2 3 4

*

State Key Laboratory of Marine Resource Utilization in South China Sea, Hainan University, Haikou 570228, China; [email protected] (F.Y.); [email protected] (C.A.); [email protected] (P.X.) College of Materials and Chemical Engineering, Hainan University, Haikou 570228, China; [email protected] Ames Laboratory, U. S. Department of Energy, and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA; [email protected] School of Chemistry, Sun Yat-Sen University, Guangzhou 510275, China; [email protected] Correspondence: [email protected]; Tel.: +86-898-662-76115

Received: 17 May 2018; Accepted: 19 June 2018; Published: 21 June 2018

 

Abstract: The physical and chemical properties of V-M00 and Nb-M00 (M00 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-M00 co-doping is more favorable than Nb-M00 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. Keywords: BaTiO3 ; co-doping; first-principles; photoelectrical

1. Introduction Perovskites have been extensively studied because of their unique structure and properties. Over the past decade, organic-inorganic hybrid perovskite iodides have received considerable attention due to their high efficiency in the photovoltaic process [1]. However, stability is a major issue, hindering a large-scale commercialization of the perovskite for photovoltaic applications [2–5]. To overcome this problem, inorganic perovskites, especially ferroelectric oxide perovskites, have attracted much current interest [6]. For example, Bi2 FeCrO6 as a double perovskite material with its bandgap tunable by bandgap engineering has been reported [7]. [KNbO3 ]1−x [BaNi1/2 O3−δ ]x has a bandgap adjustable in the range of 1.1–3.8 eV [8]. Other perovskites, such as BaTiO3 [9–11], BiFeO3 [12–15], LiNbO3 [16–19] and PbTiO3 [20–22] have also been extensively studied. Inorganic oxide perovskites ABO3 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 Nanomaterials 2018, 8, 455; doi:10.3390/nano8070455

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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 BaTiO3 [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 Cr3+ and Ta5+ co-doped SrTiO3 can improve photocatalytic activities. Kako et al. [30] reported a visible-light sensitive TiO2 with Fe-Ta co-doping ((Fe,Ta)x Ti1−x O2 , 0 ≤ x ≤ 1) that has a higher photocatalytic activity than the Fe3+ doped TiO2 . Masahiro et al. [31] also reported that N and La co-doped SrTiO3 had better visible-light absorption (≥400 nm) compared with the pure SrTiO3 . 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 BaTiO3 . 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 BaTiO3 bandgap at atomic scale for visible-light utilization. 2. 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 BaTiO3 unit cell, as shown in Figure 1a. The dopant concentration was 3.3%. Two Ti atoms are substituted by two different transition metals (M0 and M00 ) and the chemical formula can be expressed as Ba8 (M0 M00 ) Ti6 O24 , where M0 refers to V or Nb, while M00 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 BaTiO3 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%. The spin-polarized first-principles density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP, Version 5.2, Materials Design Inc., Vienna, Austria) [32–34]. We used the generalized gradient approximation (GGA) [35] with the Perdew– Burke–Ernzerhof formulation (PBE) [36] to treat the exchange and correlation energy. The plane-wave energy cutoff was set as 500 eV within the projector-augmented-wave method (PAW). The Monkhorst–Pack scheme K-points mesh was set as 4 × 4 × 2 [37]. The structure optimization was performed until the residual force was less than 0.01 eV/Å on every atom [38]. In the process of calculating the band structure, the special points are X→R→M→Г→R (1 × 1 × 1 and 2 × 2 × 2 supercell) and Г→F→Q→Z→Г (2 × 2 × 3 supercell). The special points coordinates are shown in Table S1.

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Figure Figure1.1. Models Modelsfor forthe the calculation. calculation. (a) (a)the the structure structure of of 22 ××22××3 3supercell supercellmodel modelofofBaTiO BaTiO3;3 ;(b–d) (b–d) configurations configurationsfor fortransition transitionmetals metalsco-doping co-dopingin inBaTiO BaTiO3.3 .The Thepurple purpleand andgreen greenspheres spheresindicate indicatethe the transition transitionmetal metaldopants. dopants.The Thepink, pink,blue blueand andred redspheres spheresindicate indicateBa, Ba,Ti Tiand and O O atoms, atoms, respectively. respectively.

3.3.Results Resultsand andDiscussion Discussion 3.1. 3.1.Structure Structure The Thecalculated calculatedlattice latticeparameter parameterof ofpure pureBaTiO BaTiO33isis4.03 4.03Å, Å,which whichisisin ingood goodagreement agreementwith withthe the experimental experimentalvalue valueof of4.0 4.0ÅÅ(within (withinan anerror error of of 0.07%) 0.07%) [39]. [39]. The Thelattice latticeparameter parameterof ofthe thetransition transition metal 3 was also obtained after geometric structure optimization. The The volume of the metalco-doped co-dopedBaTiO BaTiO also obtained after geometric structure optimization. volume of 3 was co-doped structure is not onlyonly dependent on on thethe radii of of thethe doped the co-doped structure is not dependent radii dopedelements, elements,but butrelated relatedtotothe the interaction interactionbetween betweenatoms. atoms.As Asshown shownininFigure FigureS1, S1,after afterco-doping, co-doping,the thelattice latticeconstants constantsaaand andbb decrease (except V-Ni V-Niand andNb-Ni) Nb-Ni) while c increases oscillates. It indicates that the decrease slightly (except while c increases and and oscillates. It indicates that the crystal crystal cell is slightly in the c direction. in and Tables S3, the interatomic cell is slightly enlargedenlarged in the c direction. As shownAs in shown Tables S2 S3, S2 theand interatomic bond length bond duedistortion to the lattice co-doping. This means that the center of after the varieslength due tovaries the lattice after distortion co-doping.after This means that the center of the positive charge positive charge after co-doping into octahedral not coincide with the center of the metal co-doping into metal the octahedral does notthe coincide with does the center of the negative charge, resulting negative charge, resulting in theSince internal dipole moment. Since different causes in the internal dipole moment. different elements co-doping causes elements a differentco-doping interaction force, athe different interaction force, the deformation degree of the octahedral is different and the lattice deformation degree of the octahedral is different and the lattice constant accordingly changes. constant accordingly changes. In as this study, chose V elements. or Nb as one of thethe co-doping elements. In this study, we chose V or Nb one of thewe co-doping Namely, co-doping systems Namely, the co-doping systems be00divided into00 .two V-M″ and Nb Nb-M″. On one3dhand, V can be divided into two groups:can V-M and Nb-M Ongroups: one hand, V and are typical and 4d and Nb aremetals, typicalrespectively. 3d and 4d transition metals, respectively. Onofthe hand, theperiodic locations of V transition On the other hand, the locations V other and Nb in the table of and Nb in are the close periodic table elements are close Ti, and Thus, their atomic radii are similar. it is elements to Ti, andoftheir atomic radii aretosimilar. it is more suitable for V Thus, and Nb to 00 more suitable for V and Nb to replace Ti. In addition, the radius of V is less than Nb, so the volume replace Ti. In addition, the radius of V is less than Nb, so the volume of the V-M co-doping system of V-M″ co-doping system smaller than that of the the Nb-M″ co-doping Also, the is the smaller than that of the Nb-Mis00 co-doping system. Also, volume of the 3dsystem. transition metals volume of systems the 3d is transition metals than co-doping is usually smaller than systems. that of the 4d co-doping usually smaller that of systems the 4d transition metals co-doping transition metals co-doping systems.

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Defect Formation Energy 3.2. 3.2. Defect Formation Energy defect formation energy ( EForm ) oftransition transitionmetals metalsco-doping co-doping BaTiO BaTiO3 can be calculated TheThe defect formation energy (EForm ) of 3 can be calculated according to the formulas: according to the formulas: E Form = E co  doped -E pure - M '   M ''  2  Ti EForm = Eco−doped − E pure − µ M0 − µ M00 + 2µ Ti

(1) (1)

 M '/ M ''    O  nO / m µ M0 /M00 = µ( 0 M '/ 00M )'' mOnn − nµO /m

(2) (2)

ETiO=   +2µ 2O ETiO 2 µ Ti Ti O 2

(3)(3)





M /M

m

a

2

b

4

Formation energy(eV)

0

Formation energy(eV)

where Eco-doped is the energy co-dopedBaTiO BaTiO 3 system, Epure is the total energy of pure BaTiO3 where Eco-doped is the energy of of thethe co-doped 3 system, Epure is the total energy of pure BaTiO3 supercell, μ M′ and μ M″ are the chemical potentials ofthe theco-doping co-doping metal metal elements, elements, and supercell, µM 0 and µM 00 are the chemical potentials of and μµTiTiisisthe the chemical potential of Ti. The μ M′ and μM″ are defined and calculated from Equation (2), and the μTi is chemical potential of Ti. The µM 0 and µM 00 are defined and calculated from Equation (2), and the µTi is is the energyofofthe themost moststable stableoxide oxide of of the the doping defined by Equation defined by Equation (3).(3). TheThe µ( 0 M00'/)M ''OmnOis the energy dopingmetal metal n M /M m atom. µO can from thethe ground state energy condition, 2 .2. Under O be cancalculated be calculated from ground state energyofofOO Under the the equilibrium equilibrium condition, atom. the concentrations of point defects are controlled by their formation energies, which rely on the 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 chemical potentials of impurity atoms and host [6]. Thus, the smaller the defect formation energy is, the more the co-doped defect formation energies of all co-doped BaTiO3 are 3 is. The value is,stable the more stable theBaTiO co-doped BaTiO 3 is. The defect formation energies of all co-doped 00 co-doping are energetically shown in Figure 2. In comparison, the defect formation energies of Nb-M BaTiO3 are shown in Figure 2. In comparison, the defect formation energies of Nb-M″ co-doping are 00 co-doping. It is difficult to find the tendency of E more favorable than the increase Form withof energetically moreV-M favorable than V-M″ co-doping. It is difficult to find the tendency EForm with 00 (Cr, Fe and Ni) and Nb-M00 (Cr, Mn, of the number M00 . The formation of V-Menergies theatomic increase of the of atomic number of M″.energies The formation of V-M″ (Cr, Fe and Ni) and Fe, Co, Ni, Mo, negative, means that the co-doping system energetically Nb-M″ (Cr, Tc, Mn,Ru, Fe,and Co,Pd) Ni,are Mo, Tc, Ru, which and Pd) are negative, which means that is the co-doping favorable could be easily prepared the experiment. From Tables and S3, the average bond systemand is energetically favorable andincould be easily prepared in the S2 experiment. From Tables S2 andofS3, the appears average identical bond length Nb-O appears identicalthe with that ofofTi-O. Therefore, length Nb-O withofthat of Ti-O. Therefore, influence Nb doping intothe the influence of Nb structure of BaTiO 3 is smaller, andand thus formation energy is structure of BaTiO smaller,into andthe thus the formation energy is smaller thethe structure is more stable. 3 isdoping 00 smaller and the structure is more stable. The deformation of the octahedral in the V-M″ co-doping The deformation of the octahedral in the V-M co-doping system is thus more serious, corresponding system is thus more stress serious, corresponding to the stronger internal stress and unstable structure. to the stronger internal and unstable structure.

2

-2 -4 -6 V Nb

-8 -10

Cr

Mn

Fe

Co

Ni

V Nb

0 -2 -4 -6

Mo

Tc

Ru

Pd

Figure 2. The defect formation energies transition metalsco-doped co-dopedcubic cubicBaTiO BaTiO3.. (a) V or Nb with Figure 2. The defect formation energies of of transition metals 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). 3d metal M00 (Cr, Mn, Fe, Co, and Ni); (b) V or Nb with 4d metal M00 (Mo, Tc, Ru, and Pd).

3.3. Electronic Properties 3.3. Electronic Properties Figure 3 shows the calculated band structure and density of states (DOS) of pure cubic BaTiO3. Figure 3 shows the calculated band structure and density of states (DOS) of pure cubic BaTiO . The band structure shows an indirect bandgap of 1.56 eV, which is smaller than the experimental3 The value band structure shows an indirect bandgap of 1.56iseV, which is smaller than experimental (3.2 eV) as the small calculated bandgap a systematic error in thethe DFT calculation value [40]. (3.2 However, eV) as the the small calculated bandgap is a systematic error in the DFT calculation [40]. However, DFT calculation can still give a reliable description of the result on the trend of the DFT calculation can still a reliable description of the result on the trend ofderived bandgap variation bandgap variation due togive doping. The valence band maximum (VBM) is mainly from the Ti due 3d to doping. The valence band maximum (VBM) is mainly derived from the Ti 3d and O 2p states and O 2p states [41]. The conduction band minimum (CBM) is derived from the Ti 3d states. [41]. Ba The does conduction band minimum is derived from the Ti 3d states. Ba does not contribute to not contribute to the VBM(CBM) and CBM, although it does provide electrons to balance the system the VBM CBM, although it does provide to balance the relative system energy chargepositions [42]. Therefore, chargeand [42]. Therefore, the bandgap value ofelectrons BaTiO3 depends on the of the the bandgap value of BaTiO3 depends on the relative energy positions of the Ti 3d and O 2p states.

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Ti 3d and 2p states. However, as a light 3 is too large to However, as O a light absorbing material, theabsorbing bandgap material, of BaTiOthe too largeoftoBaTiO efficiently absorb the 3 is bandgap efficiently visible light. absorb the visible light.

Figure Band structure,total totaland andpartial partialdensity density of of states states of Figure 3. 3. Band structure, of pure pure cubic cubicBaTiO BaTiO3.3 .

In order to clarify the co-doping effects with different transition metals on the electronic In order to clarify the co-doping effects with different transition metals on the electronic properties properties of the cubic BaTiO3, we systematically and carefully compared the band structures and of the cubic BaTiO , we systematically and carefully compared the band structures and density of density of states 3of the different co-doping systems. The co-doping systems can be divided into two states of different The3dco-doping canMn, be Fe, divided into two types: the BVM″TO and co-doping BNbM″TO.systems. M″ includes transition systems metals (Cr, Co, and Ni) andtypes: 4d 00 00 00 BVM TO and BNbM TO. M includes 3d transition metals (Cr, Mn, Fe, Co, and Ni) and 4d transition transition metals (Mo, Tc, Ru, and Pd). Accordingly, the classified discussion is conducted in detail metals (Mo, Tc, Ru, and there Pd). Accordingly, classified is conducted detail as follows. as follows. Although exist the spin the channels, the discussion magnetic properties of theinsystem have not Although there exist the spin channels, the magnetic properties of the system have not been discussed been discussed in the article. The main reason is that this article mainly focuses on the change of the in the article.inThe main reason is that mainly focuses on change of the bandgap in the bandgap the co-doped system andthis the article effect on the absorption of the light. 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) 3.3.1. V and 3d M00 Co-Doping (Cr, Mn, Fe, Co and Ni) Figure 4 reveals that the bandgap of BaTiO3 after co-doping is narrowed due to the Figure 4 reveals the bandgap BaTiO is narrowed due to the introduction introduction of thethat impurity energy of levels (IELs). It co-doping is noticed that BaTiO3, after V-M″ co-doping, 3 after 00 co-doping, of the impurity energy levels (IELs). It is noticed that BaTiO , after V-M exhibits exhibits ferromagnetism, except for V-Co co-doping. The ferromagnetism caused by transition 3 metal doping is also found in other doped semiconductors, such as V-Cr co-doped ZnO [43], Mn ferromagnetism, except for V-Co co-doping. The ferromagnetism caused by transition metal doping doped GaNin[44], and Mn doped AIN [45]. The majority spin (up-spin) DOS hasMn a smaller is also found other doped semiconductors, such as V-Cr co-doped ZnO [43], dopedbandgap GaN [44], minority spinThe (down-spin) DOS.(up-spin) The bandgaps on aboth spin bandgap states arethan formed by the andthan Mn the doped AIN [45]. majority spin DOS has smaller the minority interaction of the V 3d or M″ 3d states with the O 2p states. The electronic structure of BaTiO 3 isor spin (down-spin) DOS. The bandgaps on both spin states are formed by the interaction of the V 3d 00 significantly modified by the dopants. The V 3d states are located at the bottom of the conduction M 3d states with the O 2p states. The electronic structure of BaTiO3 is significantly modified by the band (CB), the 3d of Cr, Mn,bottom Fe, Co,ofand show up at the (CB), top ofwhile valence (VB)of dopants. The Vwhile 3d states arestates located at the theNi conduction band theband 3d states V-Mn and Ni V-Fe co-doping) in of thevalence middleband of the bandgap (V-Co and and V-Fe V-Nico-doping) co-doping).or Cr, (V-Cr, Mn, Fe, Co, and show up at theortop (VB) (V-Cr, V-Mn Thus, the energy states from the dopants form new CBM, VBM, or a transition state in the bandgap, in the middle of the bandgap (V-Co and V-Ni co-doping). Thus, the energy states from the dopants leading to a relatively narrow bandgap. Figure 4 shows that the IELs (from Cr, Mn, Co, and Ni) form new CBM, VBM, or a transition state in the bandgap, leading to a relatively narrow bandgap. move from left to right, which means the highest occupied energy level of the 3d states is arranged Figure 4 shows that the IELs (from Cr, Mn, Co, and Ni) move from left to right, which means the in the order of Cr < Mn < Co < Ni from lower to higher energy, consistent with the number of the d highest occupied energy level of the 3d states is arranged in the order of Cr < Mn < Co < Ni from lower electrons in these atoms. to higher energy, consistent number of the electrons in these atoms. For further analysis with of thethe effect of IELs in d the co-doping systems, we compared the band For further analysis of the effect of IELs in the co-doping systems, we compared band structures of the V-Cr (a) and V-Co (b) co-doping systems (Figure 5). The bandgaps of V-Crthe (a) and 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 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

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to theshift middle result inresult a smaller bandgap. But the areare located of the to theand middle and in a smaller bandgap. But Co the 3d Co states 3d states locatedininthe the middle middle of shift to the middle and result in a smaller bandgap. But the Co 3d states are located in the middle of bandgap, forming an intermediate level. Such a level in the bandgap usually plays two roles. One the bandgap, forming an intermediate level. Such a level in the bandgap usually plays two roles. is the bandgap, forming an intermediate level. Such a level in the bandgap usually plays two roles. to form a step theaelectron and the other is to electron-hole recombination One is to for form step for transition the electron transition and thework otheras is the to work as the electron-hole One is to form a step for the electron transition and the other is to work as the electron-hole recombination centerconcentration when the doping concentration is too high. The former isvisible beneficial toabsorption, visible center when the doping is too high. The former is beneficial to light 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 andshow but the latter hinders electron-hole separation. Therefore, combining Figures 4 and 5, the results 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 that V-Cr, V-Mn, andshow V-Fethat co-doping should bandgap and better visible light absorption Figure 5, the results V-Cr, V-Mn, andhave V-Fesuitable co-doping should have suitable bandgap and better visible light absorption than V-Co and V-Ni. better visible light absorption than V-Co and V-Ni. than V-Co and V-Ni.

20 20 0 0

TDOS TDOS V-3d V-3d Cr-3d Cr-3d O-2p O-2p

-20 -20 10 10

-10 -10 20 20 0 0

TDOS V-3d Fe-3d O-2p

DOS

DOS

0

TDOS TDOS V-3d V-3d Mn-3d Mn-3d O-2p O-2p

0

-20 -20 20 20 0

TDOS TDOS V-3d V-3d Co-3d Co-3d O-2p O-2p

0

-20 -20 10 10 0

TDOS V-3d Fe-3d O-2p

TDOS TDOS V-3d V-3d Ni-3d Ni-3d O-2p O-2p

0

-10 -10 -4

-4

-2

-2

0

0

Energy(eV) Energy(eV)

2

2

4

4

Figure 4. The total and partial density of states of the V-M″ (3d metal elements: Cr, Mn, Fe, Co, and

00 (3d Figure 4. The of of states of the V-M″ (3d metal elements: Cr, Mn, Co, and Figure Thetotal totaland andpartial partialdensity density states of the V-M metal elements: Cr,Fe, Mn, Fe, Co, and Ni) Ni) co-doped BaTiO3. The black dashed line indicates the position of the Fermi level. Ni) co-doped BaTiO 3 . The black dashed line indicates the position of of thethe Fermi level. co-doped BaTiO3 . The black dashed line indicates the position Fermi level.

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

FigureCr5.3dThe band structures theblue V-Cr (a) indicate and V-Co (b)states. co-doped BaTiO3 . The red lines indicate Cr states or Co 3d states.ofThe lines V 3d Cr 3d states or Co 3d states. The blue lines indicate V 3d states. 3d states or Co 3d states. The blue lines indicate V 3d states.

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3.3.2. V and 4d M″ Co-Doping (Mo, Tc, Ru and Pd) 00 Co-Doping Asand shown Figure 6, the IELs 3.3.2. V 4d Min (Mo, Tc, introduced Ru and Pd) 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 As shown in Figure 6, the IELs introduced by V-4d M00 co-doping emerges in the middle of the IELs of 3d metals. The reason is that the 4d states have higher energy than the 3d states of the bandgap and CB. Compared with Figure 4, the IELs of the 4d metals are even closer to the CB than transition metals. Therefore, the IELs of V co-doping with the 4d transition metals are closer to the the IELs of 3d metals. The reason is that the 4d states have higher energy than the 3d states of the conduction band and belong to the significant n-doping. The Fermi level (EF) gradually shifts from transition metals. Therefore, the IELs of V co-doping with the 4d transition metals are closer to the the conduction band to the valence band with the increase of the atomic number of the M″ elements. conduction band and belong to the significant n-doping. The Fermi level (EF ) gradually shifts from The definition of the Fermi level is the highest energy level of the electron at the absolute zero the conduction band to the valence band with the increase of the atomic number of the M00 elements. degree, which corresponds to the energy state at 0 eV. It can act as a reference to discuss the effects The definition of the Fermi level is the highest energy level of the electron at the absolute zero degree, of the transition metal co-doping on the band edge modification and the bandgap variation. The which corresponds to the energy state at 0 eV. It can act as a reference to discuss the effects of the IELs in the bandgap and near the bottom of the CB partially (V-Tc, V-Ru and V-Pd co-doping transition metal co-doping on the band edge modification and the bandgap variation. The IELs in the systems) or wholly overlap with the CBM (V-Mo co-doping system). Both cases can lead to the bandgap and near the bottom of the CB partially (V-Tc, V-Ru and V-Pd co-doping systems) or wholly CBM downward shifting, while the valence bands remain barely unchanged upon the co-doping. overlap with the CBM (V-Mo co-doping system). Both cases can lead to the CBM downward shifting, The Fermi levels of the V-M″ (Mo, Tc, Ru and Pd) co-doping systems pass through the IELs, that is while the valence bands remain barely unchanged upon the co-doping. The Fermi levels of the V-M00 to say, the electrons can occupy the IELs below the Fermi level in the ground state. Due to the small (Mo, Tc, Ru and Pd) co-doping systems pass through the IELs, that is to say, the electrons can occupy distance between this energy level and the bottom of the CB, electrons can be excited by absorbing the IELs below the Fermi level in the ground state. Due to the small distance between this energy level small photon energy [46,47]. and the bottom of the CB, electrons can be excited by absorbing small photon energy [46,47].

20

TDOS V-3d Mo-4d O-2p

0 -20 20

TDOS V-3d Tc-4d O-2p

DOS

0 -20 20

TDOS V-3d Ru-4d O-2p

0 -20 20

TDOS V-3d Pd-4d O--2p

0 -20 -4

-2

0

Energy(eV)

2

4

00 Figure Figure6.6.The Thetotal totaland andpartial partialdensity densityofofstates statesofofthe theV-M V-M″(4d (4dmetal metalelements: elements:Mo, Mo,Tc, Tc,Ru Ruand andPd) Pd) co-doped BaTiO . The black dashed line indicates the position of the Fermi level. 3 co-doped BaTiO3. The black dashed line indicates the position of the Fermi level.

00 3.3.3. 3.3.3.Nb Nband and3d 3dM M″Co-Doping Co-Doping(Cr, (Cr,Mn, Mn,Fe, Fe,Co Coand andNi) Ni) 00 (Cr, Mn, Fe, Co Figure effects of of this series of co-doping areare similar to the V-MV-M″ Figure7 7shows showsthat thatthe the effects this series of co-doping similar to the (Cr, Mn, Fe, and described in Figure 4. The 4. only is that the energy the Nbof4dthe states Co Ni) andco-doping Ni) co-doping described in Figure Thedifference only difference is that theof energy Nb is 4d higher than that of the V 3d states. Consequently, the V 3d states are located at the CBM but the Nb 4d states is higher than that of the V 3d states. Consequently, the V 3d states are located at the CBM states are Nb in the the Nb 4dTherefore, states havethe littleNb effect the bandgap and thereon is no but the 4dupper statesCB. areTherefore, in the upper CB. 4d on states have little effect the synergistic effect between the co-dopants. The Fermi level moves from CB to VB with the increase bandgap and there is no synergistic effect between the co-dopants. The Fermi level moves from of CB the atomic of M00ofelements. The Cr, Mn,ofand 3d statesThe occur theand middle ofstates the bandgap to VB withnumber the increase the atomic number M″Ni elements. Cr, in Mn, Ni 3d occur in and intermediate state might be beneficial to the electron the become middlethe of intermediate the bandgaplevel. and The become the intermediate level. The intermediate statetransition might be under visible-light irradiation. However, it might not be conducive to the effective separation of the beneficial to the electron transition under visible-light irradiation. However, it might not be

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conducive conducive to to the the effective effective separation separation of of the the electron-hole electron-hole since since it it could could also also act act as as the the recombination recombination centers on the other hand. In addition, the Fe and Co 3d states are divided into two parts, where centers on thesince other In addition, the Fe and Co 3dcenters states are divided two where the electron-hole it hand. could also act as the recombination on the otherinto hand. Inparts, addition, thethe Fe high energy part is weak the bottom of the low energy part is strong, which is highCo energy partare is divided weak at atinto the two bottom ofwhere the CB, CB, and the low part energy part at is the strong, which is and 3d states parts, theand highthe energy is weak bottom of the located at the top of the VB. Both cases can lead to the bandgap narrowing and are beneficial to located at the top of the VB. Both cases can lead to the bandgap narrowing and are beneficial to CB, and the low energy part is strong, which is located at the top of the VB. Both cases can lead to the visible-light absorption. visible-light absorption. bandgap narrowing and are beneficial to visible-light absorption. 00 co-doping In Nb-M″ these Nb-M Nb-M″ Nb-Co In these these co-doping systems, systems, we we chose chose two two typical typical doping doping forms, forms, the the Nb-Mn Nb-Mn and and Nb-Co Nb-Co co-doping systems, to further investigate their band structures, as shown in Figure 8. The bandgaps further investigate their band structures, as as shown shown in in Figure Figure 8. 8. The The bandgaps bandgaps co-doping systems, to further are found eV, the co-doping IELs in are found foundtoto tobebe be 1.2 and 0.96 eV, respectively. respectively. In the Nb-Mn Nb-Mn co-doping system, thethe IELs in the the are 1.21.2 andand 0.960.96 eV, respectively. In theIn Nb-Mn co-doping system, system, the IELs the in middle of middle of bandgap are contributed by the Mn 3d states. However, in the Nb and Co co-doping middle of bandgap are contributed by the Mn 3d states. However, in the Nb and Co co-doping bandgap are contributed by the Mn 3d states. However, in the Nb and Co co-doping system, the Co system, 3d 2p states form hybridization the original VB system, the Co 3d and and Othe 2pp-d states form the the p-d p-d hybridization and locate above above the original VB or or 3d and Othe 2pCo states formO hybridization and locate aboveand the locate original VB or partly coincided partly coincided with the CB. both co-doping could the partlythe coincided with the bottom ofboth theco-doping CB. Overall, Overall, both co-doping could reduce reduce the bandgap bandgap with bottom of the the CB. bottom Overall,of could reduce the bandgap effectively but with effectively but causes. It necessary that Mn heavy effectively but with with different causes. It is is also alsothat necessary to consider that Nb Nb and and Mn heavy different causes. It is different also necessary to consider Nb andto Mnconsider heavy co-doping might lead to a co-doping might lead to a serious recombination due to the IELs in the bandgap. co-doping might lead to a serious recombination due to the IELs in the bandgap. serious recombination due to the IELs in the bandgap. 20 20

TDOS TDOS Nb-4d Nb-4d Cr-3d Cr-3d O-2p O-2p

00 -20 -20 20 20

TDOS TDOS Nb-4d Nb-4d Mn-3d Mn-3d O-2p O-2p

00

DOS DOS

-20 -20 20 20

TDOS TDOS Nb-4d Nb-4d Fe-3d Fe-3d O-2p O-2p

00 -20 -20 20 20

TDOS TDOS Nb-4d Nb-4d Co-3d Co-3d O-2p O-2p

00 -20 -20 20 20

TDOS TDOS Nb-4d Nb-4d Ni-3d Ni-3d O-2p O-2p

00 -20 -20 -4 -4

-2 -2

00

22

44

Energy(eV) Figure of the Nb-M″ Figure 7. 7. The The total total and and partial partial density density of of states states of of the the Nb-M Nb-M″ (3d metal metal elements: elements: Cr, Cr, Mn, Mn, Fe, Fe, Co, Co, and and 00 (3d Figure 7. The total and partial density of states (3d metal elements: Cr, Mn, Fe, Co, and Ni) co-doped BaTiO 33.. The black dashed line indicates the position of the Fermi level. Ni) co-doped BaTiO The black dashed line indicates the position of the Fermi level. Ni) co-doped BaTiO3 . The black dashed line indicates the position of the Fermi level.

Figure 8. The band structures of Nb-Mn (a) and Nb-Co (b) co-doped BaTiO Figure 8. 8. The The band band structures structures of of Nb-Mn Nb-Mn (a) (a) and and Nb-Co Nb-Co (b) (b)co-doped co-doped BaTiO BaTiO33... The The red red lines lines indicate indicate Figure 3 The red lines indicate Mn 3d states (a) and Co 3d states (b). Mn 3d states (a) and Co 3d states (b). Mn 3d states (a) and Co 3d states (b).

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3.3.4.Nb-4d Nb-4dMM″ Co-Doping(Mo, (Mo,Tc, Tc,Ru Ruand andPd) Pd) 00 Co-Doping 3.3.4. Asshown shownininFigure Figure9,9,Nb-Mo, Nb-Mo,Nb-Tc, Nb-Tc,Nb-Ru, Nb-Ru,and andNb-Pd Nb-Pdco-doping co-dopinghave havevery verylittle littleinfluence influence As on the top of valence band, but it changes the distribution of the electron states at the bottom the on the top of valence band, but it changes the distribution of the electron states at the bottom ofofthe conduction band. The Nb 4d states are in the middle of the conduction band, while the Mo, Tc, Ru, conduction band. The Nb 4d states are in the middle of the conduction band, while the Mo, Tc, Ru, andPd Pd3d 3dstates statesare arelocated locatedatatthe theconduction conductionband bandbottom bottomororininthe thebandgap. bandgap.Hence Hencethis thisseries seriesofof and co-dopings have no synergistic influence, and the doping effects around the bandgap are similar co-dopings have no synergistic influence, and the doping effects around the bandgap are similar to theto the individual Mo,Ru, Tc,orRu, Pd doping. individual Mo, Tc, Pdor doping. 20 TDOS Nb-4d Mo-4d O-2p

0

DOS

-20 20

TDOS Nb-4d Tc-4d O-2p

0 -20 20

TDOS Nb-4d Ru-4d O-2p

0 -20 20

TDOS Nb-4d Pd-4d O-2p

0 -20 -4

-2

0

2

4

Energy(eV) 00 (4d Figure9.9.The Thetotal totaland andpartial partialdensity densityofofstates statesofofthe theNb-M Nb-M″ (4dmetal metalelements: elements:Mo, Mo,Tc, Tc,Ru Ruand andPd) Pd) Figure co-dopedBaTiO BaTiO 3. The black dashed line indicates the position of the Fermi level. co-doped 3 . The black dashed line indicates the position of the Fermi level.

Generally, according to the results above, transition metal co-doping can have three effects on 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 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 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. above the VB, overlap with the top of VB in different degrees, and make the VBM move up. Thirdly, Thirdly, the IELs lie in the middle of the bandgap to form the intermediate energy level. In the the IELs lie in the middle of the bandgap to form the intermediate energy level. In the actual co-doping actual co-doping system, two or more effects can coexist to modify the energy bandgap. 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 In order to further study the difference between the single doping and co-doping systems, calculated the band structures and total and partial DOS of V doped BaTiO3, Nb doped BaTiO3, and we calculated the band structures and total and partial DOS of V doped BaTiO3 , Nb doped BaTiO3 , Cr doped BaTiO3, as shown in Figure 10. The band structures clearly show that V doping reduces 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 to 1.15 eV since the V 3d states appear at the bottom of CB and form a new CBM. But the the bandgap after Nb doping is 1.63 eV, which is even a bit larger than pure BaTiO3 (1.56 eV). The bandgap after Nb doping is 1.63 eV, which is even a bit larger than pure BaTiO3 (1.56 eV). The reason reason is that the Nb 4d states are located in the CB and far away from CBM, which have little effect is that the Nb 4d states are located in the CB and far away from CBM, which have little effect on the on the bandgap. Thus, in the Nb-M″ co-doping system, the doping effect mostly depends on the bandgap. Thus, in the Nb-M00 co-doping system, the doping effect mostly depends on the single M00 single M″ doping. In the Cr-doped BaTiO3, an IEL emerges in the bandgap, which is quite different doping. In the Cr-doped BaTiO3 , an IEL emerges in the bandgap, which is quite different from the V from the V and Nb doping systems. and Nb doping systems.

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Figure 10. Band structures and total and partial density of states (DOS) of (a,b) Ba8Ti7VO24, (c,d) Figure 10. Band structures and total and partial density of states (DOS) of (a,b) Ba8 Ti7 VO24 , Ba8Ti7NbO24, and (e,f) Ba8Ti7CrO24. (c,d) Ba8 Ti7 NbO24 , and (e,f) Ba8 Ti7 CrO24 .

In addition, we compared the band structure and DOS of V, Cr, and V-Cr doped BaTiO3. In the In addition, the band structure DOS ofIn V, the Cr, and V-Cr doped V-doped BaTiO3, we the compared IELs are located at the bottomand of the CB. Cr-doped BaTiO3,BaTiO the IELs 3 . In the V-doped are bandgap located atand the bottom of intermediate the CB. In theenergy Cr-doped BaTiO , the IELs appear appear inBaTiO the middle of the form the level. But3 in the V-Cr 3 , the IELs in the middle of the bandgap and form the intermediate energy level. But in the V-Cr co-doped

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co-doped BaTiO3 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 BaTiO3 as shown in Figure 4, the IELs divided into two parts. One was situated at the bottom of from the single Cr, doping disappeared, as confirmed in Figure 5a. Thus, the V-Cr co-doping can the CB, and the other at the top of the VB. Finally, as the intermediate energy level raised from the overcome the shortcoming of the single Cr doping and combine the advantages of the V and Cr single Cr, doping disappeared, as confirmed in Figure 5a. Thus, the V-Cr co-doping can overcome the doping in reducing the bandgap to effectively shift the CBM and VBM toward the bandgap. shortcoming of the single Cr doping and combine the advantages of the V and Cr doping in reducing Through such synergistic effect, the light absorption range could be expanded and the visible-light the bandgap to effectively shift the CBM and VBM toward the bandgap. Through such synergistic photoelectrical activity is expected to improve. effect, the light absorption range could be expanded and the visible-light photoelectrical activity is Furthermore, the charge density distribution was investigated for the V-doped, Cr-doped, and expected to improve. V-Cr co-doped BaTiO3 as shown in Figure 11, which indicates that Ti-O, Cr-O, and V-O form Furthermore, the charge density distribution was investigated for the V-doped, Cr-doped, and covalent bonds. Due to different electronegativity (Ti < V < Cr < O), the covalent bond strength is V-Cr co-doped BaTiO3 as shown in Figure 11, which indicates that Ti-O, Cr-O, and V-O form covalent different. The greater the metal electronegativity is, the smaller the electronegativity difference bonds. Due to different electronegativity (Ti < V < Cr < O), the covalent bond strength is different. between the metal and oxygen atoms, and the more uniform is the charge density distribution. The greater the metal electronegativity is, the smaller the electronegativity difference between the According to an effective empirical determining method, the electronic energy level of an element is metal and oxygen atoms, and the more uniform is the charge density distribution. According to an usually inversely proportional to its electronegativity. That is to say, the higher the effective empirical determining method, the electronic energy level of an element is usually inversely electronegativity, the lower the position of the energy level and the lower the position of the proportional to its electronegativity. That is to say, the higher the electronegativity, the lower the corresponding energy band [48]. Therefore, when Cr or V with larger electronegativity was doped position of the energy level and the lower the position of the corresponding energy band [48]. Therefore, into BaTiO3, the IELs with a relatively low energy position were introduced around the CBM or in when Cr or V with larger electronegativity was doped into BaTiO3 , the IELs with a relatively low energy the bandgap, leading to a narrower bandgap after doping. The results are verified by the line position were introduced around the CBM or in the bandgap, leading to a narrower bandgap after profile of the charge density as displayed in Figure 11a–c. The charge density of Ti, O, Cr, and V is doping. The results are verified by the line profile of the charge density as displayed in Figure 11a–c. slightly decreased in various degrees after Cr-V co-doping compared to the single Cr or V doping. The charge density of Ti, O, Cr, and V is slightly decreased in various degrees after Cr-V co-doping It can be found that in comparison to the single doping, where the charge density is more localized compared to the single Cr or V doping. It can be found that in comparison to the single doping, where around the atoms, V-Cr co-doping could result in a relatively evener charge distribution. This not the charge density is more localized around the atoms, V-Cr co-doping could result in a relatively only causes the hybridization of the newly introduced IELs and the initial CBM or VBM of the pure evener charge distribution. This not only causes the hybridization of the newly introduced IELs and BaTiO3, but is associated with the interaction among the newly introduced energy states due to the the initial CBM or VBM of the pure BaTiO3 , but is associated with the interaction among the newly V-Cr synergistic effect, which accounts for the bandgap engineering by the co-doping for introduced energy states due to the V-Cr synergistic effect, which accounts for the bandgap engineering visible-light activation. by the co-doping for visible-light activation.

Figure Charge-density distributions metal doped BaTiO (100) surfaces: (a–c) Line profiles 3 in Figure 11.11.Charge-density distributions ofof metal doped BaTiO 3 in (100) surfaces: (a–c) Line profiles corresponding to the black dotted lines; (d) V and Cr co-doped BaTiO ; (e) Cr doped 3 doped BaTiO3;BaTiO corresponding to the black dotted lines; (d) V and Cr co-doped BaTiO3; (e) Cr (f) V 3 ; (f) V doped BaTiO . 3 doped BaTiO3.

order furtheranalyze analyze thecharge chargedensity densitynear near thebandgap, bandgap, wecalculated calculated the distribution InIn order totofurther the the we the distribution ofof the partial charge density from the top ofof the valence band toto the bottom ofof the conduction band, the partial charge density from the top the valence band the bottom the conduction band, asasshown shownininFigure Figure12,12,which whichcould couldreveal revealthe thevisual visualinformation informationofofthe theelectron electrondensities densitiesmainly mainly derived doped/co-doped atoms. atoms.The The calculated partial electron density in the V-Cr derivedfrom from the doped/co-doped calculated partial electron density in the V-Cr co-doped co-doped BaTiO3 distributed around the V and Cr dopants is shown in Figure 12a, and is mainly

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BaTiO around the V and Cr dopants is shown in Figure and is mainly derived from 3 distributed derived from the Cr 3d isolated non-bond states and the hybrids12a, between the V 3d and O 2p the Cr 3d isolated non-bond states and the hybrids between the V 3d and O 2p electronic states, electronic states, as suggested by Figures 4 and 5. Figure 12b presents the partial electron density on as by Figures 5. Figure presents the partial electron density onconfirmed Cr in the Cr Cr suggested in the Cr doped BaTiO43,and which consists12b significantly of the isolated Cr 3d orbitals by doped BaTiO , which consists significantly of the isolated Cr 3d orbitals confirmed by Figure 10f. 3 Figure 10f. From Figure 12c, the partial electron density calculated in the V doped BaTiO3 distributed From Figure the partial electronoriginates density calculated the Varising dopedfrom BaTiO distributed around around the V 12c, atom, which primarily from V-O in bonds the3 hybridization of the the V atom, which primarily originates from V-O bonds arising from the hybridization of the 2p O 2p and V 3d orbitals. As such, the doped/co-doped atoms play a key role in narrowingOthe and V 3d orbitals. As such, the doped/co-doped atoms play a key role in narrowing the bandgap of bandgap of BaTiO3. These results also reveal that the appropriate selection of co-doping elements, BaTiO Theseco-doping, results alsocan reveal that appropriate selection co-doping elements, such as V-Cr 3 . V-Cr such as result in the synergistic effects by theof two co-dopants that can effectively co-doping, can result in synergistic effects by the two co-dopants that can effectively manipulate manipulate the bandgap. Before choosing the pair of dopants for co-doping, it is importantthe to bandgap. Before choosing the pair of of the dopants for co-doping, it is important to examine thethe electronic examine the electronic structures individual doping and their interaction so that pair of structures the individual doping and their to interaction that the of dopants in the co-doping dopants inof the co-doping system can coexist properly so modify thepair bandgap edge and improve the system can coexist to properly modify the bandgap edge and improve the visible-light adsorption visible-light adsorption properties. Besides the electronic structure, charge mobility and surface properties. Besides the electronic structure, mobility and surface which properties/states also play properties/states also play important roles incharge the photoelectric behavior, should be addressed important roles in the photoelectric behavior, which should be addressed in the future. in the future.

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

4. Conclusions 4. Conclusions In summary, the formation energy and electronic properties of the transition metal V-M00 and In summary, the formation energy and electronic properties of the transition metal V-M″ and Nb-M00 co-doped BaTiO3 have been studied by first-principles calculations. The results indicate that Nb-M″ co-doped BaTiO3 have been studied by first-principles calculations. The results indicate that the V-M00 co-doping is more suitable than the Nb-M00 co-doping for narrowing the bandgap of BaTiO3 the V-M″ co-doping is more suitable than the Nb-M″ co-doping for narrowing the bandgap of and increasing the absorption of visible light, since the V-M00 co-doping can form shallow levels BaTiO3 and increasing the absorption of visible light, since the V-M″ co-doping can form shallow around the bandgap edge while those energy levels induced by the Nb-M00 co-doping are usually levels around the bandgap edge while those energy levels induced by the Nb-M″ co-doping are deep levels in the energy band or bandgap. The optimal co-doping model is proposed as the V-Cr usually deep levels in the energy band or bandgap. The optimal co-doping model is proposed as co-doped BaTiO3 , which not only has favorable defect formation energy, but also significantly reduce the V-Cr co-doped BaTiO3, which not only has favorable defect formation energy, but also the bandgap. Simultaneous introduction of V and Cr results in a synergistic effect, which has been significantly reduce the bandgap. Simultaneous introduction of V and Cr results in a synergistic demonstrated by the detailed analysis of the density of states, band structure, and charge-density effect, which has been demonstrated by the detailed analysis of the density of states, band structure, distribution of the doping systems. V-Cr co-doping could overcome the shortcoming of the single Cr and charge-density distribution of the doping systems. V-Cr co-doping could overcome the doping and combine the advantages of both the V and Cr doping. For this optimal co-doped BaTiO3 shortcoming of the single Cr doping and combine the advantages of both the V and Cr doping. For system, the Cr 3d states are located just above the VBM and the V 3d states occupied band just below this optimal co-doped BaTiO3 system, the Cr 3d states are located just above the VBM and the V 3d the CBM, corresponding to a bandgap narrowing of about 0.4 eV, which is beneficial for efficient states occupied band just below the CBM, corresponding to a bandgap narrowing of about 0.4 eV, visible-light adsorption. The results can provide an important guideline for future experiments to which is beneficial for efficient visible-light adsorption. The results can provide an important modify the wide BaTiO3 bandgap for visible-light driven solar applications. guideline for future experiments to modify the wide BaTiO3 bandgap for visible-light driven solar applications. Materials: The following are available online at http://www.mdpi.com/2079-4991/8/7/455/s1, Supplementary Figure S1: The lattice constants of transition metals co-doped cubic BaTiO3 , Table S1: The special K points 00 co-doping system, coordinates, Table S2: The The average bond length obtained afteratoptimization of the V-M Supplementary Materials: following are available online www.mdpi.com/link, Figure S1: The lattice 00 Table S3: The average bond length obtained after optimization of the Nb-M co-doping system. constants of transition metals co-doped cubic BaTiO 3, Table S1: The special K points coordinates, Table S2: The average Contributions: bond length obtained after optimization of the co-doping system, Tableand S3:P.X. Theperformed average bond Author S.L. conceived and designed theV-M″ experiments; F.Y., L.Y., C.A. the theoretical; F.Y., C.W. X.L. analyzed data; co-doping F.Y. wrote system. the paper. length obtained after and optimization of thethe Nb-M″

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.

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Funding: This research was funded by the Key Research and Development Program of Hainan Province (ZDYF2017166) and National Natural Science Foundation of China (Grant Nos. 51462008, 61764003). Work at Ames Laboratory was supported by the US Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering under Contract No. DE-AC02-07CH11358, including a grant of computer time at the National Energy Research Scientific Computing Centre (NERSC) in Berkeley, CA. Acknowledgments: This work is supported by the Key Research and Development Program of Hainan Province (ZDYF2017166) and National Natural Science Foundation of China (Grant Nos. 51462008, 61764003). Work at Ames Laboratory was supported by the US Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering under Contract No. DE-AC02-07CH11358, including a grant of computer time at the National Energy Research Scientific Computing Centre (NERSC) in Berkeley, CA. Conflicts of Interest: The authors declare no conflict of interest.

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