Physics Letters A 374 (2010) 4919–4927

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Density functional theory study of doping effects in monoclinicclinobisvanite BiVO4

Zongyan Zhao a,c, Wenjun Luo a,c, Zhaosheng Li a,b,c,∗, Zhigang Zou a,c,∗a Ecomaterials and Renewable Energy Research Center (ERERC), Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of Chinab Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, People’s Republic of Chinac National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 May 2010Received in revised form 4 October 2010Accepted 9 October 2010Available online 13 October 2010Communicated by R. Wu

Keywords:Doping effectsMonoclinic BiVO4

Density functional theory calculations

The doping effects of several transition metal impurities for monoclinic BiVO4 are studied by DFTcalculations. The results indicated that transition metal doping could reduce the effective mass of holeson the top of valence band, except Zr doping. In particular, we found the “e” states of impurities havesignificant influence on the photophysical properties of BiV1−xMxO4 under visible-light irradiation.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Since the entry of industrialization, environmental pollutionand energy crisis are increasingly serious. Scientific research, tech-nical development, and governments around the world have givengreat concerns. In a variety of solutions, heterogeneous photocat-alytic and photoelectrochemical technologies are extremely poten-tial and promising, because they can utilize or convert the harm-less inexhaustible solar energy. In the past decades, titanium diox-ide (TiO2) has been attracted extensively attention because of itsexcellent photocatalytic activity and stability, comparing with otherphotocatalysts [1–3]. However, as a wide band gap (3.0–3.2 eV)semiconductor, TiO2 only shows photocatalytic activity under UV-light irradiation. This intrinsic drawback significantly restricts itscapability to effectively utilize solar energy. Therefore, in order totake full advantage of solar energy, there are two main guidelinesto develop efficient visible-light driven photocatalyst. The first isto modify TiO2, such as ionic doping (including metal and non-metal), noble metal loading, and dye sensitizing [4]. Although, themodification on TiO2 has been extensively investigated, the re-sults are not always matched with expectations, for example: iondoping could not make the absorption threshold of TiO2 to dra-matically red-shift towards visible-light region; noble metal load-ing has very great cost; dye sensitizing system is unstable; etc.

* Corresponding authors at: Ecomaterials and Renewable Energy Research Center(ERERC), Department of Physics, Nanjing University, Nanjing 210093, People’s Re-public of China. Tel.: +86 25 83686603; fax: +86 25 83686632.

E-mail addresses: zsli@nju.edu.cn (Z. Li), zgzou@nju.edu.cn (Z. Zou).

0375-9601/$ – see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.physleta.2010.10.014

Thus, researchers pay more attention to the progress in the sec-ond guideline, design and development of novel non-titania basedphotocatalyst, such as: In1−xNixTaO4 (x = 0–0.2) [5], CdIn2S4 [6],Ag3VO4 [7], BiVO4 [8], InNbO3 [9], InVO4 [10].

Bismuth vanadate (BiVO4) is a non-toxic yellow pigment whichhas been considered as a very interesting alternative for heavymetals pigment [11,12]. Besides application as a pigment, BiVO4has other important properties such as ferroelasticity, ionic con-ductivity and photocatalytic activity. Recently, the photocatalyticactivity of BiVO4 is particularly concerned [8,13–15]. Furthermore,it is intensively studied as an extremely promising photoelectrodematerial, due to its visible-light response and long-term stability[16–20]. However, the activity of the pure clinobisvanite BiVO4was still low in the visible-light region [21]. And the depen-dence of the activity of BiVO4 on the wavelength shown that itsworking wavelength threshold is locate about 480 nm, which isblue-shifted compared with that of its absorption spectrum (thewavelength threshold is located about 500–520 nm) [13,16,20]. Es-pecially, for the diffusion length of photo-excited carries in BiVO4is not enough long, so its photoelectrode thin films could nothave enough thickness. Another serious limitation is that BiVO4has no photocatalytic activity for H2 evolution, resulting in in-completely splitting water [8]. These deficiencies greatly limit itsapplications in practices. In order to enhance the photocatalyticand photoelectrochemical activity of BiVO4, researchers adoptedsome modification methods, such as: ion doping (including transi-tion metals [22,23], and rare earth [11,24–27]), noble metal loading[14,28–32], and semiconductor heterojunction [17,33,34]. Other re-searchers attempted to transform its microstructure to obtain high

4920 Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927

Fig. 1. Conventional unit cell of BiVO4 in the clinobisvanite structure (a). And the supercell model considered in the present work (b). The top view (c) and side view (d) ofthe supercell are also given.

activity (for example: nanoparticles [35], thin films [16,19], hollownanospheres [36], nanosheets [37], and nanotube [38,39]).

Among these solutions, the ion doping is simple preparationtechnology and low cost. In our previous work and other groups’reports [8,11,13,15,16,22,23,40], we found that: (i) the monoclinicclinobisvanite BiVO4 shows very higher photocatalytic activity forO2 evolution and organics degradation under visible-light irradia-tion, compared with the other polymorphs of BiVO4 (orthorhombicpucherite, and tetragonal dreyerite), and (ii) the photocatalytic andphotoelectrochemical activity of BiVO4 could be remarkably en-hanced by molybdenum or other metal doping. Even though theeffects of metal doping on the activity of BiVO4 have been a fre-quent topic, it remains difficult to make direct comparison andunifying conclusions due to the widely varying experimental con-ditions, materials preparation and the evaluation system of pho-tocatalytic activity. In contrast to the experimental investigation,theoretical analysis by computer simulation is expected to clar-ify in details the metal doping effects. In recent years, DensityFunctional Theory (DFT) calculations have made important con-tributions for this issue. To the best of our knowledge, there hasbeen few theoretical calculations regarding the origin of the metaldoping effects on clinobisvanite BiVO4, and some basic questionsare still open, such as differences of metals doping, what kinds ofchemical environment of impurities determining electronic prop-

erties. To address these purposes, in the present work, we studiedthe structural and electronic properties of several transition metals(Ti, Cr, Zr, Nb, Mo and W), which are around vanadium in peri-odic table, doping into BiVO4 using DFT calculations, and made astraightforward comparison between different metal doping effect.We will attempt to discuss the relationship between activity andstructure of the samples, and provided a possible explanation forexperimental observations.

2. Computational methods and details

The conventional cell of clinobisvanite BiVO4 and the 2 × 1 × 2supercell model (BiV1−xMxO4, M denotes a metal element, x =0.0625) considered in the present work are shown in Fig. 1. Clino-bisvanite BiVO4 has a monoclinic structure (point group: C6

2h , spacegroup: C2/c) and contains four bismuth or vanadium atoms andsixteen oxygen atoms in the unit cell. Our models consist of twounit cells stacked both along the a-axes and c-axes, in which a Vatom is substituted by a metal atom. Thus, one supercell that con-sists of 96 atoms has sufficient length to avoid the self-interactionsof impurity on each direction, and the impurity concentration isabout 1.04% (atomic fraction) in total, which is comparable to thatused in the experiments.

Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927 4921

Table 1Calculated lattice distortion and average dipole moment of tetrahedrons.

�a/Å �b/Å �c/Å �β/deg �V /Å3 Dipole moment/Debye

VO4 MO4

pure 0.0009Ti-doped 0.020 −0.020 0.016 −0.95 0.99 0.0186 0.0279Cr-doped 0.012 0.010 0.009 −0.96 1.06 0.0220 0.0249Zr-doped 0.044 −0.018 0.033 −0.93 2.93 0.0379 0.0064Nb-doped 0.035 −0.010 0.025 −0.95 2.40 0.0250 0.0082Mo-doped 0.032 0.000 0.024 −0.93 2.35 0.0179 0.0003W-doped 0.034 −0.004 0.026 −0.93 2.48 0.0209 0.0010

Fig. 2. Calculated impurity formation energies of metal doping into BiVO4 vary as a function of the difference of oxygen chemical potential.

(a)

Fig. 3. (a) Calculated band structure of BiV1−xMxO4 (M = Ti, Zr, or Nb), and the corresponding total density of states (b), and local partial density of states (c). The values ofband gap and width of energy band are also illustrated.

4922 Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927

(b)

(c)

Fig. 3. (Continued)

All of the DFT calculations in the present work had been per-formed with the Cambridge Serial Total Energy Package (CASTEP)codes [41]. The ultrasoft pseudopotential was chosen in the cal-culations, because it has several advantages both in efficiency andvelocity. The Kohn–Sham wave functions of the valence electronswere expanded using a plane wave basis set within a specified en-ergy cutoff that was chosen as 380 eV. Exchange and correlationeffects were described by the Perdew–Burke–Ernzerhof (PBE) gen-eralized gradient approximation [42]. The Monkhorst–Pack schemeK-points grid sampling was set as 2 × 2 × 3 for the irreducibleBrillouin zone. A 100 × 90 × 75 mesh was used for fast Fouriertransformation. The minimization algorithm was chosen Broyden–Fletcher–Goldfarb–Shanno (BFGS) scheme [43]. In order to get ac-curate results, we optimized atomic coordinates, which obtainedby minimizing the total energy and atomic forces. This was doneby performing an iterative process in which the coordinates of theatoms are adjusted so that the total energy of the structure is min-imized. By doing so, we could obtain stable structures for all the

models. The relaxation run was considered converged when theforce on the atom was less than 0.01 eV/Å, the stress on the atomwas less than 0.02 GPa, the displacement of the atom was lessthan 5 × 10−4 Å, and the energy change per atom was less than5 × 10−6 eV. Then we calculated the electronic structures for eachoptimized supercell model.

3. Results and discussions

3.1. Crystal structure

By optimizing the pure clinobisvanite BiVO4 structure, we gotthe lattice parameters as follows: a = 7.223 Å, b = 11.523 Å, c =5.107 Å, β = 134.994◦ . They were in good agreement with ex-perimental values [44]: a = 7.253 Å, b = 11.702 Å, c = 5.096 Å,β = 134.233◦ . These results implied that our calculation methodsare reasonable, and the calculated results should be authentic.

Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927 4923

(a)

Fig. 4. Same as Fig. 3, but for BiV1−xMxO4 (M = Cr, Mo, or W).

We firstly analyzed the lattice parameters of metal doping mod-els, and the results are displayed in Table 1. When impurities dop-ing into host lattice, the lattice distortion usually occurs, owingto the differences of ion radius and electronic states. But in thepresent work, we found that the lattice distortions are not obviousfor all metals doping. The reason maybe their radii and electroneg-ativities are very close. At this point, BiVO4 could keep its excellentphotocatalytic performance after doping with these metal impuri-ties. By structure optimizing, we get the atomic coordinates andthe electronic distributions of every atoms in the model. Thus, wecould calculate the center of positive charge and negative chargefor every tetrahedron, respectively. Then, the dipole moment couldbe calculated, too. In clinobisvanite BiVO4 structure, the centers ofpositive charge and negative charge in the VO4 tetrahedron do notmatch together, because there are two unequal type V–O bonds.So the dipole moment of VO4 tetrahedron is slightly deviate fromzero. By these metals doping, this deviation becomes more obvi-ous. Sato et al. reported that the local internal fields due to thedipole moment of distorted polyhedron can promote the chargeseparation in the very initial process of photo-excitation and areuseful for enhancing photocatalytic activity [45]. In Table 1, wealso gave the average dipole moments of tetrahedrons. This changecould make the photo-excited electron–hole pairs easier separat-ing, so metal doping could improve the photocatalytic performanceof BiVO4.

Then, we analyze the impurity formation energy (E f ), whichis a widely accepted method, to compare the relative degree ofdifficulty (or the solubility in host) for different metal impuritiesincorporate into the lattice of BiVO4. E f is calculated by the for-mula that is defined by Van de Walle et al. [46] as follows:

E f = Etot[BiV1−xMxO4] − Etot[BiVO4] − Etot[M] + μV (1)

where Etot[BiV1−xMxO4] and Etot[BiVO4] are the total energy ofdoping system and pure system using the same supercells, re-spectively; Etot[M] is the total energy of pure bulk metal; μV isthe chemical potential of V. The chemical potentials depend on

the experimental growth conditions (oxidizing conditions or re-ducing conditions). For pure BiVO4, μBi, μV, and μO satisfy therelationship: μBi +μV + 4μO = Etot[BiVO4]. Under extreme oxidiz-ing conditions, μO = 1

2 Etot[O2] in which Etot[O2] is the total energyof O2 molecule in gas phase; while under extreme reducing con-ditions, μV = Etot[V] in which Etot[V] is the total energy of bulkbcc V. The value of μBi is equal to Etot[Bi], the total energy of pureBi in rhombohedral structure, and does not change. Fig. 2 showsthe results for the metal doped BiVO4. These results indicate thatit is energetically unfavorable to dope metal ion into substitutionalsite under reducing conditions. In the case of Zr-doped, the impu-rity formation energy is the minimum, while that of Cr-doped isthe maximum. The energy of Nb-doped is nearly equal to that ofZr-doped. Based on the results of impurity formation energy, theequilibrium impurity concentrations (or the solubility in host) ofZr and Nb will be relatively higher than that of other metal impu-rities, according to the formalism by Van de Walle et al. [46].

3.2. Electronic structure

The calculated band structure and Density of States (DOS) of allsupercells are plotted and compared in Figs. 3 and 4. As shownin Fig. 3 or Fig. 4, we found that pure clinobisvanite BiVO4 is anindirect band gap semiconductor. And the calculated band gap ofpure clinobisvanite BiVO4 is 2.047 eV, which is smaller than theexperimental observe, 2.4 eV, due to the well known shortcomingof DFT. Although the absolute values of the calculated band gapsare not reliable [47], the relative value is reliable under the samecalculation protocols to compare different metal doping. The va-lence band (VB) and conduction band (CB) mainly consist of boththe O 2p states and V 3d states. The Bi 6p and 6s states also con-tribute to the composition of VB and CB. Because the V 3d statesare split into two parts (“e” state and “t2” state, respectively) owingto the tetrahedron ligand field effect, the CB is divided into lowerand upper parts. These features of pure BiVO4 are consistent withprevious calculations [20,48]. In the case of metal doping, their ndstates are somewhat delocalized, thus contributing significantly to

4924 Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927

(b)

(c)

Fig. 4. (Continued)

the formation of impurity energy levels that are constituted by theinterplay with around oxygen anions. And the width of VB or CB ischanged. These effects could impact the photophysical propertiesof BiVO4. For a systematic comparison and explanation, the result-ing electronic structures in BiV1−xMxO4 are classified into threegroups according to the relative energy of the impurity states. (i)BiV1−xTixO4, and BiV1−xZrxO4; (ii) BiV1−xNbxO4; (iii) BiV1−xCrxO4,BiV1−xMoxO4, and BiV1−xWxO4.

(i) BiV1−xTixO4, and BiV1−xZrxO4: Because Ti and Zr atom haveone less valence electron compared with V atom, so this type im-purity plays the role of acceptor energy level. As shown in Fig. 3(a),one could see that there are little empty energy levels above theFermi energy level that moves into the top of CB. Thus, BiVO4 willhave more hole-carriers by doping with Ti or Zr. The main impu-rity energy levels are located at the upper CB, which means thatTi or Zr doping influence the CB composition of BiVO4. So, the CB

Table 2The minimum effective mass of holes on the top of VB, and that of electrons on thebottom of CB. The corresponding k-point and direction are also given (see Fig. 3 andFig. 4).

m∗h/m0 m∗

e/m0

pure 0.41 VBM(� → Z) 0.55 D(D → B)Ti-doped 0.35 VBM(� → Z) 0.83 D1(D → B)*

Cr-doped 0.36 VBM(� → Z) 1.44 CBM(Y → A)Zr-doped 0.45 VBM(Z → �) 0.72 D1(D → B)Nb-doped 0.39 VBM(Z → �) 0.73 D1(D → B)Mo-doped 0.34 VBM(� → Z) 1.16 Y(Y → A)W-doped 0.35 VBM(� → Z) 0.78 D1(D → B)

* D1: the first extreme point close to the D k-point.

width is obviously broadened, while the VB width is slightly nar-rowed. This type metal doping does not obviously influence thephotocatalytic activity of BiVO4 under visible-light irradiation.

Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927 4925

(a) (b)

(c)

Fig. 5. The three typical electron density maps projected onto the (010) lattice plane: (a) the bottom of valence band; (b) the top of valence band; (c) the bottom ofconduction band. The slice is passing through impurity, and its position is also illustrated in (a). The labels of atom are same as in Fig. 1.

4926 Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927

(ii) BiV1−xNbxO4: Because Nb atom has equal valence electronsto V atom, so this type of ion does not obviously change the bandcomposition of the top of VB and the bottom of CB, and the Fermienergy level still located at the valence band maximum (VBM). Themain impurity energy levels are located at the upper part CB, inwhich interplay with O 2p states. At the same time, the impurityenergy levels in VB are more obvious than that of Ti or Zr dop-ing. So, the CB width is obviously broadened, while the VB widthis slightly narrowed. This type of metal doping is neither n-typedoping nor p-type doping, so Nb doping will not provide more ad-ditional carriers. As well as Ti or Zr doping, the impurity energylevels will not pronounce influence the photocatalytic activity ofBiO4 in visible-light irradiation.

(iii) BiV1−xCrxO4, BiV1−xMoxO4, and BiV1−xWxO4: Be oppositeto Ti or Zr doping, because Cr, Mo and W atom has one more va-lence electron compared with V atom, so this type impurity playsthe role of donor energy level. As shown in Fig. 4(a), one couldsee that there are little occupied energy levels below the Fermienergy level, which moves into the bottom of CB. Thus, BiVO4 willhave more electron-carriers by doping with Cr, Mo, or W. The mainimpurity energy levels are located at the bottom of CB or VB. Sothe VB width of Mo (or W) doping is obviously broadened, whilethat of Cr doping is slightly narrowed. In the opposite with thechange of VB width, the CB width of Cr doping is obviously broad-ened, while that of Mo (or W) doping is slightly broadened. Inthese entire metals doping, only Cr doping forms isolated impu-rity energy band in the forbidden band, whose distance is 1.77 eVfrom the VBM. For Mo or W doping, the impurity energy levelsform by the interaction between nd states of impurity and O 2pstates. Therefore, this type of metal doping could obviously en-hance the photocatalytic performance of BiVO4 under visible-lightirradiation.

In brief summary, these metals doping change the VB and CBcompositions of BiVO4, especially the top of VB and the bottom ofCB. But the band gap is not obviously changed. This means thatthese metals doping will not affect the optical absorption wave-length threshold. These results are in agreement with experimentalobservations. Another noteworthy feature is that the differencesbetween the energy eigenvalues at the top of VB and the bottomof CB are become smaller than that of pure BiVO4. Thus, in visible-light region, the electronic transition probability will increase alongall symmetry directions. In order to further explain the doping ef-fect, we fit the energy–momentum dependence of the states, andgot the minimum of effective mass for electrons or holes, and theresults displayed in Table 2. We found that these metals doping re-duce the effective mass of holes on the top of VB, except Zr doping.This result means that these metals doping could increase the dif-fusion length of photo-excited holes, so more holes could achieveto the surface reaction sites during their limited lifetime. Thus thephotocatalytic oxidizability and photoelectrochemical acitivity willbe enhanced under visible-light irradiation. However, at the sametime, the effective mass of electrons on the bottom is increasedby metal doping, so these metals doping are disadvantage for theBiVO4 photocatalytic reducibility.

To deepen the understanding of metal doping effects on theelectronic structure of BiVO4, we further analyzed the electronicdensity on three specific typical energy ranges, and plotted theprojected contour map in Fig. 5, respectively (in order to facilitatecomparison, we arranged these figures according to the position ofimpurity element in the periodic table). The first projection is lo-cated at the bottom of VB. In this energy range, for pure BiVO4,O 2p states occupy the entire space, and interplay with the neigh-boring V 3d states. By metal doping, the interaction between O2p states and V 3d states is gradually declining, as the atomicnumber of impurity is increasing; on the contrary, the interac-tion between O 2p states and nd states of impurity is gradually

enhanced. For Mo-doped or W-doped BiVO4, the projection is pre-dominately formed by the impurity states. The second projectionis located at the top of VB. In this energy range, for pure BiVO4,the Bi 6s states separate from the interaction states between O 2pstates and V 3d states. And metal doping make this phenomenonmore pronounced. At the same time, metal doping weakens the in-teraction between O 2p states and impurity’s nd states. The largeratomic number is, the more obvious corresponding effects are. Thefinal projection is located at the bottom of CB. As previous dis-cussion, there are impurity energy band in the forbidden bandfor Cr-doped, so we plotted two type projections: the “I” type islocated at CBM, and the “II” type is locate at the impurity en-ergy levels, in which V does not contribute as shown in Fig. 5(c).In this energy range, for pure BiVO4, the V 3d states, which aremainly constituted by 3dx2−y2 and 3dz2 states, occupy absolutepredominance, and there are small amount of Bi 6p states. ExceptCr-doped, CBM is mainly constituted by 3dz2 states, and the im-purity energy band (type “II”) is also constituted by 3dz2 states. Atthe same time, as the distance with the impurity is increasing, theimpacts on the states of V are decreasing. In the same group, thesmaller atomic number is, the more obvious this phenomenon. Inparticular, the CBM of Cr doping case is still constituted by 3dx2−y2

states, and the electronic states of impurity do not contribute tothe composition of CBM for Ti (Zr, and Nb) doping cases compre-hensively analyze and compare these results, we found that the estates (3dx2−y2 states and 3dz2 states) is the main factor to impactthe electronic structure of BiVO4. The photophysical properties ofsemiconductors are governed by the electronic structure. Thus, thee states of the impurities play a vital role for the photocatalyticactivity of BiVO4 under visible-light irradiation.

4. Conclusions

We have investigated the geometrical structure and electronicproperties of substitutional metal-doped monoclinic clinobisvaniteBiVO4 on the basis of density functional theory calculations. Fromthe thermodynamics point of view, the solubility of Cr in host isthe lowest, while that of Zr(or Nb) doping is the highest. The dop-ing effects are manifest as following aspects: (i) The changes ofgeometrical structure and band gap of BiVO4 are not pronouncedby doping all of these metals. (ii) The VO4 tetrahedron in BiVO4will distort, resulting in the local internal electric field, which isfavorable for the separation of photo-excited electron–hole pairs.(iii) The dispersion characteristics of band structure of BiVO4 arechanged by these metals doping, so the electrons in VB have moreopportunities to transit to CB by visible-light excitation. (iv) The estates of the impurity play a vital role for the photocatalytic activ-ity of BiVO4 under visible-light irradiation. (v) Especially, we foundthat these metals doping could reduce the effective mass of holeson the top of VB, except Zr doping, while implies that the diffusiondistance of photo-excited hole could be lengthened. These dopingeffects can dramatically enhance the photocatalytic oxidizabilityof BiVO4 under visible-light irradiation. However, because the im-pacts on the band gap are very small, and the electronegativitiesare similar with the vanadium, these metals do not significantlychange the CB electric potential of BiVO4, and cannot solve thedrawback of non-hydrogen evolution. It is need to be further in-vestigations.

Acknowledgements

The authors acknowledge the financial support from the Na-tional Basic Research Program of China (973 Program, Grant Nos.2007CB613301 and 2007CB613305).

Z. Zhao et al. / Physics Letters A 374 (2010) 4919–4927 4927

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