DSpace at VNU: Influences of metallic doping on anatase crystalline titanium dioxide: From electronic structure aspects to efficiency of TiO2-based dye sensitized solar cell (DSSC)

Materials Chemistry and Physics xxx (2014) 1e8 Contents lists available at ScienceDirect Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys Influences of metallic doping on anatase crystalline titanium dioxide: From electronic structure aspects to efficiency of TiO2-based dye sensitized solar cell (DSSC) Thuy Trang Nguyen*, Tran Van Nam, Bach Thanh Cong Computational Materials Science Laboratory, Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam h i g h l i g h t s  Ca,  Nb  Nb  Be,  Nb Al and W dopants strongly distort the lattice and narrowed the band gap negatively shifts while the others positive shift the conduction band bottom and W dopants reduce Ti4ỵ to Ti3ỵ without forming oxygen vacancy Mg, Ca, Zn and Al dopants induce oxygen vacancy without Ti3ỵ and W inhibit the surface defects while the others the reversed manner a r t i c l e i n f o a b s t r a c t Article history: Received 24 April 2013 Received in revised form September 2013 Accepted 21 December 2013 In this work, we examined the influences of metallic X dopants (X ¼ Be, Mg, Ca, Zn, Al, W and Nb) on the electronic structure of anatase TiO2 in the framework of density functional theory (DFT) The dopantinduced electronic structure modifications are believed to directly change the photovoltaic (PV) behaviors of the X-doped TiO2 based DSSCs The dopants are shown to either directly inhibit the intrinsic Ti3ỵ and oxygen vacancy surface defects of TiO2 or enhance these defects depending on their valence states These dopant-induced defect modifications, in turn, strongly affect the PV behaviors of the DSSCs The combined effect of electronic structure and surface-defect modifications determined the photoelectric efficiency of the device Ó 2013 Elsevier B.V All rights reserved Keywords: Ab initio calculations Band structure Electronic structure Defects Introduction Titanium dioxides, TiO2, have been a productive plot for application researches due to their stability, high refractive index, strong UV light absorbing capability and photo-activities Recently, numerous works have been devoted to TiO2 films with anatase nanocrystalline structures as working electrodes in dye-sensitized solar cells (DSSCs) Although many metallic oxides have been tested for DSSC electrode [1e5], efforts on improving DSSCs’ performance were focused on TiO2 anatase which leads to the highest efficiency w7.4% [6] However, this is still lower than that of conventional silicon solar cells Improving DSSC efficiency is still a major ongoing field of research Doping the TiO2 electrode with metallic elements is a useful way to improve the photovoltaic (PV) performance of DSSCs The Nb* Corresponding author Tel./fax: ỵ84 5583980 E-mail address: trangnguyenphys@gmail.com (T.T Nguyen) dopant was shown to raise up the short-circuit current JSC of the Nb-doped TiO2 based DSSCs owing to the dopant-induced up-shift of the Fermi level and the lowering of the conduction band (CB) bottom as well as the formation of the intra-band states [7,8] The Fermi level up-shift and the formation of the intra-band states increase the electron diffusion coefficient while the lowering of the CB bottom improves the electron injection possibility The best cell efficiency, h ¼ 8.0%, was obtained for 2.5% Nb doping (for the undoped case, h ¼ 6.8%) The similar effects were observed for the Ta-doped case in which a PV efficiency h ¼ 8.18% was achieved owing to both the enhancement of electron transport driving force and the doping-induced increase of the electron concentration [9] It was reported that Al and W dopants modified the electrical surface state of the Al and W doped TiO2 anatase nanoparticles, which significantly changes the powder aggregation, chargetransfer kinetics, dye absorption characteristics and indirectly affects the quality of DSSCs [10] The Al-induced reduction of the surface Ti3ỵ defect concentration enhanced the dye absorption 0254-0584/$ e see front matter Ó 2013 Elsevier B.V All rights reserved http://dx.doi.org/10.1016/j.matchemphys.2013.12.025 Please cite this article in press as: T.T Nguyen, et al., Influences of metallic doping on anatase crystalline titanium dioxide: From electronic structure aspects to efficiency of TiO2-based dye sensitized solar cell (DSSC), Materials Chemistry and Physics (2014), http://dx.doi.org/ 10.1016/j.matchemphys.2013.12.025 T.T Nguyen et al / Materials Chemistry and Physics xxx (2014) 1e8 ability and decreased the TiO2/electrolyte interface area This led to the suppression of the dark-current IDC which corresponds to the electron recombination at the TiO2/electrolyte interface Consequently, the short circuit voltage VOC is remarkably increased On the contrary, the W-dopant increased the surface Ti3ỵ defect concentration, reducing VOC However, the W-induced enhancement of the surface defects elongated the life time of electrons, improving the short-circuit current ISC while the opposite effect occurred in the Al-dopant case The surface Ti3ỵ defects was shown to make the W-doped TiO2 based DSSCs more strongly deviate from the ideal one while Zn-doped ones follows the opposite tendency [11] Therefore, the fill factor (FF) was increased by Zn-doping but decreased by W-doping In an attempt to provide useful information for optimizing TiO2 based DSSCs, we investigated the electronic structures of some metal-doped TiO2 compounds including X0.0625Ti0.9375O2 with X ¼ Be, Mg, Ca, Zn, W, Al and Nb in the framework of density functional theory (DFT) Our results suggest that the PV behaviors of metallic doped-TiO2 electrodes in previous studies resulted from the combined effect of electronic structure and surface-defect modifications induced by dopants We also distinguished the surface defect Ti3ỵ formed with oxygen vacancy (Ti3ỵ/OV) from that one without oxygen vacancy The differences between them led to the opposite changes in the VOC of the DSSC when the TiO2 electrode was doped with W and Nb at low concentration ( 2%) despite of the similarity in valence Calculation details The equations for ground states of investigated systems were built up and solved in the DFT framework (these equations are colloquially called KohneSham equations) [12] with the Dmol3 package [13] DFT methods deal with the most complicated potential term, the electroneelectron interaction by splitting it into two separated parts, i.e the classical Coulomb potential and the exchange-correlation potential In our calculations, the former was evaluated by solving the Poisson equations for charge density in a completely numerical approach [13] The later was formulated within the local density approximation (LDA) which is based on the well-known exchange-correlation energy of the uniform electron gas by J.P Perdew and Y Wang and parametrized by Ceperley and Alder as a functional of electron densityePWC functional [14] All electrons of the examined systems, i.e core, semi-core and valence electrons, were treated equally in building up electroneelectron interaction potential which is so-called all electron potential (AE) In order to solve KohneSham equations, a self-consistent field (SCF) procedure is provided by the Dmol3 package because of the mutual dependence between electron density and electroneelectron interaction potential [13] The initial wave function was produced by linear combination atomic orbital (LCAO) method with the numerical atomic-like basis set named DNP [13] Within this basis set, each occupied atomic orbital is represented by one numerical atomic-like wave function A second set of wave-functions is added for the valence orbitals The polarization d-functions are also added The orbital cut off was 5.2  A and the energy convergence criterion was 10À6 eV/atom Examined systems were the bulk and the surface of 6.25% Xdoped anatase TiO2 compounds with X ¼ Be, Mg, Ca, Zn, Al, W and Nb In order to simulate these systems, we started from the unit cell of anatase TiO2 crystal which belongs to I41/amd space group (Fig 1a) It should be noted that in anatase crystalline form, the titanium atoms are put within the octahedral ligand field of its six neighboring oxygen atoms We labeled the corner oxygen atoms of the octahedron O(1) and apical oxygen atoms O(2) A super-cell of the size   I41/amd unit cells with space group P1 was built to represent the unit cell of X0.0625Ti0.9375O2 (Fig 1b) There are 16 Ti sites in the new P1 unit cell, one of which is substituted with an impurity X atom (X ¼ Be, Mg, Ca, Zn, W, Al and Nb) The MonkhortPack k-point mesh corresponding to this unit cell was   The surface was simulated using a vacuum slab super-cell of P1 space group which is a large unit cell composed of a TiO2 slab and a vacuum slab The vacuum slab must be thick enough to screen the interaction between atomic slabs (in our case, it was 20  A) (Fig 1c) The k-point mesh for the vacuum slab unit cell was   The surface and doping-induced structure relaxations were calculated from the first principles using NewtoneRaphson geometry optimization scheme [15] The convergence criterion for the optimization was 10À5 eV/atom for energy, 0.002 Ha  AÀ1 for force,  0.005 A for displacement Results and discussions 3.1 Undoped TiO2 anatase Electronic structure of un-doped anatase TiO2 has been intensively studied in the density functional theory (DFT) framework [16e20] A wide range of the DFT methods spanning from traditional one-electron local density approximations (local density approximation e LDA and generalized gradient approximation e GGA) [16,17,19,20], hybrid functional (B3LYP) [18] to many-body corrected DFT method GW [19] has been applied for TiO2 anatase using various types of basis sets including Gaussian type orbital (GTO, 6-31G) [16,18], augmented plane wave (APW) [17], plane wave (PW) with pseudopotential (PP) [19,20] and all-electron potential (AE) [16e18] The most common problem of conventional DFT methods (LDA and GGA) is the band-gap underestimation The band-gap values of TiO2 anatase extracted from LDA and GGA calculations are about eV [16,17,19,20] Our calculation indicates a band-gap of 2.04 eV, which well agrees with the previous results The exact exchange functional correction of the hybrid functional B3LYP method and the many-body correction of the GW method, otherwise, w15% overestimated the band-gap value (Ecal g w3.7 eV while Eexp g w3.2 eV) [18,19] Another band gap problem for TiO2 is the nature of the band gap, i.e whether it is direct or indirect and where it occurs in the k-space Although all calculations agreed that the global minimum of the conduction band (GMCB) is at G point k ¼ [0 0], the global maximum of the valence band (GMVB) positions from different methods are various, i.e G k ¼ [000],M k ẳ [ẵ ẵ 0] or near X point k ¼ [0 0.44 0] point Our result shows the GMVB near the M point k ẳ 5/6[ẵ ẵ 0] so that the band gap is indirect (see Fig 2a) Unfortunately, we could not find any experimental evidence to clarify this confusion On the other hand, the position of GMVB is sensitive to bond-lengths and lattice parameters The divergence of the calculation results may be due to the disagreement in optimizing the lattice structure Fig presents the band structure, the density of states (DOS) diagram and some orbitals at the G point located near the top of VB and the bottom of CB The k-path was chosen with respect to the I41/amd space group of which the reciprocal space (k-space) contains the following high symmetry points: G point k ¼ [0 0], X point k ¼ [0 ½ 0], Z point k ẳ [0 ẵ 0], M point k ẳ [ẵ ẵ 0], R point k ẳ [0 ½ ½] and A point k ¼ [½ ½ ½] The energy off-set is at the Fermi level denoted by the horizontal dash line in Fig 2a and b The band structure from our calculation is in good agreement with that one produced by R Asahi et al on the base of their LDA/AE/LAPW calculation [17] We can see that an oxygen 2p-like-band was observed at about 16.3 eV below the Fermi level within a narrow energy range w 1.9 eV The valence band (VB) spans in an energy range of w eV which agrees quite well with the X-ray photoemission spectroscopy measurement (XPS) [21] The CB and VB are Please cite this article in press as: T.T Nguyen, et al., Influences of metallic doping on anatase crystalline titanium dioxide: From electronic structure aspects to efficiency of TiO2-based dye sensitized solar cell (DSSC), Materials Chemistry and Physics (2014), http://dx.doi.org/ 10.1016/j.matchemphys.2013.12.025 T.T Nguyen et al / Materials Chemistry and Physics xxx (2014) 1e8 Fig Unit cells used in our calculations (a) The I41/amd unit cell of anatase crystalline titanium dioxide; (b) The P1 unit cell of 6.25%-X-doped TiO2, X0.0625Ti0.9375O2, where X ¼ Be, Al, Nb, Mg, Zn and Ca; (c) The P1 vacuum-slab supercell to model the (101) surface formed by the overlap between O 2p, Ti 3d and Ti 4s orbitals Because of the strong overlap between O 2p and Ti 4s orbitals, the O 2peTi 4s bonding states are located at the bottom of the VB and the anti-bonding counterpart should be at the higher energy region of CB which falls out of the our calculated energy region The small contribution of Ti 4s orbital to the Ti 4seO 2p bonding states exhibits the ionicity of the electron Ti 4seO 2p transfer The bondinge anti-bonding interaction between Ti 3d and O 2p orbitals seems to Fig (a) The energy band structure and (b) partial density of states (PDOS) of undoped TiO2 anatase crystal from our calculations with respect to the I41/amd unit cell The high symmetry points in the k-space corresponding to this unit cell are G point k ¼ [0 0], X point k ẳ [0 ẵ 0], Z point k ẳ [0 ½ 0], M point k ¼ [½ ½ 0], R point k ẳ [0 ẵ ẵ] and A point k ¼ [½ ½ ½] The horizontal dash line denotes the Fermi level which is also the energy off-set (b) Some orbitals around HOMO and LUMO at G point k ¼ (0 0) including HOMO, LUMO, LUMO ỵ and LUMO ỵ Please cite this article in press as: T.T Nguyen, et al., Influences of metallic doping on anatase crystalline titanium dioxide: From electronic structure aspects to efficiency of TiO2-based dye sensitized solar cell (DSSC), Materials Chemistry and Physics (2014), http://dx.doi.org/ 10.1016/j.matchemphys.2013.12.025 T.T Nguyen et al / Materials Chemistry and Physics xxx (2014) 1e8 be weaker with higher bonding states in VB and lower anti-bonding states in CB than the Ti 4seO 2p ones The electron Ti 3deO 2p transfer exhibits more covalency than the Ti 4seO 2p one with significant Ti 3d composition in O 2p dominated bonding states and O 2p composition in Ti 3d dominated anti-bonding states The O 2p states and the non-bonding Ti 3dxy states were at the top of the VB and at the bottom of the CB, respectively (see Fig 2c for some orbitals at G point located at the bottom of CB and at the top of VB) 3.2 6.25% Metallic doped TiO2 anatase The effects of doping are summarized in Table which includes lattice parameters, bond-lengths and important electronic structure information Firstly, we discuss about the variation of the lattice parameters and the bond-lengths in accordance with the ionic radii of the dopants, which is schematically demonstrated in Fig The octahedron bond-lengths at impurity site, i.e XeO(1,2) bonds, increase with respect to the increase of the impurity ionic radius The bond-lengths of surrounding TieO6 octahedrons slightly change, except for the cases of Ca, W and Al doping in which the bond-lengths suddenly increase regardless of the impurity ionic radius Therefore, the lattice constants alter similarly to the change in ionic radius of impurity in the cases of Be, Mg, Zn and Nb doping but strongly increase in the cases of Ca, W and Al doping In order to get a deep insight into the anomalous changes of TieO bondlengths induced by Ca, W and Al dopants, electronic structure aspects should be involved as discussed below Figs and show the band structures and the partial DOS of the un-doped and doped TiO2 anatase compounds with a k-path through high symmetry points of P1 space group, i.e G point k ¼ [0 0], F point k ¼ [0 ½ 0], Q point k ¼ [0 ½ ½] and Z point k ¼ [0 ½] It is noticed that the higher part of CB was not calculated with the P1 unit cell used in case of doped compounds The energy off-set was put at the Fermi level There are several important points inferred from these energy band structures: - All of our dopants produce no separated impurity bands occurring in the VB-CB band gap They are quite different from transition metal dopants which introduces 3d impurity states into the VB-CB band gap of anatase crystalline TiO2 [22] However, it is worth-while to note that there are some impurityinduced bands occurring in the other band gaps in the case of Ca, Al and W doping They are three pure Ca 3p bands located at 0.68 eV below the O 2s band and six impurity-surrounding oxygen 2s bands located 0.27 eV above the O 2s band of the host lattice in the case of Ca doping; one Al 3seO 2p bonding band situated 0.35 eV below the VB in the case of Al doping and five W 5deO 2p bonding bands locates at 0.49 eV below the VB Fig The variation of the lattice constants a, b and c and TieO(1), TieO(2), XeO(1) and XeO(2) bond-lengths upon the ionic radius of the atom X at the doped site in the P1 unit cell shown in Fig 1b with X ¼ Be, Al, Ti, W, Nb, Mg, Zn and Ca (ascending order in ionic radius) in the case of W doping We suggest that these additional bands put a strong Coulomb repulsion on VB which enhances Coulomb repulsion of octahedral ligand field on Ti Consequently, the Tie O bond-lengths are anomalously increased in the cases of Ca, Al and W doping In particular, the appearance of the 3p Ca bands right below the O 2s band of the host lattice also puts the strong Coulomb repulsion on the 2s states of oxygen atoms surrounding impurity sites so that they are up-shifted, resulting in impurity-induced O 2s bands above the main O 2s band This interaction is also observed in CaO, where the O 2s semi-core band is slightly shifted up (w1 eV) in comparison with other alkaline earth oxide (MgO, SrO and BaO) due to the Ca 3peO 2s Coulomb interaction [23] - The contribution of alkaline earth (AE) metallic impurities (X ¼ Be, Mg, Ca) to the VB is so small that the nature of XeO bonds can be considered to be strong ionic The AE oxides are well-known as typical ionic crystals with wide band gaps ranging from to 10 eV (10 eV for BeO, 7.8 eV for MgO and 6.9 eV for CaO) [24,25] Their VBs are primarily composed of O 2p states and their CBs are s states of AE metal Therefore, the wide band gaps are corresponding to the large energy difference between O 2p and AE metallic s states We suggest that the absence of AE compositions in the VB and the strong ionic nature of XeO bonds are due to the large energy difference between O 2p and Table A summarization of lattice parameters and electronic structure information of undoped and doped anatase TiO2 X Lattice parameters a ¼ b ( A) c ( A) Octahedral bond-lengths TieO(1,2) ( A) TieO(3) ( A) XeO (1,2) ( A) XeO(3) ( A) Ionic radius of impurity ( A) Electronic structure information CB-VB gap (eV) Fermi energy (eV) Valence band width (eV) Dispersion of 3dxy Ti band (eV) Undoped Be Mg Ca Zn W Al Nb 3.758 9.506 3.752 9.414 3.769 9.509 3.949 9.936 3.762 9.558 3.925 9.815 3.912 9.769 3.772 9.544 1.923 1.968 e e 0.605 (Ti4ỵ) 1.920 1.975 1.878 1.852 0.45 (Be2ỵ) 1.924 1.971 1.988 2.105 0.72 (Mg2ỵ) 2.009 2.051 2.181 2.335 1.00 (Ca2ỵ) 1.922 1.973 1.978 2.126 0.74 (Zn2ỵ) 2.006 2.061 1.943 1.967 0.62 (W5ỵ) 2.001 2.055 1.921 1.903 0.535 (Al3ỵ) 1.928 1.973 1.95 2.013 0.64 (Nb5ỵ) 2.04 À7.79 4.95 0.98 2.04 À8.94 5.12 0.93 2.10 À8.91 4.97 0.91 1.71 À8.75 4.59 0.80 2.14 À8.80 5.58 0.92 1.78 À6.19 4.44 0.73 1.69 À8.58 4.76 0.76 2.12 À6.04 5.27 1.03 Please cite this article in press as: T.T Nguyen, et al., Influences of metallic doping on anatase crystalline titanium dioxide: From electronic structure aspects to efficiency of TiO2-based dye sensitized solar cell (DSSC), Materials Chemistry and Physics (2014), http://dx.doi.org/ 10.1016/j.matchemphys.2013.12.025 T.T Nguyen et al / Materials Chemistry and Physics xxx (2014) 1e8 Fig The band structures of undoped and 6.25%-X-doped anatase TiO2 with X ¼ Be, Al, W, Nb, Mg, Zn and Ca The energy off-set was put at Fermi level which was denoted by the red dash lines (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) AE metallic s states The contributions of the AE s states will appear in the higher part of the CB (w eV above GMVB or even higher, primarily depending on the O 2pemetallic s gap) which is not included in our calculations The same situation is observed in Al doping case even though Al2O3 were shown to be less ionic than AE oxides with a large band gap of 8.8 eV [26] - The contributions of impurities to CB and VB become more significant in the case of Zn, W and Nb doping Those contributions primarily come from 3d states of Zn, 5d states of W and Fig The DOS of dopant within the host lattice of anatase TiO2: (a) Be-DOS, (b) AlDOS, (c) W-DOS, (d) Nb-DOS, (e) Mg-DOS, (f) Zn-DOS and (g) Ca-DOS The energy off-set was put at Fermi level which was denoted by the vertical dash lines 4d states of Nb It should be noted that the Zn 3d states contribute only in the VB while the W 5d and Nb 4d contributions appear both in VB and CB This difference originates from the fact that the W 5d and Nb 4d electrons take part in crystal binding as valence electrons but Zn 3d electrons not (semicore electrons) Therefore, the contributions of W 5d and Nb 4d states to the VB and the CB correspond to the formation of the bonding and anti-bonding states caused by the overlap between the metallic d orbitals and the O 2p orbitals Meanwhile, it was shown that the VB-CB energy gaps of zinc oxides result from the bondingeantibonding interaction between O 2p and Zn 4s states [27] This interaction energetically pushes down the O 2p dominated bonding states and pushes up the Zn 4s dominated antibonding states The lowered O 2p states energetically reach to the Zn 3d states so that they can hybrid with the Zn 3d states Consequently, Zn 3d-like band is broadened and joins the VB Although the p-d hybridization was shown to be weakened when the ligand field transforms from tetrahedron to octahedron (corresponding to the crystal structure transition of ZnO from Zinc-blende or wurtzit to rock-salt) [28], we still imply a pd hybridization for our Zn-doping case in which Zn impurity atoms are put inside octahedral ligand field of TiO2 anatase host lattice - As expected from the oxidization states of impurity elements, the dopants Be (II), Mg (II), Ca (II), Zn (II) and Al (III) shift the Fermi level downwards to overlap the top of the VB which is mainly composed of oxygen 2p states while the dopants W (V) and Nb (V) shift the Fermi level upwards to overlap the bottom of the CB By this way, holes corresponding to acceptors are formed and located on the oxygen 2p like orbitals in the former Please cite this article in press as: T.T Nguyen, et al., Influences of metallic doping on anatase crystalline titanium dioxide: From electronic structure aspects to efficiency of TiO2-based dye sensitized solar cell (DSSC), Materials Chemistry and Physics (2014), http://dx.doi.org/ 10.1016/j.matchemphys.2013.12.025 T.T Nguyen et al / Materials Chemistry and Physics xxx (2014) 1e8 cases and the extra electrons corresponding to donors are formed and located in the titanium 3dxy orbitals in the later cases The role of these dopant-induced charge carriers will be discussed in detail later - The impurities noticeably change the width of the VB, the dispersion of 3dxy Ti band at the bottom of the CB and the CBe VB gap (see Table 1) According to the band structure of undoped TiO2 anatase described above, these properties strongly depend on the Coulomb interactions of Ti 3d states with the octahedral ligand field and on the bondingeantibonding interaction between Ti 3d, 4s and O 2p states Therefore, the TieO bond-lengths play the key role in this situation The correlation between the bond-lengths, the VB width and the band gap is suggested that the longer the bond-lengths are, the weaker the Ti 3d/4seO 2p bondingeantibonding interactions become The bottom of the VB composed of d/s-p bonding states is up shifted, so the VB is shrunken Meanwhile, the d-p anti-bonding states, which is the main composition of the CB, is down shifted, hence, CBeVB gap is narrower This is the case of Ca, W and Al doped compounds Besides, the large expansion of TiO6 octahedron in Ca, W and Al doped TiO2, corresponding to the extension of Tie Ti distance, reduces the 3dxy e 3dxy overlap, hence reduces the 3dxy e 3dxy hopping elements between Ti sites Accordingly, the non-bonding bands Ti 3dxy situated at the bottom of the CB become less dispersive L Thulin and J Guerra proposed to apply a strain to modify the band gap and carrier effective mass of anatase TiO2, which agrees with our observations of the bondlengtheband gapeband dispersion relation [19] Other impurities (Be, Mg, Zn and Nb) induce a slight increase of the band gap (