J. Phys. Chem. C 2010, 114, 12777–12783
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DFT-Based Theoretical Calculations of Nb- and W-Doped Anatase TiO2: Complex Formation between W Dopants and Oxygen Vacancies Hideyuki Kamisaka,* Takahiro Suenaga, Hisao Nakamura,† and Koichi Yamashita* Department of Chemical System Engineering, School of Engineering, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ReceiVed: May 13, 2010; ReVised Manuscript ReceiVed: June 23, 2010
The structure and electronic states in Nb-doped TiO2 (TNO) and W-doped TiO2 (TWO) having the anatase phase were investigated using a first-principles DFT-based band structure method. In addition to the cases where the dopant substituted for a Ti atom, cells containing a dopant (MTi, where M ) Nb and W) and an oxygen vacancy (VO) were calculated to clarify the role of oxygen vacancies in the system. Furthermore, cells containing two dopants and an oxygen vacancy (2MTi-VO) and cells with a dopant and two oxygen vacancies (MTi-2VO) were calculated. Energetically stable structures were found in the 2WTi-VO and WTi-2VO cells sampled, whereas the corresponding structures in TNO did not show any significant energy stabilization. Impurity states were found in the stable 2WTi-VO and WTi-2VO structures, and an approach of the two WTi atoms was found in 2WTi-VO. These findings suggest the possible formation of complex structures consisting of WTi dopants and oxygen vacancies. Our results are consistent with recent experiments on TWO by Takeuchi et al., and they rationalize the lower electronic conductivity of TWO versus TNO. I. Introduction Transparent conductive materials, which have a high transparency in the visible light region and a high electronic conductivity, are widely used in the fabrication of various optoelectronic devices, such as flat-panel displays, light-emitting diodes, and solar cells. Their infrared reflection properties are exploited in heat-reflective glass. The industrial use of transparent conductive materials is increasing rapidly.1 The most utilized transparent conductive material is an alloy of indium oxide and tin oxide, known as indium tin oxide (ITO).2 Indium is a rare element that has only a limited availability in the earth’s continental crust,3 so there is a strong demand for the development of alternative transparent conductive oxides (TCOs). In 2005, Furubayashi et al. discovered that Nb-doped TiO2 in the anatase phase (TNO) has a high transparency (>97% at thickness ) 40 nm) and a low electronic resistivity (2 × 10-4 Ω · cm),4,5 which are comparable to the values in ITO. TiO2 is a safe and low-cost compound, and the availability of Nb in the earth’s upper continental crust is much higher than that of In.3 The first reports on the fabrication of TNO were on SrTiO3 substrates using a pulse laser deposition technique. Later, Hitosugi et al. succeeded in fabricating a TNO layer on a glass surface using radio frequency (rf) magnetron sputtering,6 which is applicable to industrial production over a large surface area. For these reasons, TNO is considered a promising alternative candidate for ITO and is receiving much attention. Despite several experimental and theoretical efforts aimed at clarifying the conducting properties of TNO,7-14 little is * To whom correspondence should be addressed. E-mail:
[email protected] (H.K.),
[email protected] (K.Y.). Tel: +81(Japan)3-5841-8753 (H.K.), +81(Japan)-3-5841-7228 (K.Y.). Fax: +81(Japan)3-3818-5643 (H.K.), +81(Japan)-3-3818-5012 (K.Y.). † Permanent address: Nanosystem Research Institute (NRI), National Institute of Advanced Industrial Science and Technology (AIST), Umezono 1-1-1, Tsukuba Central 2, Tsukuba, Ibaraki 305-8568, Japan. E-mail:
[email protected].
known of its microscopic mechanisms. Some basic questions remain unanswered, such as why a similar conductivity is not observed for the rutile phase13 or W-doped anatase TiO2 (TWO).15 The temperature dependence of the electric conductivity of Nb-doped TiO2 shows a strong dependence on the polymorphism.13 In the anatase form, the electronic conductivity increases as the temperature decreases (i.e., metallic behavior). In contrast, Nb-doped rutile TiO2 shows the opposite behavior, resulting in a lower conductivity at lower temperatures (i.e., semiconductor-like behavior). Yildiz et al. investigated the conduction mechanism of TNO in the anatase form at a low doping rate of 0.35%.14 They concluded that the electrical conduction can be described by small polaron hopping at temperatures above 325 K and that variable range hopping (VRH) occurred between 200 and 325 K. There is a complex electronic conduction in TNO, and the qualitative change of the conduction mechanism occurs depending on the form of TiO2, the temperature, and the doping rate. TWO was fabricated by Takeuchi et al. in an attempt to improve the properties of TNO.15 The atomic configuration of W is [Xe] 4f145d46s2, and that of the Nb atom is [Kr] 4d45s1. Takeuchi et al. anticipated that the W dopant would act as a double donor. However, the electronic resistivity in TWO was found to be as low as 2.6 × 10-3 Ω · cm, regardless of the partial pressure of oxygen during processing. The carrier density in TWO was low, and the active ratio of the W dopant was estimated to be 10%. TiO2 is a transition-metal oxide. The conduction band of TiO2 consists of the Ti 3d orbitals, and the valence band consists of the O 2p orbitals. The spatial size of the Ti 3d orbitals is smaller than that of the O 2p orbitals. Therefore, an electron in the conduction band has a strong localized character, and a formation of a polaron state (Ti4+ + e- f Ti3+) is agreed on, especially in the rutile form.16 If an electron in the conduction band forms a polaron state Ti3+, then this state acts as an
10.1021/jp104355q 2010 American Chemical Society Published on Web 07/07/2010
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electron-trapping site and the temperature dependence of the electrical resistivity becomes semiconductor-like. Such localized states are often treated using the Hubbard+U coefficient in first-principles calculations.17,18 A rigorous identification of the +U parameter value suffers from the double counting of exchange/correlation effects between the Hubbard term and the DFT functional.19,20 Nevertheless, this method remedies several serious deficiencies of standard DFT calculations and is used in calculations involving transition oxides. Deskins et al. investigated the difference in the electronic conductivity between anatase and rutile TiO2 using DFT+U calculations21 and a polaron-hopping model.22 In their analysis, a hot electron was assumed to be trapped at a Ti4+ cation site, forming Ti3+, and then this was transferred to the nearest or next-nearest Ti4+ cation site, accompanied by a structural deformation. The transition state during the course of the transfer was inferred from a linear interpolation, and the electronic coupling between the two localized states was approximated using an unrestricted Hartree-Fock wave function. Despite the previous successful application of this method to R-Cr2O3 and R-Fe2O3, even a qualitative tendency was not reproduced for the TiO2 system. In the results of Deskins et al., rutile TiO2 had higher mobility polarons than anatase, which contradicts the experimental data. Di Valentin et al. performed calculations on a TiO2 system containing several dopants using the DFT+U scheme.23,24 They revealed that the localized electronic state at oxygen vacancies only emerged when the “+U” scheme was adapted and that other electronic states lying very close in energy with a delocalized electron occur after a slight structural change. Di Valentin et al. further investigated several n-type doped TiO2 (F-, Nb-, Sb-, H-doped systems, VO, and interstitial Ti). These reports indicate the importance of a proper treatment of the electronic correlation effect in the description of the localized electronic state, as the transfer between them is complex and is affected by surrounding impurities. Morgan et al. reported on the effect of the +U term on Nband Ta-doped TiO225 and on oxygen vacancies and titanium interstitial sites in pure anatase TiO2.26 They confirmed that a small polaron with a localized gap state emerges in all of the considered cases. However, the difference between Nb-doped rutile and anatase TiO2 was not significant in their results, and the experimental data were not explained. They concluded that the cause of the difference between the two phases should be understood in terms of a structural factor other than the polaron. Recently, we have published a density functional theory (DFT)-based study on TNO and pointed out the importance of nonstoichiometry in the system.27,28 In the present work, we report on our recent progress in a theoretical survey of TNO. The sampling scheme for the structures with NbTi and VO has been extended, and three-body complexes consisting of these impurities have been analyzed. The electronic structure calculation method was updated to the GGA+U method. The same calculation scheme was applied to TWO. A significant difference between TNO and TWO was revealed in terms of a complex formation with dopant atoms and oxygen vacancies. The inclusion of the +U term was found to be unessential for clarification of the difference between Nb-doped and W-doped anatase TiO2. Our results rationalize the experimental reports on TWO and explain the differences between TNO and TWO, bringing insight into the conduction mechanism of TNO. The difference of rutile and anatase phases of Nb-doped TiO2 will be studied in our other paper.
Kamisaka et al. TABLE 1: Number of Calculated Structures for Each Dopant Combination type
number
MTi 2MTi MTi-VO 2MTi-VO MTi-2VO
1 5 9 48 103
This paper is arranged as follows. Section I contains the Introduction. In section II, the computational method and the model system are explained. Several abbreviations are introduced for the calculated structures. The calculated results are summarized in section III. The total energy of the sampled structures, the optimized structures, and their electronic band structure and density of states (DOS) are also presented in section III. On the basis of our calculations, a detailed discussion is presented in section IV. The effect of the W dopant, the Nb dopant, and defects is discussed in terms of the total energy stabilization and associated impurity states. The origin of the low carrier density in TWO is discussed in connection with experimental X-ray photoelectron spectroscopy (XPS) data. Concluding remarks are provided in section V. II. Calculation Method The doped system was modeled using a periodic unit cell with a Born-von Ka´rma´n periodic boundary condition. The primitive unit cell of anatase titanium (Ti2O4) has a bodycentered tetragonal shape and a space group symmetry of D194h-I41/amd.29 The initial lattice constants were taken from experimental values, a ) 3.782 Å and c ) 4.751 Å.30 The primitive cell was enlarged by extending the lattice vectors as t1′ ) 2t1, t2′ ) 2t2, and t3′ ) -t1 - t2 + 2t3, resulting in an eight-times cell (Ti16O32). The introduction of impurities breaks the symmetry of t1 and t2. In the following, we refer to the direction of the t1, t2, and t3 axes as being the x, y, and z axes, respectively. These axes are labeled consistently in the main text, tables, and figures for all of the calculated structures. Several combinations of dopants (M ) Nb or W) and vacancies (VO) were introduced as (1) a dopant (MTi), (2) two dopants (2MTi), (3) a dopant and an oxygen vacancy (MTi-VO), (4) two dopants and an oxygen vacancy (2MTi-VO), and (5) a dopant and two oxygen vacancies (MTi-2VO). The Nb dopant has been confirmed experimentally to substitute for a Ti atom from backward Rutherford scattering data.13 All symmetrically independent structures for a given number of impurities within the enlarged unit cell were considered.31 The number of calculated structures for each dopant combination is summarized in Table 1. In the following discussion, unless otherwise stated, the distance between the impurities was determined referring to the nonoptimized structure (bulk cut). An optimized position for VO could not be determined. Except for some special cases, the structural changes in the MTi atoms because of the optimization were small. The structures were optimized using the DFT-based firstprinciples band structure method. The restricted Kohn-Sham (KS) orbitals of the valence electrons were expanded using a plane-wave basis set. The effect of the core electrons was included using a projector augmented wave function (PAW) approach,32 as described in ref 33. A generalized gradient approximation (GGA)-type functional, Perdew-Wang 91 (PW91),34,35 was employed. The +U parameter was chosen to be 3.0 eV for the Ti 3d and W 5d orbitals23,36,37 and 4.0 eV for the Nb 4d orbitals.38 The k-points in the Brillouin zone (BZ)
DFT Calculations of Nb- and W-Doped Anatase TiO2 were sampled according to the Monkhorst-Pack scheme,39 and the tetrahedron interpolation with a Blo¨chl correction40 was adapted. These optimizations were performed using the Vienna Ab Initio Simulation Package (VASP).41,42 The optimization was carried out in two stages. First, the positions of all the atoms were optimized within a fixed cell. A cutoff energy of 400 eV (29.4 Ry) and k-points of 3 × 3 × 3 were employed for the 2MTi and MTi-VO cells. A lower cutoff energy of 300 eV (22.1 Ry) was adapted for the 2MTi-VO and MTi-2VO cells. Some cells optimized with the lower cutoff energy were reoptimized with the higher cutoff energy. No significant changes emerged on reoptimization. Optimization continued until the residual force on all the nuclei was
