First-principles study of Oxygen deficiency in rutile Titanium Dioxide
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First-principles study of Oxygen deficiency in rutile Titanium Dioxide Hsin-Yi Lee,1 Stewart J. Clark,2 John Robertson1 1 Engineering Department, Cambridge University, Cambridge, CB2 1PZ, UK 2 Physics Department, Durham University, Durham, DH1 3LE, UK ABSTRACT The energy levels of the different charge states of an oxygen vacancy and titanium interstitial in rutile TiO2 were calculated using the screened exchange (sX) hybrid functional [1]. The sX method gives 3.1 eV for the band gap of rutile TiO2, which is close to the experimental value. We report the defect formation energy of the oxygen deficient structure. It is found that the defect formation energies, for the neutral charge state, of oxygen vacancy and titanium interstitial are quite similar, 2.40 eV and 2.45 eV respectively, for an oxygen chemical potential of the O-poor condition. The similar size of these two calculated energies indicates that both are a cause of oxygen deficiency, as observed experimentally [2]. The transition energy level of oxygen vacancy lies within the band gap, corresponding to the electrons located at adjacent titanium sites. The sX method gives a correct description of the localization of defect charge densities, which is not the case for GGA [3-6]. INTRODUCTION Titanium dioxide (TiO2) is a widely used material ranging from a substance used in solar cells, photocatalysts and nano-scale electronic devices. It has received a great deal of attention because it possesses many useful properties, such as high dielectric constant, good chemical stability, low cost and high refractive index [7]. Understanding the electronic and structural properties of the bulk and defective structures of TiO2 is essential to improve the practical applications. There are three different polymorphs of TiO2 in nature: rutile, anatase, and brookite. Out of the three phases, the rutile is the most abundant naturally occurring phase and is the stable state under atmospheric conditions [3], hence it has been chosen as the major subject of this work. Figure 1 shows the crystal structure of rutile TiO2.
Figure 1. The unit cell of rutile TiO2. Red spheres represent O atoms and light grey spheres represent Ti atoms.
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First-principles calculations provide the methods that can be used to simulate a wide range of material properties. For many years, the local-density approximation (LDA) and generalized gradient approximations (GGA) within density functional theory (DFT) provided an efficient method for such calculations in solids, giving both lattice constants and bulk moduli with reasonable accuracy [1]. However, even though LDA and GGA gives acceptable crystal structures and ground state properties, it has the well-known band gap errors [8-11]. A more accurate description of the electronic structures is required. In this paper, we use a non-local exchange-correlation functional, the screened exchanged (sX) method [12], in order to correct the size of band gap and to improve the computational accuracy for TiO2. METHOD The sX method is based on the Hartree-Fock me
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