Optical properties of anatase and rutile titanium dioxide: Ab initio calculations for pure and anion-doped material
Introduction
Since the pioneering work of Fujishima and Honda [1], titanium dioxide (TiO2) has received special attention as a prime candidate material for photo-electrochemical water-splitting and other photo-catalytic applications [2], [3], [4]. TiO2 holds considerable promise due to its chemical stability in aqueous environments and under high-energy illumination [3]. However, due to its large band gap, ∼3–3.2 eV (for the rutile and anatase phases, respectively), TiO2 lacks sensitivity to visible light which is necessary for high performance under solar illumination. This is especially the case for the generation of hydrogen from water to reach commercial efficiencies [3]. Hence, efforts have been made to increase the visible light sensitivity through band gap modification [3], [4]. However, an understanding of how the band gap can be manipulated in practice is limited and made more difficult by discrepancies in the reported band gap literature. Values ranging from 2.86 to 3.34 eV have been reported for undoped TiO2, while Cr and Nb doping has yielded band gaps of 2.41 and 3.2 eV, respectively [5]. These discrepancies are due to variations in the extent of non-stoichiometry and/or impurity content; both of which are rarely assessed and reported in literature. Thus, there exists a need to establish the band gap of rutile and anatase in a controlled manner. However, before an understanding of their band gaps can be achieved, there is a requirement for a thorough knowledge of the optical properties of both phases. The present paper first provides optical data of rutile and anatase TiO2 that is stoichiometric and free of impurities. This provides a solid foundation for the second part that reports on calculations on the electronic structure of C-, N-, and S-doped anatase TiO2.
Section snippets
Method of calculation
The calculations are based on plane wave pseudopotential density functional theory (DFT) approach. Geometry optimization of rutile and anatase TiO2 unit-cell and C-, N-, and S-doped anatase super-cell were performed using Vanderbilt ultrasoft pseudopotential (USP) method [6] in order to fix the lattice parameters and to obtain an energetically stable structure. In this iterative process the coordinates of atoms and cell parameters are adjusted so that the total energy of the structure is
Energy band structure and optical properties of unit cell
In order to confirm the accuracy of this method and to determine the exact scissors operator for calculation of optical properties we first calculate the energy band structure for the unit cell of anatase and rutile TiO2. The underestimated band gap (1.8 and 1.95 eV for rutile and the anatase, respectively) produced by this calculation is corrected allowing the scissors operator of 1.1 eV, which rigidly shifts the unoccupied CB states with respect to the completely occupied VB states. The
Conclusion
The optical properties are strongly dependent on the direction of incoming polarized light due to the large-anisotropic nature of the tetragonal cells of rutile and anatase. The anatase structure showed more anisotropy than that of rutile. The lower energy peak P for anatase holds promise for an effective band gap modification with positive visible-light response to the photocatalytic activity of TiO2. The first step of our calculation obtained for the stoichiometric and impurity-free structure
Acknowledgment
This work has been supported by the Australian Research Council under the Discovery Project and Linkage Project Grants Schemes.
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