Bulk defects

The catalytic reduction and oxidation reactions utilized in water and air purification, as well as in hydrogen production, crucially depend on the fate of the photo-generated carriers, on their way from the bulk toward the surface. Point defects, impurities and dopants used for band gap engineering (to increase the utilization of sun light) are obviously influencing the balance of electrons and holes in these applications just as well as in the TiO2 crystallites of electrochemical solar cells or sensor layers. Understanding doping mechanisms is of course crucial for the application of titania as transparent conductive oxide (TCO), dilute magnetic semiconductor (DMS) or hydrogen storage material. Since application oriented experimental research has been sofar mainly carried out on layers, rather than single crystals, the knowledge base required for successful defect engineering could mainly come from theoretical investigations. Unfortunately, standard methods of defect calculations have failed at the very first question: the origin of self-doping in TiO2. Due to the band gap error, standard implementations of density functional theory (DFT), like the local density approximation (LDA), or the semi-local generalized gradient approximation (GGA) were not able to reproduce the measured ionization energy of the intrinsic defects leading to oxygen deficiency [B1]. Using correction methods, like the LDA+U, however, this has lately become possible [B2,B3]. Standard hybrid functionals (PBE0, B3LYP) have also proved successful without materials-specific empirical parameter adjusting [B4,B5]. Although unresolved questions remain regarding the intrinsic defects [6], efforts to investigate n- and p-type doping as well as codoping have intensified, particularly with the aim of band gap engineering [B5,B7,B8]. Hydrogen has also been investigated [B11,B13], as well as n-type doping for TCO or DMS purposes [B3,B7,B10]. 

The application of new electronic structure methods could also shed light on bulk properties, like the effective mass, which is difficult to access experimentally [B11-B13]. Hybrid functional calculations, in agreement with the results of many-body GW methods [B13,B14] have all resulted in a larger band gap for both rutile and anatase, as the conventionally cited low temperature experimental values of 3.035 eV and 3.420 eV respectively [B15,B16].  It was recently shown that these values are likely to be the excitonic band gaps, due to a very large exciton binding energy [B17]. In fact newer experiments indicate higher gaps of 3.25 and 3.75 eV (at room temperature) as well [B18] This new knowledge changes quite a lot in the interpretation of erlier results, clearly showing the need of bringing together experiment and theory.

Surfaces

Due to their key role in photocalysis and photovoltaics, there has been an increasing interest in the fundamental physical and chemical properties of TiO2 surfaces over the last decade. Unfortunately, however,  most of the  experimental surface science studies have focused on rutile TiO2(110), which is easy to prepare experimentally but is not the most relevant surface for photocatalytic applications [S1].  Thus, a great deal of fundamental information on more technologically relevant surfaces, such as the surfaces of anatase,  has been  provided by theoretical investigations based on first principles calculations.  A variety of  surface properties have been addressed, ranging from  the structure and energetic [S2,S3] and the reactivity  toward adsorption of small molecules [S4-S13] to  the role of TiO2  as a support for metal catalysts [S14-S17],  the geometry and electronic structure of  surface and subsurface defects [S8,S18-S23],  the surface sensitization with molecular dyes, including the closely related issues of the electron injection and recombination mechanisms [S24-S30].  Because of the large size of the models required to describe the surface systems of interest, the theoretical approach used in most of the studies is based on DFT in the Generalized Gradient Approximation (GGA). As already pointed out in our discussion of bulk defects, however, it is now generally agreed that approaches beyond standard DFT-GGA are necessary to obtain a more reliable description of the electronic structure of point defects  in TiO2. A few DFT+U and hybrid functional calculations of surface oxygen vacancies in TiO2 have already been reported, but many uncertainties  remain,  especially concerning  the sites and degree of localization of the excess electron states [S18,S21,S31,S32]. Time Dependent (TD)-DFT has been used to model the electron injection process in dye-sensitized solar cells [S24-S28]. One of the important issues in such studies is the correct alignment of the energy levels of the molecular dye with respect to  the valence and conduction band edges of the TiO2 nanoparticle [S30].  A theoretical approach that accurately predicts the lineups would be extremely useful for the design of new and more efficient solar cell dye sensitizers.   Also in this case local and semilocal DFT functionals yield results that are often in disagreement with experimental observations. In a few investigated cases, hybrid functionals have been found  to overcome these difficulties  but the general  predictive capability of this approach is not yet established, whereas many-body techniques are for these systems still beyond current computational capabilities.   

Nanostructures

Interest on titanium oxide is rapidly growing. This is not only due to several nice characteristics of the material, such as not toxicity, cheapness and the wide band gap, useful for optoelectronics applications, but also for the capability of being nanostructured with ease. TiO2 in fact can be manipulated using a wide spectrum of techniques and shaped in a large class of nanostructures: nanoparticles, nanowires, nanorods and nanotubes. Moreover, it can be aggregated to form different phases like mesoporous materials, TiO2 aereogels, opals and photonic crystals. This remarkable versatility has produced interest in many fields ranging from electronics, sensing and photonics through electrolysis to photovoltaics [N1-N10]. For example, in photovoltaic applications people use mesoporous layers of TiO2, made of small nanoparticles sintered together by heating a semi-liquid paste, as a core for dye sensitized solar cells. The TiO2 is the substrate on which the molecules (dyes) to harvest light are physisorbed, while in the meantime the TiO2 semiconductor functions as electron conductor.   

As pointed before, there is a large spectrum of techniques that can be used to shape and manipulate TiO2 at the nanoscale. Nanoparticles and amorphous materials are obtained using sol-gel techniques, chemical vapour deposition, hydro and solvothermal, direct oxidation of titanium and micelles and inverse micelles processes [N11-N17]. A big effort has been devoted in trying to have a complete control on the size, shape and size distribution of the nanoparticles. On one side the size control allows a fine tuning of the optical properties which are in many cases the key properties of the semiconductor exploited into the device, in other cases, i.e. dye sensitized solar cells, the size of the particle must be tuned in order to have a large effective surface and in the meantime a reasonable conductivity for the electrons. Studies have been made to use sol-gel techniques to create nanoparticles of TiO2 with different size and shape tuning the reaction parameters [N18], a statistical experimental design method was conducted by Kim et al. to optimize experimental conditions for the preparation of the nanoparticles [N12]. 

Combining instead sol-gel with anodic aluminia template nanowires and nanorods can be produced [N19-N22]. Other techniques, like hydrothermal and solvothermal can be used to grow nanorods and nanotubes [N23-N25]. In particular with the latter, the morphology can be tuned by changing surfactanct or solvent composition [N26-N29]. The hydrothermal method has been also widely used to prepare TiO2 nanotubes since it was introduced by Kasuga et al. in 1998 [N30-N34]. Arrays of nanowires have been grown successfully also using chemical vapour deposition, physical vapour deposition and electrodeposition. The study of TiO2 aerogels is worthy of special mention [N35-N38]. The combination of sol-gel processing with supercritical drying offers the synthesis of TiO2 aerogels with morphological and chemical properties that are not easily achieved by other preparation methods, i.e., with high surface area.

This very brief summary gives a perspective of the huge amount of experimental and industrial work made in titanium oxide, in spite of the numerous experimental data the theoretical studies of TiO2 nanostructures are limited. Some simple semi-empirical calculations of cylindrical TiO2 nanotubes were performed without geometry optimization [N39,N40]. Moreover, despite models of possible growth mechanisms of titania tubes are discussed [N41-43], the details of the atomic structure of the nanotube walls and their stacking mode remain unknown. Some phenomenological models have been developed to investigate the percolation, trap assisted, of the electrons inside the amorphous  material [N44]. 

A larger effort, using mainly linear response and DFT, has been devoted to investigate the physisorption of dyes on anatase surface inside solar cells and the optical absorption [N45,N46]. More recently Kaxiras and co-workers and Prezhdo et al. have studied the charge transfer allowing the full time propagation of the electron [N47-,N48]. However, also for these optical simulations, most of the work was devoted to the investigation of the molecule than to the study of the semiconductor substrate. 

The theoretical interest to titanium oxide is rapidly growing following experimentalists and industry. The large amount of applications of the material in very different class of devices allows the application of a wide spectrum of theoretical models: TDDFT for optical excitation, Monte Carlo methods for the percolation of the electrons in nanoparticles, drift-diffusion models for the transport in mesoporous materials or fully quantum models like non-equilibrium Green’s functions to investigate ballistic transport in small nanotubes and nanowires, especially to study the differences in the conductivity when molecules are absorbed to the surface or defects and vacancies are present.